WEBVTT 00:00:00.000 --> 00:00:02.458 SPEAKER: The following content is provided under a Creative 00:00:02.458 --> 00:00:03.730 Commons license. 00:00:03.730 --> 00:00:06.030 Your support will help MIT OpenCourseWare 00:00:06.030 --> 00:00:10.060 continue to offer high-quality educational resources for free. 00:00:10.060 --> 00:00:12.690 To make a donation or to view additional materials 00:00:12.690 --> 00:00:16.560 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.560 --> 00:00:17.904 at ocw.mit.edu. 00:00:21.120 --> 00:00:23.870 PROFESSOR: It's a pleasure to get the chance to talk, 00:00:23.870 --> 00:00:26.370 particularly [AUDIO OUT] because I think this, in some ways, 00:00:26.370 --> 00:00:29.940 is the first big punch line of the term, something 00:00:29.940 --> 00:00:32.040 that-- material you've been hearing about 00:00:32.040 --> 00:00:33.000 has been leading up to. 00:00:33.000 --> 00:00:35.125 I guess it depends on whether you consider yourself 00:00:35.125 --> 00:00:36.480 an engineer or a theoretician. 00:00:36.480 --> 00:00:37.890 If you're a theoretician, this is 00:00:37.890 --> 00:00:41.047 going to seem kind of pretty simplistic. 00:00:41.047 --> 00:00:42.630 If you're a practitioner, an engineer, 00:00:42.630 --> 00:00:43.838 you're going to say this is-- 00:00:43.838 --> 00:00:47.490 I hope you'll say this is what we've been waiting for. 00:00:47.490 --> 00:00:50.220 And what it is really how we take a lot of the stuff 00:00:50.220 --> 00:00:53.610 that you've been learning about physical processes 00:00:53.610 --> 00:00:59.250 and the reasons they go bad and some basic theory 00:00:59.250 --> 00:01:03.330 on statistics, particularly normal statistics, 00:01:03.330 --> 00:01:05.880 and actually put it into some sort of use. 00:01:05.880 --> 00:01:08.910 And we'll do this-- 00:01:08.910 --> 00:01:12.060 this is really sort of SPC in-- 00:01:12.060 --> 00:01:17.050 I was going to say 90 minutes, but in less than 90 minutes. 00:01:17.050 --> 00:01:21.540 And if you follow everything that's in today's lecture 00:01:21.540 --> 00:01:24.090 and follow what's in the book, you kind of have it all, OK? 00:01:24.090 --> 00:01:25.590 And then it's just a matter of a lot 00:01:25.590 --> 00:01:27.720 of shades of gray around that. 00:01:27.720 --> 00:01:32.030 Making it more applicable, and understanding 00:01:32.030 --> 00:01:33.320 some of the subtleties. 00:01:33.320 --> 00:01:36.260 The other part of it, if I don't get too wordy 00:01:36.260 --> 00:01:38.750 and we don't have any technical problems, 00:01:38.750 --> 00:01:40.910 is process capability. 00:01:40.910 --> 00:01:43.490 And process capability in my mind 00:01:43.490 --> 00:01:48.110 is the meeting of the two great forces in manufacturing 00:01:48.110 --> 00:01:49.970 or in a manufacturing company. 00:01:49.970 --> 00:01:52.520 And that's the relationship-- 00:01:52.520 --> 00:01:56.055 those are the organizations of design and manufacturing. 00:01:56.055 --> 00:01:58.430 And it really is just where the two are brought together. 00:01:58.430 --> 00:02:01.678 And it's ultimately very simple. 00:02:01.678 --> 00:02:03.720 It has a lot of implications, but it's ultimately 00:02:03.720 --> 00:02:06.540 a very simple concept. 00:02:06.540 --> 00:02:10.380 And both of these things are things that historically you 00:02:10.380 --> 00:02:15.540 might say were discovered or put together and learned 00:02:15.540 --> 00:02:16.920 in the United States. 00:02:16.920 --> 00:02:19.230 They were unlearned-- it's an interesting history 00:02:19.230 --> 00:02:23.400 on this-- completely unlearned and transferred 00:02:23.400 --> 00:02:26.400 to other countries, in particular Japan, 00:02:26.400 --> 00:02:28.390 and then relearn back in this country. 00:02:28.390 --> 00:02:30.060 So there's some interesting history. 00:02:30.060 --> 00:02:35.040 If you read about Shewhart, if you read about Edwards Deming, 00:02:35.040 --> 00:02:39.120 and you read about Juran, these are the people 00:02:39.120 --> 00:02:43.770 that kind of invented and then brought it back 00:02:43.770 --> 00:02:45.000 to this country. 00:02:45.000 --> 00:02:49.980 And it's now-- you know, again, I find myself now having 00:02:49.980 --> 00:02:53.370 worked in this area long enough to tell stories that you have 00:02:53.370 --> 00:02:56.250 to understand that your background, this has probably 00:02:56.250 --> 00:02:59.010 been in your entire adult life, this has just 00:02:59.010 --> 00:03:01.020 been standard practice in industry 00:03:01.020 --> 00:03:02.370 pretty much around the world. 00:03:02.370 --> 00:03:05.330 But I can tell you, 15 years ago, 00:03:05.330 --> 00:03:08.623 which for me wasn't-- which, for me, is yesterday, 00:03:08.623 --> 00:03:10.540 this stuff was still kind of being discovered. 00:03:10.540 --> 00:03:14.230 But now, at least, it maybe isn't dogma yet everywhere, 00:03:14.230 --> 00:03:17.490 but it's pretty close to that. 00:03:17.490 --> 00:03:18.330 OK. 00:03:18.330 --> 00:03:20.820 So enough of my soapbox. 00:03:20.820 --> 00:03:22.410 There's an interesting paper that 00:03:22.410 --> 00:03:26.630 was written by Shewhart back when 00:03:26.630 --> 00:03:28.430 he was with Bell Laboratories. 00:03:28.430 --> 00:03:32.420 Bell Laboratories used to be the premier industrial research 00:03:32.420 --> 00:03:36.520 laboratory in the United States, maybe in the world. 00:03:36.520 --> 00:03:40.660 And of course, did a lot of work on communications and telephony 00:03:40.660 --> 00:03:42.910 and things like that and a lot of things 00:03:42.910 --> 00:03:45.640 on basic information-- on, of course, 00:03:45.640 --> 00:03:47.075 on the hardware of that. 00:03:47.075 --> 00:03:48.700 Software didn't really exist back then, 00:03:48.700 --> 00:03:52.600 but the hardware of it and other things was done there. 00:03:52.600 --> 00:03:56.630 And they had a large theoretical group. 00:03:56.630 --> 00:04:01.220 And Shewhart, as I understand, was a statistician. 00:04:01.220 --> 00:04:04.850 And Bell Labs also, in their connection 00:04:04.850 --> 00:04:05.810 with Western Electric-- 00:04:05.810 --> 00:04:09.950 Western Electric was the manufacturing arm 00:04:09.950 --> 00:04:12.110 of the Bell System, which was the one 00:04:12.110 --> 00:04:15.350 big monopoly in the United States at that time. 00:04:15.350 --> 00:04:17.870 So they owned the phone system, and they 00:04:17.870 --> 00:04:19.040 manufactured all the phones. 00:04:19.040 --> 00:04:21.477 That was an interesting era in history, too. 00:04:21.477 --> 00:04:23.060 You could get your phones from anybody 00:04:23.060 --> 00:04:24.518 as long as it was Western Electric. 00:04:24.518 --> 00:04:28.400 And you could get any color you wanted as long as it was black. 00:04:28.400 --> 00:04:32.490 They made very solid phones, but there wasn't a lot of variety. 00:04:32.490 --> 00:04:35.250 But they always worked. 00:04:35.250 --> 00:04:38.730 Anyway, they did a lot of work on improving 00:04:38.730 --> 00:04:40.450 telephony and other things like that, 00:04:40.450 --> 00:04:43.290 and a lot of statistics and mathematics 00:04:43.290 --> 00:04:45.320 got developed around control systems. 00:04:45.320 --> 00:04:48.570 Those if you who've taken control courses, I think-- 00:04:51.090 --> 00:04:53.970 I'm trying to think, well, I might get some of these names 00:04:53.970 --> 00:04:56.070 wrong, but some of the techniques and other things 00:04:56.070 --> 00:04:58.740 that are there came from the concept 00:04:58.740 --> 00:05:03.360 of developing better amplifiers for undersea 00:05:03.360 --> 00:05:06.780 cables and other things like that for telephony. 00:05:06.780 --> 00:05:11.370 At the same time this development of statistics 00:05:11.370 --> 00:05:14.040 and applied statistics was being used in that area, 00:05:14.040 --> 00:05:18.520 this guy Shewhart comes along and says, wait a second. 00:05:18.520 --> 00:05:20.440 We have this manufacturing. 00:05:20.440 --> 00:05:24.755 And what this little quote here, which 00:05:24.755 --> 00:05:26.380 is the introduction to this one paper-- 00:05:26.380 --> 00:05:27.547 he wrote a series of papers. 00:05:27.547 --> 00:05:28.930 It basically says is that-- 00:05:28.930 --> 00:05:32.020 he's stating what maybe is the obvious back in, I think, 00:05:32.020 --> 00:05:35.470 1925, which is the objective of manufacturing 00:05:35.470 --> 00:05:38.200 typically is to create a products that 00:05:38.200 --> 00:05:40.160 are as uniform as possible. 00:05:40.160 --> 00:05:41.830 And you can set up all the conditions 00:05:41.830 --> 00:05:45.190 you want around the production to make things 00:05:45.190 --> 00:05:47.320 as uniform as possible, which is exactly what we've 00:05:47.320 --> 00:05:48.130 been talking about. 00:05:48.130 --> 00:05:49.780 Control your inputs. 00:05:49.780 --> 00:05:53.720 Control your process variables, things like that. 00:05:53.720 --> 00:05:57.260 But there will still be variation in it. 00:05:57.260 --> 00:05:59.360 He's basically saying, if you ever 00:05:59.360 --> 00:06:01.490 make things in any sort of quantity, 00:06:01.490 --> 00:06:04.100 you will always see variation. 00:06:04.100 --> 00:06:07.880 And he basically did from that is-- 00:06:07.880 --> 00:06:09.320 and I don't know how much of this 00:06:09.320 --> 00:06:13.580 came from the idea of quantum mechanics, which was becoming 00:06:13.580 --> 00:06:19.250 popular at that time or was coming into being well known 00:06:19.250 --> 00:06:21.320 by the scientific community at least, which 00:06:21.320 --> 00:06:26.180 is that at some point, once you reduce things down, 00:06:26.180 --> 00:06:28.880 sort of explain everything that is to be explained, 00:06:28.880 --> 00:06:31.680 there's still some inherent randomness in things. 00:06:31.680 --> 00:06:33.950 And so this view of the idea that there's inherent 00:06:33.950 --> 00:06:38.240 randomness in any physical thing. 00:06:38.240 --> 00:06:41.430 Our ability to describe exactly what's going on eventually 00:06:41.430 --> 00:06:42.540 gets limited. 00:06:42.540 --> 00:06:46.500 And so that kind of led to this idea of statistical process 00:06:46.500 --> 00:06:49.410 control, which is really based on the idea 00:06:49.410 --> 00:06:53.520 that if I do everything I can to know everything 00:06:53.520 --> 00:06:57.060 I can about a process, then the only thing that's left 00:06:57.060 --> 00:06:58.890 is that unknowable part, if you will. 00:06:58.890 --> 00:07:01.360 The purely random part. 00:07:01.360 --> 00:07:04.420 And at one level, SPC is all about, 00:07:04.420 --> 00:07:06.970 first of all, determining, have I indeed 00:07:06.970 --> 00:07:09.580 taken care of all those things that I should know about 00:07:09.580 --> 00:07:12.920 or could know about? 00:07:12.920 --> 00:07:14.840 And those are things that are related 00:07:14.840 --> 00:07:17.810 to the physics of the process that we've 00:07:17.810 --> 00:07:19.560 been talking about so far. 00:07:19.560 --> 00:07:26.070 And once that's done, what is the underlying 00:07:26.070 --> 00:07:29.190 statistical behavior, random behavior of the process, 00:07:29.190 --> 00:07:31.530 and how well can I characterize that. 00:07:31.530 --> 00:07:35.110 And SPC all gets down to really basically saying, 00:07:35.110 --> 00:07:40.230 have I achieved this state of pure randomness? 00:07:40.230 --> 00:07:43.350 And SPC-- another way of looking at the Shewhart hypothesis 00:07:43.350 --> 00:07:48.090 is, if the process is acting in any way except purely random, 00:07:48.090 --> 00:07:50.380 then you haven't done your job. 00:07:50.380 --> 00:07:53.060 Then you can still improve the process. 00:07:53.060 --> 00:07:53.560 OK? 00:08:00.010 --> 00:08:00.510 OK. 00:08:00.510 --> 00:08:03.550 So I think you can probably read that on your print out. 00:08:03.550 --> 00:08:04.800 I can't read it here. 00:08:04.800 --> 00:08:06.360 So, OK. 00:08:06.360 --> 00:08:09.450 So the hypothesis in effect, or the approach, 00:08:09.450 --> 00:08:11.160 is to basically say, all processes 00:08:11.160 --> 00:08:13.128 have a certain degree of randomness. 00:08:16.120 --> 00:08:21.040 And this idea of assignable causes, which are really what-- 00:08:21.040 --> 00:08:24.340 if you're in a control systems, from a control systems 00:08:24.340 --> 00:08:27.520 background, it would say disturbances or changes. 00:08:27.520 --> 00:08:30.380 If they've all been eliminated, then it 00:08:30.380 --> 00:08:33.179 is a purely random process. 00:08:33.179 --> 00:08:35.900 So this concept of common causes or, again, 00:08:35.900 --> 00:08:39.669 purely random effects, if that's all that's left, 00:08:39.669 --> 00:08:44.360 then you do indeed have a process 00:08:44.360 --> 00:08:47.670 that is in a state of statistical control. 00:08:47.670 --> 00:08:49.490 Now, the other problem here again, 00:08:49.490 --> 00:08:51.620 and the reason I go on about this, 00:08:51.620 --> 00:08:54.920 is I came to this whole field-- 00:08:54.920 --> 00:08:57.830 all my formal education, with the exception of one or two 00:08:57.830 --> 00:09:00.980 classes, never talked about the concept 00:09:00.980 --> 00:09:03.350 of uncertainty or randomness. 00:09:03.350 --> 00:09:07.590 And particularly in the area of control systems, 00:09:07.590 --> 00:09:11.130 you think of control as actively watching something and doing 00:09:11.130 --> 00:09:15.600 something about it in a closed loop fashion. 00:09:15.600 --> 00:09:18.880 Statistical process control is quite different from that. 00:09:18.880 --> 00:09:20.940 And the term is used quite differently. 00:09:20.940 --> 00:09:26.730 It really means, have I eliminated or controlled 00:09:26.730 --> 00:09:29.220 everything external to the process 00:09:29.220 --> 00:09:31.470 that could cause it to vary? 00:09:31.470 --> 00:09:34.980 And indeed, is it in a state of what 00:09:34.980 --> 00:09:38.460 you'll see in a moment we'll define as purely 00:09:38.460 --> 00:09:42.150 random, stationary behavior. 00:09:42.150 --> 00:09:46.150 There's nothing active about the control at all. 00:09:46.150 --> 00:09:51.270 Now, for those of you who have come up with a control systems 00:09:51.270 --> 00:09:54.285 or system dynamics point of view-- 00:09:54.285 --> 00:09:56.910 and I think I warned you this is the last time I talked to you. 00:09:56.910 --> 00:09:59.350 I do everything with block diagrams. 00:09:59.350 --> 00:10:01.200 So I have to do this. 00:10:01.200 --> 00:10:03.750 We have this manufacturing process. 00:10:03.750 --> 00:10:10.350 And we have certain inputs to the process. 00:10:10.350 --> 00:10:14.820 And these again, are the things that we can control, 00:10:14.820 --> 00:10:16.380 and we should be able to control. 00:10:16.380 --> 00:10:21.150 And we either set them and leave them alone, 00:10:21.150 --> 00:10:23.790 or we control them in a way that makes the process do 00:10:23.790 --> 00:10:26.280 what we want to do. 00:10:26.280 --> 00:10:27.840 And that produces a certain output 00:10:27.840 --> 00:10:29.490 through all of the different materials 00:10:29.490 --> 00:10:32.800 and other things like that. 00:10:32.800 --> 00:10:35.130 And then in a control system sense, 00:10:35.130 --> 00:10:38.790 there are two reasons that the relationship between these two 00:10:38.790 --> 00:10:41.560 would vary. 00:10:41.560 --> 00:10:44.950 And again, the purely deterministic view of the world 00:10:44.950 --> 00:10:45.500 says, look. 00:10:45.500 --> 00:10:48.560 If I set some inputs, I'll get a certain output. 00:10:48.560 --> 00:10:52.910 There's a unique mapping between the inputs and the outputs. 00:10:52.910 --> 00:10:54.290 But two things can happen. 00:10:57.080 --> 00:11:02.080 You can have things that are called noise. 00:11:02.080 --> 00:11:04.930 And you'll hear that term throughout the term, actually. 00:11:04.930 --> 00:11:06.070 Or disturbances. 00:11:08.780 --> 00:11:11.495 And you'll notice that's sort of external to the-- this 00:11:11.495 --> 00:11:13.370 is shown as external to the process. 00:11:13.370 --> 00:11:15.680 And from a mathematical point of view, 00:11:15.680 --> 00:11:18.830 it's shown as being additive. 00:11:18.830 --> 00:11:21.590 So imagine that this is a purely deterministic process. 00:11:21.590 --> 00:11:24.290 I hold the input perfectly constant. 00:11:24.290 --> 00:11:26.540 The output stays perfectly constant, 00:11:26.540 --> 00:11:30.120 except that I have a noise up here that's described, 00:11:30.120 --> 00:11:34.180 let's say, by a normal distribution. 00:11:34.180 --> 00:11:37.410 So at any instant in time, this variable 00:11:37.410 --> 00:11:39.640 will be following a normal distribution. 00:11:39.640 --> 00:11:44.160 So the output will follow normal distribution. 00:11:44.160 --> 00:11:48.350 And you might say that one way of looking at the Shewhart 00:11:48.350 --> 00:11:51.050 hypothesis is, yeah, here's this process, 00:11:51.050 --> 00:11:52.830 and I've got it completely under control. 00:11:52.830 --> 00:11:54.622 I know everything that's going on about it. 00:11:54.622 --> 00:11:57.530 Nothing inherent in the process is changing, 00:11:57.530 --> 00:12:00.290 but there's this noise process out here somehow, 00:12:00.290 --> 00:12:01.310 and it adds in. 00:12:01.310 --> 00:12:04.400 And it's always there. 00:12:04.400 --> 00:12:09.230 Now, this turns out to be a bit of an artifice 00:12:09.230 --> 00:12:12.710 because what we all know is what's really 00:12:12.710 --> 00:12:14.600 causing most of the changes that we 00:12:14.600 --> 00:12:16.245 see is a change in the process. 00:12:23.460 --> 00:12:26.790 So we have things like a process noise or disturbance. 00:12:31.200 --> 00:12:33.560 And so that means something inside here, 00:12:33.560 --> 00:12:35.600 like those alphas that we talked about. 00:12:35.600 --> 00:12:38.330 The basic parameters of the process. 00:12:38.330 --> 00:12:43.580 The equipment states, the equipment the parameters. 00:12:43.580 --> 00:12:45.260 The material again. 00:12:45.260 --> 00:12:46.940 Especially the material changes. 00:12:46.940 --> 00:12:48.930 Material is inherent in here. 00:12:48.930 --> 00:12:50.700 And so that's going to change. 00:12:50.700 --> 00:12:53.180 One of the reasons we actually do 00:12:53.180 --> 00:12:55.430 this out here is that again, mathematically, 00:12:55.430 --> 00:12:57.740 having this change, having the function change, 00:12:57.740 --> 00:12:59.840 becomes really hard to handle. 00:12:59.840 --> 00:13:02.246 Additive disturbances are easy to handle. 00:13:02.246 --> 00:13:03.100 Simon. 00:13:03.100 --> 00:13:04.930 AUDIENCE: Would you say that temperature 00:13:04.930 --> 00:13:08.480 and material and everything across [INAUDIBLE]?? 00:13:08.480 --> 00:13:12.358 What examples do you have for the noise disturbance? 00:13:12.358 --> 00:13:13.650 PROFESSOR: Yeah, good question. 00:13:13.650 --> 00:13:17.140 I was going to ask you the same thing. 00:13:17.140 --> 00:13:20.170 You can see that everything we talked 00:13:20.170 --> 00:13:22.780 about when we talked about the process modeling 00:13:22.780 --> 00:13:24.740 had to be here. 00:13:24.740 --> 00:13:25.340 OK? 00:13:25.340 --> 00:13:27.240 So a couple of things here. 00:13:27.240 --> 00:13:30.720 So if the output from here is a dimension 00:13:30.720 --> 00:13:32.760 and you think of the output of the process 00:13:32.760 --> 00:13:36.180 here being a dimension that results 00:13:36.180 --> 00:13:39.420 from the combination of temperature, pressure, force, 00:13:39.420 --> 00:13:44.950 displacement, machine parameters and all those, 00:13:44.950 --> 00:13:46.190 what would ever mess that up? 00:13:53.480 --> 00:13:54.310 Measurement. 00:13:54.310 --> 00:13:55.460 Yeah. 00:13:55.460 --> 00:13:55.960 OK. 00:13:55.960 --> 00:13:58.060 So now, we aren't going to actually talk 00:13:58.060 --> 00:14:01.390 a whole lot about measurement in this class. 00:14:01.390 --> 00:14:05.200 But indeed, one of the good examples of this 00:14:05.200 --> 00:14:05.980 is measurement. 00:14:05.980 --> 00:14:09.940 So your perceived output is different from the real output 00:14:09.940 --> 00:14:12.560 because of some uncertainty from the measurement. 00:14:12.560 --> 00:14:16.090 So this is also a way of dealing with measurement noise. 00:14:16.090 --> 00:14:17.950 And indeed, we deal with measurement noise 00:14:17.950 --> 00:14:21.740 exactly the same way we do with processed noise. 00:14:21.740 --> 00:14:25.000 So that's why I was saying that this is a bit of an artifice. 00:14:25.000 --> 00:14:28.120 If I assume perfect measurement, then this 00:14:28.120 --> 00:14:31.760 is really a better model of doing it. 00:14:31.760 --> 00:14:34.700 Either way, our point is going to be 00:14:34.700 --> 00:14:37.190 that, and the reason I put this in here-- 00:14:37.190 --> 00:14:42.330 let's assume we did the best job we ever could with this. 00:14:42.330 --> 00:14:45.810 In some senses, the Shewhart hypothesis doesn't matter. 00:14:45.810 --> 00:14:47.700 Always going to have something here. 00:14:47.700 --> 00:14:50.602 And he doesn't really try to explain where it comes from. 00:14:50.602 --> 00:14:52.060 That's one of the differences here. 00:14:52.060 --> 00:14:54.815 This is not really physical origins of variation. 00:14:54.815 --> 00:14:55.440 It's just, hey. 00:14:55.440 --> 00:14:56.310 Look. 00:14:56.310 --> 00:15:00.090 Based on observation, no matter what you do, 00:15:00.090 --> 00:15:02.400 you get some of this variability. 00:15:02.400 --> 00:15:05.520 And your job is to get it down to the point where 00:15:05.520 --> 00:15:09.980 it's, in effect, unexplainable. 00:15:09.980 --> 00:15:11.270 OK. 00:15:11.270 --> 00:15:14.630 So here's the concept of being in control. 00:15:14.630 --> 00:15:18.470 And this is really an iconic diagram. 00:15:18.470 --> 00:15:22.500 And it tries to illustrate a number of things. 00:15:22.500 --> 00:15:24.740 And I think if you understand this diagram, 00:15:24.740 --> 00:15:30.980 then you really have the essence of statistical process control. 00:15:30.980 --> 00:15:33.590 Now, what you see here are-- 00:15:33.590 --> 00:15:36.620 again, this is, as the chart says, going in this way, 00:15:36.620 --> 00:15:38.930 you're going in time. 00:15:38.930 --> 00:15:41.510 And think of these as samples or instance of time 00:15:41.510 --> 00:15:43.790 or, from a manufacturing point of view, 00:15:43.790 --> 00:15:46.260 it's cycles of the process. 00:15:46.260 --> 00:15:49.070 So I make something at time I, and then 00:15:49.070 --> 00:15:53.210 I make something at time I plus 1 and I plus 2. 00:15:53.210 --> 00:15:55.100 Or a better way to think of it is 00:15:55.100 --> 00:15:59.720 I measure what I've made at I. I measure something else at I 00:15:59.720 --> 00:16:00.380 plus 1. 00:16:00.380 --> 00:16:04.730 I measure another product at I plus 1 and I plus 2, and so on. 00:16:07.440 --> 00:16:10.440 Each of these, of course, is representing a probability 00:16:10.440 --> 00:16:12.000 distribution. 00:16:12.000 --> 00:16:15.560 And they're normal here because the Shewhart stuff is all 00:16:15.560 --> 00:16:21.410 based on assuming the underlying statistics are normal. 00:16:21.410 --> 00:16:25.700 What this is illustrating is not the data itself 00:16:25.700 --> 00:16:29.770 but the distribution of the data as time moves on. 00:16:29.770 --> 00:16:32.110 And what this diagram tells you is the distribution 00:16:32.110 --> 00:16:33.740 is identical. 00:16:33.740 --> 00:16:37.550 It doesn't mean we're getting the same part every time. 00:16:37.550 --> 00:16:42.700 It just means the probability of getting a particular dimension 00:16:42.700 --> 00:16:44.720 never changes. 00:16:44.720 --> 00:16:45.500 OK? 00:16:45.500 --> 00:16:49.190 This is the concept of statistical-- 00:16:49.190 --> 00:16:51.140 a state of statistical control. 00:16:51.140 --> 00:16:54.230 The underlying parent distribution, 00:16:54.230 --> 00:16:57.530 the true random behavior of the process, 00:16:57.530 --> 00:17:02.000 is following this curve and never changes. 00:17:02.000 --> 00:17:05.630 If you've achieved that, then by the Shewhart hypothesis, 00:17:05.630 --> 00:17:07.550 you're in a state of statistical control. 00:17:07.550 --> 00:17:09.380 And that's essentially the best you can do. 00:17:12.339 --> 00:17:13.730 The best you can do. 00:17:13.730 --> 00:17:18.369 And so your process will never get any better than that. 00:17:18.369 --> 00:17:20.369 That's why we have the second half of the class, 00:17:20.369 --> 00:17:23.640 by the way, because what comes up after this part, 00:17:23.640 --> 00:17:25.890 after statistical process control, we say, OK. 00:17:25.890 --> 00:17:28.630 Now, you've got it in the state of statistical control. 00:17:28.630 --> 00:17:31.410 It's following this distribution for all time. 00:17:31.410 --> 00:17:32.190 That's great. 00:17:32.190 --> 00:17:33.930 What if that's not good enough, or what 00:17:33.930 --> 00:17:35.100 if it needs to be better? 00:17:35.100 --> 00:17:37.920 What if it still has too much variability compared 00:17:37.920 --> 00:17:40.055 to a design specification? 00:17:40.055 --> 00:17:40.680 What do you do? 00:17:45.660 --> 00:17:50.310 Any ideas on what you do if it's in perfect state of control, 00:17:50.310 --> 00:17:52.080 it's doing exactly what Shewhart says 00:17:52.080 --> 00:17:54.540 it should be doing to be in a state of control, 00:17:54.540 --> 00:17:57.600 and it's not good enough? 00:17:57.600 --> 00:18:04.110 AUDIENCE: [INAUDIBLE] parameters that narrow the distribution. 00:18:04.110 --> 00:18:05.290 PROFESSOR: Yes, exactly. 00:18:05.290 --> 00:18:07.377 Did you guys hear that in Singapore? 00:18:11.950 --> 00:18:12.680 No? 00:18:12.680 --> 00:18:14.260 OK. 00:18:14.260 --> 00:18:15.640 AUDIENCE: OK, I heard that. 00:18:15.640 --> 00:18:16.765 PROFESSOR: Oh, he heard it. 00:18:16.765 --> 00:18:18.580 OK, go ahead. 00:18:18.580 --> 00:18:19.540 Oh, you heard it? 00:18:19.540 --> 00:18:21.120 [LAUGHING] 00:18:21.120 --> 00:18:24.010 AUDIENCE: The research says about just change, optimize 00:18:24.010 --> 00:18:26.000 the parameters of the process. 00:18:26.000 --> 00:18:28.010 So try to optimize the process. 00:18:28.010 --> 00:18:30.262 So I was going to say that that is one way. 00:18:30.262 --> 00:18:31.720 But the other methods, for example, 00:18:31.720 --> 00:18:37.030 like positive controls, user feedback control of the system, 00:18:37.030 --> 00:18:38.840 and try to improve the process as well. 00:18:38.840 --> 00:18:39.520 So. 00:18:39.520 --> 00:18:40.780 PROFESSOR: Yeah, exactly. 00:18:40.780 --> 00:18:45.370 If you go back to that, again, the somewhat iconic equation 00:18:45.370 --> 00:18:48.345 that we had in one of the first lectures on the variation 00:18:48.345 --> 00:18:49.720 equation and the three things you 00:18:49.720 --> 00:18:52.750 can do to reduce the variation, one 00:18:52.750 --> 00:18:55.750 was to eliminate all these influences, which 00:18:55.750 --> 00:18:59.220 is what we're talking about with SPC. 00:18:59.220 --> 00:19:04.110 Another is to try to reduce the sensitivity of the process 00:19:04.110 --> 00:19:06.270 to those inherent variations, and that's 00:19:06.270 --> 00:19:09.090 what Richard was talking about with changing process 00:19:09.090 --> 00:19:10.170 parameters. 00:19:10.170 --> 00:19:14.390 And then the third would be to actually use some-- 00:19:14.390 --> 00:19:18.000 well, we'll talk about using feedback control using 00:19:18.000 --> 00:19:21.103 some sort of feedback to improve the process. 00:19:21.103 --> 00:19:23.520 There's a fourth one, which we didn't really put in there. 00:19:26.265 --> 00:19:27.890 Well, that's what he was talking about. 00:19:27.890 --> 00:19:28.840 Active control. 00:19:28.840 --> 00:19:29.920 Yeah. 00:19:29.920 --> 00:19:30.920 Can you generalize that? 00:19:30.920 --> 00:19:31.420 Yeah. 00:19:31.420 --> 00:19:32.530 [INAUDIBLE] 00:19:32.530 --> 00:19:35.890 AUDIENCE: [INAUDIBLE] 00:19:38.780 --> 00:19:40.610 PROFESSOR: Oh, yeah, Yeah, that's cheating. 00:19:40.610 --> 00:19:42.140 Selective assembly? 00:19:42.140 --> 00:19:43.160 Ooh. 00:19:43.160 --> 00:19:44.930 [LAUGHTER] 00:19:44.930 --> 00:19:46.250 None of that. 00:19:46.250 --> 00:19:49.580 No, selective assembly-- indeed, selective assembly 00:19:49.580 --> 00:19:52.680 is something that you do when this is the best you can do, 00:19:52.680 --> 00:19:53.870 and it's not good enough. 00:19:53.870 --> 00:19:56.450 You just take individual parts and say, will these fit? 00:19:56.450 --> 00:19:58.940 Or you gauge-- and that's was also 00:19:58.940 --> 00:20:01.400 my airspace example from a couple of weeks ago 00:20:01.400 --> 00:20:03.680 where you've got the people behind the curtains 00:20:03.680 --> 00:20:05.750 with the padded table and the padded hammers, 00:20:05.750 --> 00:20:09.890 and they're pounding things, and that sort of custom assembly. 00:20:09.890 --> 00:20:13.018 So you can do those sorts of things. 00:20:13.018 --> 00:20:14.435 But the last one I was thinking of 00:20:14.435 --> 00:20:16.310 is you go out and buy a new process. 00:20:16.310 --> 00:20:16.850 OK? 00:20:16.850 --> 00:20:18.590 If this is inherent in the process 00:20:18.590 --> 00:20:20.510 and that's the best that it can do, 00:20:20.510 --> 00:20:22.760 then you sort of invent a new process, if you will, 00:20:22.760 --> 00:20:25.130 or you do things a different way that gives you 00:20:25.130 --> 00:20:27.890 a higher degree of precision. 00:20:27.890 --> 00:20:30.690 So you can take all these steps. 00:20:30.690 --> 00:20:32.790 But in effect, this is-- 00:20:32.790 --> 00:20:35.250 as you'll see, this is the cheapest, the easiest, 00:20:35.250 --> 00:20:38.010 and the first one you always do. 00:20:38.010 --> 00:20:39.660 You never make a decision about what 00:20:39.660 --> 00:20:41.880 to do until the process is in the state 00:20:41.880 --> 00:20:44.030 of statistical control. 00:20:44.030 --> 00:20:45.800 Why is that? 00:20:45.800 --> 00:20:47.260 Why am I so adamant about that? 00:20:47.260 --> 00:20:50.770 You never go to the next step until we've done this. 00:20:50.770 --> 00:20:52.270 Any of these things we talked about. 00:20:59.300 --> 00:21:01.400 No ideas? 00:21:01.400 --> 00:21:02.096 Yeah. 00:21:02.096 --> 00:21:11.000 AUDIENCE: [INAUDIBLE] involved a lot of efforts [INAUDIBLE] 00:21:11.000 --> 00:21:14.420 from a an effort point of view, resources. 00:21:14.420 --> 00:21:17.390 [INAUDIBLE] inherent to the process [INAUDIBLE].. 00:21:22.450 --> 00:21:24.200 PROFESSOR: From an economic point of view, 00:21:24.200 --> 00:21:25.460 you certainly should do it. 00:21:25.460 --> 00:21:27.710 It is essentially almost free, although it 00:21:27.710 --> 00:21:29.720 takes a little bit of someone's effort 00:21:29.720 --> 00:21:31.170 and other things like that. 00:21:31.170 --> 00:21:33.932 But there's maybe even a better reason. 00:21:33.932 --> 00:21:36.390 AUDIENCE: The process starts doing something you don't like 00:21:36.390 --> 00:21:37.320 and you're going to do a feedback 00:21:37.320 --> 00:21:38.490 system or active control. 00:21:38.490 --> 00:21:40.170 You don't really know why, so you 00:21:40.170 --> 00:21:42.780 don't know what your feedback is going to do. 00:21:42.780 --> 00:21:45.150 If it can actually make it worse because I don't know 00:21:45.150 --> 00:21:46.650 the underlying cause anymore. 00:21:46.650 --> 00:21:49.535 So it could actually spiral out of control. 00:21:49.535 --> 00:21:50.910 PROFESSOR: This is really getting 00:21:50.910 --> 00:21:52.280 at the heart of the issue. 00:21:52.280 --> 00:21:52.817 Richard? 00:21:52.817 --> 00:21:54.900 AUDIENCE: Another point is that you have no chance 00:21:54.900 --> 00:21:59.970 to actually get an approximation of the underlying distribution 00:21:59.970 --> 00:22:02.878 when the process [INAUDIBLE]. 00:22:02.878 --> 00:22:04.920 AUDIENCE: Yeah, I was going to be building on Dan 00:22:04.920 --> 00:22:07.080 and just saying, it's understanding the root cause 00:22:07.080 --> 00:22:10.620 problem, and you can't really solve anything or understand 00:22:10.620 --> 00:22:12.888 how to improve it until you understand what's causing 00:22:12.888 --> 00:22:13.930 the [? error to ?] be on. 00:22:13.930 --> 00:22:14.597 PROFESSOR: Yeah. 00:22:14.597 --> 00:22:15.210 Yeah, exactly. 00:22:15.210 --> 00:22:19.780 The whole point with SPC is, if you remember in this-- in fact, 00:22:19.780 --> 00:22:21.780 I barely remember this, and I made up the slide. 00:22:21.780 --> 00:22:25.000 But maybe back in the first or second lecture, 00:22:25.000 --> 00:22:27.480 we had a list of things that lead up 00:22:27.480 --> 00:22:28.720 to good process control. 00:22:28.720 --> 00:22:30.870 The first thing was good housekeeping. 00:22:30.870 --> 00:22:33.300 Just have to have a sensible shop 00:22:33.300 --> 00:22:37.030 and don't play around with the process. 00:22:37.030 --> 00:22:38.820 So hold these things consonant. 00:22:38.820 --> 00:22:40.930 The next-- so that's kind of obvious, 00:22:40.930 --> 00:22:43.740 but you'd be surprised how long it took companies 00:22:43.740 --> 00:22:47.235 to decide that things like standard operating procedures 00:22:47.235 --> 00:22:47.860 were important. 00:22:47.860 --> 00:22:50.910 The next thing after that is, OK. 00:22:50.910 --> 00:22:52.770 Let's take that one level better, 00:22:52.770 --> 00:22:55.860 which is if something's going wrong with the process 00:22:55.860 --> 00:22:58.885 by the definition that's here, then 00:22:58.885 --> 00:23:00.260 that means that there's something 00:23:00.260 --> 00:23:02.990 out there causing the process to deviate that I could fix. 00:23:02.990 --> 00:23:04.310 I could fix it pretty easily. 00:23:04.310 --> 00:23:06.890 Bad control over material variability. 00:23:06.890 --> 00:23:09.000 Bad temperature control. 00:23:09.000 --> 00:23:10.520 Poor maintenance of the machine. 00:23:10.520 --> 00:23:11.390 That sort of thing. 00:23:11.390 --> 00:23:13.100 Shouldn't you fix all those things first 00:23:13.100 --> 00:23:16.660 before you go investing in fancy controls or something 00:23:16.660 --> 00:23:17.160 like that? 00:23:17.160 --> 00:23:17.660 And sure. 00:23:17.660 --> 00:23:20.660 If you're going to then go on to do process optimization, 00:23:20.660 --> 00:23:22.250 it's going to assume the process is 00:23:22.250 --> 00:23:24.710 in a state of statistical control. 00:23:24.710 --> 00:23:28.490 So it's like you're applying a theory to a situation 00:23:28.490 --> 00:23:30.420 that it wasn't meant to be applied to. 00:23:30.420 --> 00:23:33.750 So this is definitely where you start. 00:23:33.750 --> 00:23:34.830 OK. 00:23:34.830 --> 00:23:36.480 I didn't mean to be so preachy today. 00:23:36.480 --> 00:23:37.800 I guess it's just the weather. 00:23:43.820 --> 00:23:44.450 OK. 00:23:44.450 --> 00:23:45.810 Why isn't this going forward? 00:23:51.790 --> 00:23:52.950 I have to do this now? 00:23:52.950 --> 00:23:53.750 OK. 00:23:53.750 --> 00:23:54.250 All right. 00:23:54.250 --> 00:23:58.270 So here's an example of a process being not in control. 00:23:58.270 --> 00:24:00.880 And this is maybe more important than the other one 00:24:00.880 --> 00:24:04.660 because this is the kind of stuff you're trying to detect. 00:24:04.660 --> 00:24:07.120 Unfortunately, when you take data, 00:24:07.120 --> 00:24:09.820 you don't get pictures that look like this. 00:24:09.820 --> 00:24:14.137 Because, for example, at time instance I, 00:24:14.137 --> 00:24:15.220 you get one piece of data. 00:24:15.220 --> 00:24:16.428 You don't get a distribution. 00:24:16.428 --> 00:24:19.000 You get one piece of data. 00:24:19.000 --> 00:24:20.530 So this, in effect, is the challenge 00:24:20.530 --> 00:24:21.670 of working with real data. 00:24:21.670 --> 00:24:24.880 Now, keep in mind, and this is a hard thing to keep in mind here 00:24:24.880 --> 00:24:30.740 in a classroom, but put yourself in the position of a production 00:24:30.740 --> 00:24:35.960 supervisor or an operator who's making something and products 00:24:35.960 --> 00:24:37.710 come out one at a time. 00:24:37.710 --> 00:24:39.383 And as they come out, you measure them. 00:24:39.383 --> 00:24:41.300 And of course, by the time you've measured it, 00:24:41.300 --> 00:24:43.092 the next one is ready to be measured 00:24:43.092 --> 00:24:44.050 and that sort of thing. 00:24:44.050 --> 00:24:45.975 So things are happening pretty fast. 00:24:45.975 --> 00:24:47.600 And what you're trying to decide as you 00:24:47.600 --> 00:24:52.050 make those measurements is, is everything OK? 00:24:52.050 --> 00:24:54.810 And you don't have, with each measurement, 00:24:54.810 --> 00:24:56.380 you don't have enough data to say, 00:24:56.380 --> 00:24:58.900 well, here's the distribution. 00:24:58.900 --> 00:25:01.420 But we do the best we can. 00:25:01.420 --> 00:25:04.370 So here's how it's done. 00:25:04.370 --> 00:25:05.870 What you're trying to do with this 00:25:05.870 --> 00:25:07.940 or what this is basically saying is, 00:25:07.940 --> 00:25:09.320 well, look what's happening here. 00:25:11.830 --> 00:25:14.620 In the first two intervals, things looked OK. 00:25:14.620 --> 00:25:16.660 And then what happened here? 00:25:16.660 --> 00:25:21.880 Well, obviously, as you can see from the diagram, 00:25:21.880 --> 00:25:25.420 the whole underlying random behavior 00:25:25.420 --> 00:25:28.600 shifted it's mean value. 00:25:28.600 --> 00:25:33.780 And it's clear, it also got greater invariance. 00:25:33.780 --> 00:25:36.480 So the underlying parent distribution, 00:25:36.480 --> 00:25:39.300 meaning the underlying random behavior of the process, 00:25:39.300 --> 00:25:40.380 did not stay the same. 00:25:40.380 --> 00:25:42.870 It changed at integral 2. 00:25:42.870 --> 00:25:46.770 And then down here somewhat later, it got even worse. 00:25:46.770 --> 00:25:48.610 It followed a bimodal distribution. 00:25:48.610 --> 00:25:52.080 So it actually meant that the probability 00:25:52.080 --> 00:25:59.430 of getting a certain dimension had two peaks. 00:25:59.430 --> 00:26:02.883 And the least likely point was maybe somewhere near-- 00:26:02.883 --> 00:26:04.550 oh, I guess I've drawn it the other way. 00:26:04.550 --> 00:26:07.160 But yeah. 00:26:07.160 --> 00:26:10.090 Well, here's the point. 00:26:10.090 --> 00:26:13.820 It's anything but a normal distribution anymore. 00:26:13.820 --> 00:26:17.910 And it's anything but the original distribution. 00:26:17.910 --> 00:26:19.910 So these are some examples of the process 00:26:19.910 --> 00:26:22.290 being not in a state of statistical control. 00:26:22.290 --> 00:26:26.790 Now, the other thing, of course, that could be happening here-- 00:26:26.790 --> 00:26:28.860 this is basically saying, with the exception 00:26:28.860 --> 00:26:31.160 of the bimodal thing, it's basically saying, OK. 00:26:31.160 --> 00:26:36.920 You got a normal distribution, but it's underlying statistics, 00:26:36.920 --> 00:26:39.613 the mean and the variance, are no longer constant. 00:26:39.613 --> 00:26:41.030 The other thing could be happening 00:26:41.030 --> 00:26:44.150 is that it's still random, but it's 00:26:44.150 --> 00:26:45.980 switched its distribution to something 00:26:45.980 --> 00:26:49.900 like a uniform distribution. 00:26:49.900 --> 00:26:52.720 The real fact of the matter is that it's probably not 00:26:52.720 --> 00:26:57.430 following any distribution because it's 00:26:57.430 --> 00:27:00.130 got a lot of deterministic behavior underneath it. 00:27:00.130 --> 00:27:03.850 But here's the challenge if you're actually applying SPC. 00:27:03.850 --> 00:27:07.300 How do I look at data in real time 00:27:07.300 --> 00:27:10.990 and distinguish the difference among something 00:27:10.990 --> 00:27:11.975 that looks like this? 00:27:11.975 --> 00:27:14.350 This is actually a mean shift here now that I look at it. 00:27:14.350 --> 00:27:16.270 Something that looks like this, which is 00:27:16.270 --> 00:27:18.070 exactly what I wanted to see. 00:27:18.070 --> 00:27:22.060 Something that looks like this, where you've got a mean shift. 00:27:22.060 --> 00:27:23.560 Something that looks like this where 00:27:23.560 --> 00:27:29.298 I've got a mean shift and standard deviation shift. 00:27:29.298 --> 00:27:30.840 And something like this, where I just 00:27:30.840 --> 00:27:34.100 change the whole probability distribution. 00:27:34.100 --> 00:27:37.330 So how could I look at individual data points 00:27:37.330 --> 00:27:41.020 one by one and decide what's going on there? 00:27:41.020 --> 00:27:43.850 So that's really the challenge. 00:27:43.850 --> 00:27:46.870 And when we do come up with these rules and say, ah, 00:27:46.870 --> 00:27:51.580 it's not in control, it's really because our hypothesis 00:27:51.580 --> 00:27:54.630 is that something like this has happened. 00:27:54.630 --> 00:27:55.890 OK. 00:27:55.890 --> 00:27:59.100 So back to Shewhart, and back to practical. 00:28:02.150 --> 00:28:05.210 What the Shewhart chart does, the classic Shewhart chart, 00:28:05.210 --> 00:28:07.970 it's an x-bar, and often, it's done 00:28:07.970 --> 00:28:10.880 as an r-chart or a range chart. 00:28:10.880 --> 00:28:14.330 I like to use the s-chart for reasons 00:28:14.330 --> 00:28:15.570 I'll get to in just a second. 00:28:15.570 --> 00:28:20.810 But what it does is it plots not the data points themselves. 00:28:20.810 --> 00:28:24.850 Not the individual run data, but a sequential average 00:28:24.850 --> 00:28:25.350 of the data. 00:28:25.350 --> 00:28:28.680 And I'll show you this diagram in just a second. 00:28:28.680 --> 00:28:33.710 But the basic approach here is not to take each measurement 00:28:33.710 --> 00:28:39.570 and put it on a plot but instead to take groups of measurements 00:28:39.570 --> 00:28:49.960 and plot the average of those. 00:28:49.960 --> 00:28:52.090 A simple arithmetic average of them. 00:28:52.090 --> 00:28:52.720 OK? 00:28:52.720 --> 00:29:01.460 So if I get a plot, a data point here, this is actually 00:29:01.460 --> 00:29:03.800 the average of a set of data that 00:29:03.800 --> 00:29:06.500 occurred around the interval i. 00:29:06.500 --> 00:29:14.600 And the next one here is the average at i plus 1. 00:29:14.600 --> 00:29:16.850 OK? 00:29:16.850 --> 00:29:18.200 Why would we do that? 00:29:18.200 --> 00:29:22.525 Why not just plot the run data, meaning the actual data? 00:29:22.525 --> 00:29:23.900 Why start off and say, now, we're 00:29:23.900 --> 00:29:25.730 going to look at averages? 00:29:32.380 --> 00:29:34.480 AUDIENCE: Because the evidence or the distribution 00:29:34.480 --> 00:29:37.533 of the evidence [INAUDIBLE]. 00:29:37.533 --> 00:29:38.200 PROFESSOR: Yeah. 00:29:38.200 --> 00:29:39.750 That's one very good reason. 00:29:39.750 --> 00:29:41.870 You get the narrowing effect with the sample. 00:29:41.870 --> 00:29:44.037 AUDIENCE: Also, you're able to calculate or estimate 00:29:44.037 --> 00:29:45.590 the standard deviation. 00:29:45.590 --> 00:29:47.090 PROFESSOR: And that's exactly right. 00:29:47.090 --> 00:29:52.640 So for each of these, I can come up with a standard deviation 00:29:52.640 --> 00:29:57.287 as long as I have enough data. 00:29:57.287 --> 00:29:57.870 Each of those. 00:29:57.870 --> 00:30:03.440 So each of these is x-bar sub i is-- well, 00:30:03.440 --> 00:30:05.120 let me just do it this way-- 00:30:05.120 --> 00:30:11.540 is, of course, a sum over n of some set of data. 00:30:14.070 --> 00:30:15.950 And so the other part of this now 00:30:15.950 --> 00:30:17.810 is how many data points do I take? 00:30:17.810 --> 00:30:20.000 OK, that's a really good reason. 00:30:20.000 --> 00:30:23.240 There's an even more fundamental reason 00:30:23.240 --> 00:30:28.470 why I would plot this x-bar. 00:30:28.470 --> 00:30:32.810 What is x-bar an estimate of? 00:30:32.810 --> 00:30:36.230 It's the estimate of the true theoretical mean. 00:30:36.230 --> 00:30:40.300 So, if you will, it's our estimate of the mean value. 00:30:40.300 --> 00:30:44.500 If the process is in a state of statistical control, 00:30:44.500 --> 00:30:49.300 this thing, what is the true value of the mean? 00:30:54.680 --> 00:30:57.440 Or maybe I didn't state that question 00:30:57.440 --> 00:30:59.370 as well as I should have. 00:30:59.370 --> 00:31:04.360 How does the true value of the mean vary over time? 00:31:04.360 --> 00:31:05.260 It doesn't. 00:31:05.260 --> 00:31:06.640 Exactly. 00:31:06.640 --> 00:31:12.250 So what my ideal for in control is 00:31:12.250 --> 00:31:16.480 that if this is the theoretical mean right here of the process, 00:31:16.480 --> 00:31:20.900 then the true mean value should be a constant. 00:31:20.900 --> 00:31:25.900 So what I'm really plotting here in a sense 00:31:25.900 --> 00:31:28.090 are my sample statistics. 00:31:28.090 --> 00:31:30.940 Not the data, but my sample statistics. 00:31:30.940 --> 00:31:34.510 And the reason is, in effect, you have to say, at this level, 00:31:34.510 --> 00:31:35.890 I don't care about the data. 00:31:35.890 --> 00:31:40.860 What I care about are the statistics of the data 00:31:40.860 --> 00:31:44.790 and what they're telling me about the underlying behavior. 00:31:44.790 --> 00:31:48.780 So that's one of the key reasons for plotting this. 00:31:48.780 --> 00:31:50.010 We're not plotting the data. 00:31:50.010 --> 00:31:52.600 We're plotting the statistics of the data. 00:31:52.600 --> 00:31:55.770 There's another reason that's even maybe-- 00:31:55.770 --> 00:31:57.870 you'll see some other reasons why. 00:31:57.870 --> 00:32:01.830 But what other advantage do I get 00:32:01.830 --> 00:32:07.500 from calculating the average instead of-- 00:32:07.500 --> 00:32:10.740 doing this kind of averaging instead of just 00:32:10.740 --> 00:32:11.890 looking at the raw data? 00:32:11.890 --> 00:32:13.860 We already said it allows us to-- 00:32:13.860 --> 00:32:16.590 I've said here, it allows us to be actually plotting 00:32:16.590 --> 00:32:18.240 our estimate of the mean. 00:32:18.240 --> 00:32:20.760 It allows us to calculate at each interval 00:32:20.760 --> 00:32:22.350 a standard deviation. 00:32:22.350 --> 00:32:23.900 What else does it allow us to do? 00:32:32.460 --> 00:32:35.100 Remember, I said earlier that this is all 00:32:35.100 --> 00:32:36.435 based on this being normal. 00:32:42.850 --> 00:32:48.730 What's the best way to guarantee that whatever 00:32:48.730 --> 00:32:52.270 it is that I'm looking at is-- 00:32:52.270 --> 00:32:54.820 whatever variable I'm actually plotting is following 00:32:54.820 --> 00:32:56.370 a normal distribution? 00:32:59.660 --> 00:33:00.350 Go ahead. 00:33:00.350 --> 00:33:01.230 AUDIENCE: Central limit theorem. 00:33:01.230 --> 00:33:02.605 PROFESSOR: Central limit theorem. 00:33:02.605 --> 00:33:03.740 Exactly. 00:33:03.740 --> 00:33:07.045 So if you go back to that, if I'm 00:33:07.045 --> 00:33:08.420 doing any sort of averaging here, 00:33:08.420 --> 00:33:10.045 I'm invoking the central limit theorem. 00:33:10.045 --> 00:33:12.710 So even if the underlying behavior of the process 00:33:12.710 --> 00:33:18.270 naturally is not purely normal, it'll 00:33:18.270 --> 00:33:20.320 tend to be normal when I do the average. 00:33:20.320 --> 00:33:24.540 So it's a sort of a self-fulfilling method 00:33:24.540 --> 00:33:25.840 by doing it that way. 00:33:25.840 --> 00:33:26.340 OK. 00:33:28.880 --> 00:33:33.910 Now, since I can, with respect to this S chart, 00:33:33.910 --> 00:33:37.340 since I can calculate these at each intervals, you might say, 00:33:37.340 --> 00:33:40.170 I could have a second chart where 00:33:40.170 --> 00:33:44.970 I could be plotting sequentially the standard deviation. 00:33:44.970 --> 00:33:47.310 And so I can actually end up plotting-- 00:33:47.310 --> 00:33:50.620 let me put that over here. 00:33:50.620 --> 00:33:54.340 I can plot my sample standard deviation. 00:33:54.340 --> 00:33:57.100 And I could have another data point here 00:33:57.100 --> 00:33:59.980 and another data point here. 00:33:59.980 --> 00:34:03.070 And so I'm actually looking at both. 00:34:03.070 --> 00:34:06.490 I'm plotting the sample statistics for the mean 00:34:06.490 --> 00:34:10.610 and the sample statistics for the standard deviation. 00:34:10.610 --> 00:34:13.699 And again, what should the underlying standard deviation 00:34:13.699 --> 00:34:14.199 be? 00:34:14.199 --> 00:34:16.520 It should be a constant. 00:34:16.520 --> 00:34:19.690 And these will be samples, estimates of that. 00:34:19.690 --> 00:34:23.980 And they'll be following a normal distribution as well. 00:34:23.980 --> 00:34:26.699 And so again, we'll have to estimate what that value should 00:34:26.699 --> 00:34:29.060 be, but we can get this. 00:34:29.060 --> 00:34:33.949 Now, in your text, in most texts on this, they talk-- 00:34:33.949 --> 00:34:37.340 I know Montgomery talks about S charts. 00:34:37.340 --> 00:34:39.560 He also talks a lot about R-charts. 00:34:39.560 --> 00:34:43.460 And R-charts basically just says, for the sample 00:34:43.460 --> 00:34:45.710 of end data, what's the range? 00:34:45.710 --> 00:34:48.170 The min-max range of it, OK? 00:34:48.170 --> 00:34:52.370 Now, range, why do you think we used range for so many years 00:34:52.370 --> 00:34:53.900 as opposed to-- 00:34:53.900 --> 00:34:58.940 we use R, and a lot of the literature is on R. Especially 00:34:58.940 --> 00:35:02.360 if, let's assume N is is a number of 5. 00:35:02.360 --> 00:35:05.360 I'm taking five samples. 00:35:05.360 --> 00:35:06.590 I'm plotting data. 00:35:06.590 --> 00:35:09.230 Making decisions on the factory floor. 00:35:09.230 --> 00:35:11.360 Why would I use range which just involves 00:35:11.360 --> 00:35:14.360 a subtraction of a minimum-maximum number 00:35:14.360 --> 00:35:18.510 versus standard deviation, which is sum of the squares and all 00:35:18.510 --> 00:35:19.470 that other stuff? 00:35:19.470 --> 00:35:22.403 Why would anybody ever want to use range? 00:35:22.403 --> 00:35:24.768 AUDIENCE: [INAUDIBLE] 00:35:27.606 --> 00:35:30.110 PROFESSOR: Um, no. 00:35:30.110 --> 00:35:31.470 But I see where you're going. 00:35:31.470 --> 00:35:34.620 Yeah, it basically-- you know, it bounds the data. 00:35:34.620 --> 00:35:36.470 But again, what we're trying to get at 00:35:36.470 --> 00:35:38.880 is the underlying random behavior. 00:35:38.880 --> 00:35:40.805 So why would I ever use R? 00:35:40.805 --> 00:35:44.530 AUDIENCE: [INAUDIBLE] 00:35:44.530 --> 00:35:47.050 PROFESSOR: Yeah, think about the most basic user. 00:35:47.050 --> 00:35:49.300 We're talking about the simplicity of SPC. 00:35:49.300 --> 00:35:54.070 You got a pad and a pencil and paper. 00:35:54.070 --> 00:35:56.410 Averaging is pretty easy to do. 00:35:56.410 --> 00:35:58.810 Subtracting two numbers is pretty easy to do. 00:35:58.810 --> 00:35:59.980 You write them down. 00:35:59.980 --> 00:36:01.480 Doesn't take a calculator. 00:36:01.480 --> 00:36:06.190 Doesn't take a computer. 00:36:06.190 --> 00:36:08.860 And I know I'm really starting to sound old now, 00:36:08.860 --> 00:36:13.720 but pocket calculators weren't around for a long time. 00:36:13.720 --> 00:36:18.660 And to something that could take a square or square root, 00:36:18.660 --> 00:36:20.910 forget it. 00:36:20.910 --> 00:36:24.158 So in the production floor basis, 00:36:24.158 --> 00:36:25.950 you can have a couple of columns of numbers 00:36:25.950 --> 00:36:28.117 and write these things down and get it very quickly. 00:36:28.117 --> 00:36:30.145 Now, the thing is that this range is actually 00:36:30.145 --> 00:36:31.770 a pretty good estimate of the variance, 00:36:31.770 --> 00:36:34.290 and there's some nice stuff in the text about this 00:36:34.290 --> 00:36:36.090 in other books on this. 00:36:36.090 --> 00:36:43.178 So range is an estimate of the sample standard deviation. 00:36:43.178 --> 00:36:44.970 So it's not bad in their correction factors 00:36:44.970 --> 00:36:46.120 and all that. 00:36:46.120 --> 00:36:48.780 But the reason I like to do the S is, look. 00:36:48.780 --> 00:36:50.010 That's what we do now. 00:36:50.010 --> 00:36:51.600 It's easy to take the data. 00:36:51.600 --> 00:36:54.505 And very few if any organizations 00:36:54.505 --> 00:36:55.630 are doing it the other way. 00:36:55.630 --> 00:36:57.970 So that's what we do. 00:36:57.970 --> 00:36:58.470 OK. 00:36:58.470 --> 00:37:01.770 Now, a little bit about the sampling because this is-- 00:37:01.770 --> 00:37:03.210 such as it is. 00:37:03.210 --> 00:37:08.220 That's the theory of SPC. Now, here's the practice of it. 00:37:08.220 --> 00:37:11.676 How do we actually do this? 00:37:11.676 --> 00:37:14.650 Well, here it is. 00:37:14.650 --> 00:37:18.850 Here's a comb, which is actually meant 00:37:18.850 --> 00:37:23.760 to show you instance in time or actual production instances. 00:37:23.760 --> 00:37:27.360 So each of these vertical lines is a product, an opportunity 00:37:27.360 --> 00:37:30.340 to make a measurement. 00:37:30.340 --> 00:37:33.180 That's the real product. 00:37:33.180 --> 00:37:35.430 When we do that sequence then, what 00:37:35.430 --> 00:37:39.120 we're saying with this sequential average, which 00:37:39.120 --> 00:37:41.100 is what the Shewhart approach does, 00:37:41.100 --> 00:37:44.930 it says, well, let's take a group of those, a sample 00:37:44.930 --> 00:37:50.090 size N, and we'll call that sample interval J. 00:37:50.090 --> 00:37:53.480 So our time, if you will, is now when did this set of samples-- 00:37:53.480 --> 00:37:55.700 when was this set of samples taken? 00:37:55.700 --> 00:38:00.380 And let's do our measurements, let's do our plotting 00:38:00.380 --> 00:38:01.440 based on that. 00:38:01.440 --> 00:38:05.060 So for this orange block, we can calculate, which has, 00:38:05.060 --> 00:38:08.360 in this case, six measurements in it. 00:38:11.320 --> 00:38:12.080 So yeah. 00:38:12.080 --> 00:38:12.850 So n is 6. 00:38:12.850 --> 00:38:16.940 So I can do an average value for that, for that set of data, 00:38:16.940 --> 00:38:18.950 and I can do a standard deviation for that. 00:38:18.950 --> 00:38:21.390 A sample standard deviation from that. 00:38:21.390 --> 00:38:25.150 And then I wait a certain amount of time. 00:38:25.150 --> 00:38:26.830 And I do it again. 00:38:26.830 --> 00:38:28.160 And so on. 00:38:28.160 --> 00:38:30.955 So for each of these, I get-- 00:38:30.955 --> 00:38:32.860 do I have one here? 00:38:32.860 --> 00:38:39.620 So for each of these, I can get, of course, an x-bar and an S. 00:38:39.620 --> 00:38:40.120 OK? 00:38:43.050 --> 00:38:45.660 So you can see there's a trade off between how many samples I 00:38:45.660 --> 00:38:49.280 take and how far apart I take them. 00:38:49.280 --> 00:38:49.780 All right. 00:38:49.780 --> 00:38:51.890 First question is-- 00:38:51.890 --> 00:38:54.560 I'll ask it before somebody does because somebody always does. 00:38:54.560 --> 00:38:55.768 How big does that need to be? 00:39:00.670 --> 00:39:02.720 Greater than 1. 00:39:02.720 --> 00:39:06.710 You can do it with 2, especially if you use the range. 00:39:06.710 --> 00:39:08.120 But how big does N need to be? 00:39:08.120 --> 00:39:09.470 How big should N be? 00:39:17.732 --> 00:39:21.620 AUDIENCE: [INAUDIBLE] 00:39:26.510 --> 00:39:27.990 PROFESSOR: Yeah. 00:39:27.990 --> 00:39:30.320 It's exactly the confidence interval issue. 00:39:30.320 --> 00:39:32.930 But look at this relationship here. 00:39:32.930 --> 00:39:35.320 Well, yeah. 00:39:35.320 --> 00:39:40.810 You remember when we talked about the mean and then 00:39:40.810 --> 00:39:42.040 the invariance of the mean. 00:39:42.040 --> 00:39:45.430 And the invariance of the mean meaning how-- 00:39:45.430 --> 00:39:49.610 or, sorry, the variance of the estimate of the mean. 00:39:49.610 --> 00:39:50.930 This job. 00:40:01.710 --> 00:40:08.560 So if I'm plotting my estimate of the mean value 00:40:08.560 --> 00:40:13.270 and N is a really small number like 1 or 2, 00:40:13.270 --> 00:40:16.120 then I get the maximum variance of that estimate. 00:40:16.120 --> 00:40:18.280 It's going to be all over the place. 00:40:18.280 --> 00:40:20.570 If I increase N, that gets tighter and tighter. 00:40:20.570 --> 00:40:22.720 So I'm getting a better and better estimate 00:40:22.720 --> 00:40:24.640 of what the true mean value is. 00:40:24.640 --> 00:40:28.690 So obviously, maximizing N minimizes the variance 00:40:28.690 --> 00:40:30.490 of my estimate of the mean. 00:40:30.490 --> 00:40:32.890 And so I'm doing a better job of estimating the mean. 00:40:32.890 --> 00:40:36.660 So why not just make N a really big number? 00:40:36.660 --> 00:40:37.160 Adam. 00:40:37.160 --> 00:40:40.611 AUDIENCE: [INAUDIBLE] 00:40:43.853 --> 00:40:44.520 PROFESSOR: Yeah. 00:40:44.520 --> 00:40:47.103 Yeah, I mean, it could take you all day to get a decent sample 00:40:47.103 --> 00:40:48.390 size, right? 00:40:48.390 --> 00:40:54.140 And something else-- there's a real issue here that comes up 00:40:54.140 --> 00:40:57.230 called time variability. 00:40:57.230 --> 00:41:02.540 So within, if you took a large sample, 50, 100, 00:41:02.540 --> 00:41:03.680 the whole day's worth-- 00:41:03.680 --> 00:41:05.360 you could take a whole day's worth of production 00:41:05.360 --> 00:41:05.870 and say, OK. 00:41:05.870 --> 00:41:08.690 That'll give me a great estimate of the mean, right? 00:41:08.690 --> 00:41:10.190 But during that time, the process 00:41:10.190 --> 00:41:11.630 could have been going all over the place, 00:41:11.630 --> 00:41:13.172 changing here and there, and you just 00:41:13.172 --> 00:41:15.810 say, well, let's wait till the day is over and see how we did. 00:41:15.810 --> 00:41:16.310 OK? 00:41:16.310 --> 00:41:18.530 So it doesn't give you a lot of time to intervene. 00:41:18.530 --> 00:41:22.250 And again, I can't do it on the screen here, 00:41:22.250 --> 00:41:28.110 but imagine that I cover this up, 00:41:28.110 --> 00:41:30.610 and all you can see-- of course, you guys can't see anything 00:41:30.610 --> 00:41:34.590 now, but all you can see is what's happening right here. 00:41:34.590 --> 00:41:37.020 You don't know what's going to happen in the future. 00:41:37.020 --> 00:41:40.890 And you're trying to estimate what's going to happen. 00:41:40.890 --> 00:41:47.490 If you wait until here to do that, think of all the product 00:41:47.490 --> 00:41:52.680 that you've made and think about trying to make your next guess. 00:41:52.680 --> 00:41:56.970 It really gets kind of ridiculous. 00:41:56.970 --> 00:41:59.160 So there's a trade off. 00:41:59.160 --> 00:42:00.390 How big should N be? 00:42:00.390 --> 00:42:03.720 Well, big enough to get a reasonable estimate. 00:42:03.720 --> 00:42:09.300 Big enough to be able to detect changes in a timely manner. 00:42:09.300 --> 00:42:11.370 So if I take a lot of data points, 00:42:11.370 --> 00:42:13.950 it's just going to take me forever to get an estimate. 00:42:13.950 --> 00:42:16.200 And then there is the issue of how far apart they are. 00:42:16.200 --> 00:42:19.590 AUDIENCE: [INAUDIBLE] depend on the value add of the process 00:42:19.590 --> 00:42:20.530 that we're looking at? 00:42:20.530 --> 00:42:22.200 Where if you're adding a lot of value, 00:42:22.200 --> 00:42:26.120 you might want to look at it or more often because it's 00:42:26.120 --> 00:42:29.690 costly to miss minor changes. 00:42:29.690 --> 00:42:30.840 PROFESSOR: Yeah, sure. 00:42:30.840 --> 00:42:31.610 Sure. 00:42:31.610 --> 00:42:35.370 I think at this point, we look at this in a value-- 00:42:35.370 --> 00:42:37.820 let's say a value-neutral fashion, saying, look. 00:42:37.820 --> 00:42:41.630 At this point, there is-- 00:42:41.630 --> 00:42:44.550 your point is well taken in the following. 00:42:44.550 --> 00:42:46.460 There's a cost to every measurement we make. 00:42:46.460 --> 00:42:50.000 There's a cost to every average that we take 00:42:50.000 --> 00:42:51.260 and all that sort of thing. 00:42:51.260 --> 00:42:53.390 In the past, those costs could be pretty high. 00:42:53.390 --> 00:42:55.340 They're tending to be much lower these days 00:42:55.340 --> 00:42:57.660 with automated inspection and things like that 00:42:57.660 --> 00:42:59.060 as a matter of course. 00:42:59.060 --> 00:43:02.700 But yes, there's a cost benefit. 00:43:02.700 --> 00:43:05.210 So if it's a part where it's not that important, 00:43:05.210 --> 00:43:07.400 you know, so forth and so on. 00:43:07.400 --> 00:43:13.110 If you look downstream and you say it's not a critical-- 00:43:13.110 --> 00:43:15.080 what's the term I'm thinking of? 00:43:15.080 --> 00:43:21.090 It's not a key characteristic of the product, it can vary, 00:43:21.090 --> 00:43:22.470 then maybe this isn't important. 00:43:22.470 --> 00:43:24.387 But that actually gets to the next step, which 00:43:24.387 --> 00:43:25.620 is, how critical is a part? 00:43:25.620 --> 00:43:27.990 So if I hurry up, we'll get to that. 00:43:27.990 --> 00:43:29.400 But you're exactly right. 00:43:29.400 --> 00:43:32.423 So there is a cost of quality associated with this. 00:43:32.423 --> 00:43:33.840 Nowadays, we tend to think there's 00:43:33.840 --> 00:43:38.730 a cost, high cost associated with not doing this. 00:43:38.730 --> 00:43:39.390 OK. 00:43:39.390 --> 00:43:44.490 What's the effective-- why would we actually wait and not 00:43:44.490 --> 00:43:46.320 have these boxes right next to each other? 00:43:46.320 --> 00:43:48.690 Sample 6, OK. 00:43:48.690 --> 00:43:51.570 So 1 through 6 is the first sample, 7 to 12 00:43:51.570 --> 00:43:53.940 is the next sample, and so on. 00:43:53.940 --> 00:43:56.310 Why would I-- why am I actually showing a gap 00:43:56.310 --> 00:43:57.660 between these two? 00:43:57.660 --> 00:44:00.300 Why don't I just don't take any measurements? 00:44:00.300 --> 00:44:01.650 Ignore the data. 00:44:01.650 --> 00:44:03.546 Why would I ever do that? 00:44:03.546 --> 00:44:07.147 AUDIENCE: [INAUDIBLE] 00:44:07.147 --> 00:44:08.480 PROFESSOR: That's exactly right. 00:44:08.480 --> 00:44:10.160 Say a little bit more about that. 00:44:10.160 --> 00:44:19.950 AUDIENCE: I guess if there is certain variation [INAUDIBLE],, 00:44:19.950 --> 00:44:22.223 It would be [INAUDIBLE] any more than other causes 00:44:22.223 --> 00:44:25.198 of the variation that we take in our data samples 00:44:25.198 --> 00:44:26.240 right next to each other. 00:44:26.240 --> 00:44:29.250 It will have the same cause of variation affect [? two ?] 00:44:29.250 --> 00:44:32.158 of our samples, and in effect, we [INAUDIBLE] same thing 00:44:32.158 --> 00:44:33.006 twice. 00:44:33.006 --> 00:44:38.062 So [INAUDIBLE] we will still have [INAUDIBLE] causes 00:44:38.062 --> 00:44:39.177 of variation. 00:44:39.177 --> 00:44:40.510 PROFESSOR: That's exactly right. 00:44:40.510 --> 00:44:42.177 I hope you guys heard that in Singapore. 00:44:42.177 --> 00:44:45.810 I couldn't I couldn't say it any better, 00:44:45.810 --> 00:44:47.250 but that's basically it. 00:44:47.250 --> 00:44:51.030 And we'll talk about this I think a little bit 00:44:51.030 --> 00:44:52.660 more theoretically later. 00:44:52.660 --> 00:44:59.850 But if there is an underlying-- if something happens here 00:44:59.850 --> 00:45:02.640 that has some memory, some history to it, 00:45:02.640 --> 00:45:05.520 which causes correlation from one incident to the next, 00:45:05.520 --> 00:45:09.360 you're violating the assumption of independent random behavior. 00:45:09.360 --> 00:45:11.760 If you make this integral large enough, 00:45:11.760 --> 00:45:14.490 there's something actually called a correlation time. 00:45:14.490 --> 00:45:17.170 You can measure that for a process, 00:45:17.170 --> 00:45:20.340 and I think you'll see that near the end of the term. 00:45:20.340 --> 00:45:22.680 If you sample outside that correlation time, 00:45:22.680 --> 00:45:25.020 even though the process is not truly independent, 00:45:25.020 --> 00:45:27.208 it will appear to be independent, which 00:45:27.208 --> 00:45:28.500 is good for what we want to do. 00:45:28.500 --> 00:45:31.350 It's sort of like the other half of using the central limit 00:45:31.350 --> 00:45:32.130 theorem. 00:45:32.130 --> 00:45:34.260 We get normal, independent behavior, 00:45:34.260 --> 00:45:38.442 even when the individual data points don't follow that. 00:45:38.442 --> 00:45:39.400 There's another reason. 00:45:43.980 --> 00:45:46.290 Which is less important today than it was in the past, 00:45:46.290 --> 00:45:48.990 and that is it takes time to do this. 00:45:48.990 --> 00:45:51.390 And you just don't have time to take all this data. 00:45:51.390 --> 00:45:52.600 So you wait. 00:45:52.600 --> 00:45:55.830 You grab six, you take them over to the bench, 00:45:55.830 --> 00:45:57.450 and you do whatever you do with them, 00:45:57.450 --> 00:45:59.908 and then you come back as soon as you can for the next one. 00:45:59.908 --> 00:46:05.070 So you have to allow for this kind of behavior. 00:46:05.070 --> 00:46:09.960 Nowadays, again, most production for anything that's critical 00:46:09.960 --> 00:46:15.170 is actually taking the data, in many cases, on every part. 00:46:15.170 --> 00:46:18.390 Every part that's coming out has some measurement made on it. 00:46:18.390 --> 00:46:19.380 I shouldn't say most. 00:46:19.380 --> 00:46:20.430 Many. 00:46:20.430 --> 00:46:23.730 And this is all available, and you can choose to use it all. 00:46:23.730 --> 00:46:24.960 You can choose to ignore it. 00:46:24.960 --> 00:46:26.752 If you think you have a lot of correlation, 00:46:26.752 --> 00:46:28.800 you might ignore it. 00:46:28.800 --> 00:46:29.593 Question? 00:46:29.593 --> 00:46:32.910 AUDIENCE: [INAUDIBLE] 00:46:32.910 --> 00:46:34.140 PROFESSOR: It should be. 00:46:34.140 --> 00:46:35.280 For these reasons, yeah. 00:46:35.280 --> 00:46:35.880 It should be. 00:46:39.200 --> 00:46:42.680 Let me go on because I'm doing exactly what I didn't want 00:46:42.680 --> 00:46:44.010 to do, which is talk too much. 00:46:44.010 --> 00:46:44.840 So, OK. 00:46:44.840 --> 00:46:46.010 I think we know all that. 00:46:55.780 --> 00:46:57.630 OK. 00:46:57.630 --> 00:47:00.360 So this is what you would actually 00:47:00.360 --> 00:47:05.970 see if you took measurements, grouped them, in this case, 00:47:05.970 --> 00:47:09.010 in groups of N, and plotted the data. 00:47:09.010 --> 00:47:11.910 This is what you would see if the process were governed 00:47:11.910 --> 00:47:18.995 by purely random stationary, meaning fixed mean invariance, 00:47:18.995 --> 00:47:20.370 normal behavior, because this was 00:47:20.370 --> 00:47:23.850 generated, in fact, in the PowerPoint that's 00:47:23.850 --> 00:47:25.890 on the website. 00:47:25.890 --> 00:47:28.140 This is-- I think you can click on this, and the Excel 00:47:28.140 --> 00:47:30.300 spreadsheet that generated it is there. 00:47:30.300 --> 00:47:32.440 So you can re-randomize it and see what happens. 00:47:32.440 --> 00:47:33.940 But it's just a normal distribution. 00:47:33.940 --> 00:47:39.340 And this is what you would get with a normal distribution. 00:47:39.340 --> 00:47:41.070 In this case, a random number generator 00:47:41.070 --> 00:47:44.610 that's following normal distribution. 00:47:44.610 --> 00:47:46.450 And you get stuff that looks like this. 00:47:46.450 --> 00:47:48.510 So these are your estimates of the mean value. 00:47:48.510 --> 00:47:50.010 So you can look at that and say, OK. 00:47:50.010 --> 00:47:53.920 Well, you know, what does it say? 00:47:53.920 --> 00:47:57.150 Well, I can observe that-- 00:47:57.150 --> 00:48:02.180 I can eyeball that the mean value of the mean value 00:48:02.180 --> 00:48:03.720 looks like a constant. 00:48:03.720 --> 00:48:06.270 So it looks to me, in this particular case, 00:48:06.270 --> 00:48:10.760 like x-bar is telling me-- my estimate of x-bar 00:48:10.760 --> 00:48:14.200 is that the underlying meaning is a constant, 00:48:14.200 --> 00:48:16.910 and it's probably about right here. 00:48:16.910 --> 00:48:20.750 And likewise, I don't see that my estimate of the invariance 00:48:20.750 --> 00:48:22.250 is telling me that the invariance is 00:48:22.250 --> 00:48:24.030 anything but a constant. 00:48:24.030 --> 00:48:27.930 And again, I can look at its average value. 00:48:27.930 --> 00:48:29.870 So this is what you get. 00:48:29.870 --> 00:48:31.520 You plot a new data point, and this 00:48:31.520 --> 00:48:32.870 is what you start to expect. 00:48:32.870 --> 00:48:37.040 Now, of course, I can look at this now and get an overall-- 00:48:37.040 --> 00:48:39.530 a grand mean, which is an average of all 00:48:39.530 --> 00:48:45.020 the average values, and a grand standard deviation estimate. 00:48:45.020 --> 00:48:47.510 I should say a grand average and a grand standard deviation 00:48:47.510 --> 00:48:49.250 estimate. 00:48:49.250 --> 00:48:50.990 And say, OK. 00:48:50.990 --> 00:48:55.020 Now I know the underlying distribution of the process. 00:48:55.020 --> 00:48:58.730 Once I say that, then I know what to expect, right? 00:48:58.730 --> 00:49:01.590 Now, I can put some lines on this chart and say, 00:49:01.590 --> 00:49:04.520 this is where the data should fall if everything's 00:49:04.520 --> 00:49:05.450 in a state of control. 00:49:08.040 --> 00:49:15.660 So this whole idea of setting chart limits 00:49:15.660 --> 00:49:19.560 is extremely important and often abused and misused. 00:49:19.560 --> 00:49:20.970 But here's the idea. 00:49:20.970 --> 00:49:23.660 I now have all this data. 00:49:23.660 --> 00:49:26.203 And this is before-- this is just taking raw data 00:49:26.203 --> 00:49:27.370 and doing the average on it. 00:49:27.370 --> 00:49:30.920 I haven't tried to quantify this other than that. 00:49:30.920 --> 00:49:34.790 Now, I need to start to put some limits on this 00:49:34.790 --> 00:49:37.225 or put some information on. 00:49:37.225 --> 00:49:39.350 So the first thing you do, of course, is say, well, 00:49:39.350 --> 00:49:41.051 there's the-- 00:49:41.051 --> 00:49:46.600 on this set of data, there's the average in each case. 00:49:46.600 --> 00:49:48.790 Now, another thing to keep in mind-- this 00:49:48.790 --> 00:49:50.350 has already happened. 00:49:50.350 --> 00:49:52.130 I'm not making any decisions based 00:49:52.130 --> 00:49:53.380 on this about what to do next. 00:49:53.380 --> 00:49:54.942 This has already happened. 00:49:54.942 --> 00:49:56.650 So the first thing I need to do, and this 00:49:56.650 --> 00:50:02.360 is part of the art of SPC, is I have to look at that and say, 00:50:02.360 --> 00:50:06.620 does it look like it's in a state of statistical control? 00:50:06.620 --> 00:50:08.555 And frankly, at this point, you eyeball it 00:50:08.555 --> 00:50:12.430 and you say, well, you know, I don't see anything 00:50:12.430 --> 00:50:14.350 that makes us look non-random. 00:50:14.350 --> 00:50:16.940 And we're going to quantify that in just a second. 00:50:16.940 --> 00:50:18.780 But what else could I do looking at, 00:50:18.780 --> 00:50:20.830 say, a run of data like this to say, yeah. 00:50:20.830 --> 00:50:25.850 It kind of looks like it's in a state of statistical control. 00:50:28.800 --> 00:50:32.130 In other words, if the process is truly stationary, 00:50:32.130 --> 00:50:35.228 if it is truly following a normal distribution, 00:50:35.228 --> 00:50:37.020 what would I expect this data to look like? 00:50:43.050 --> 00:50:44.760 Yeah, it's supposed to look random. 00:50:44.760 --> 00:50:46.050 But how do I look at it and say, oh, yeah. 00:50:46.050 --> 00:50:46.633 That's random. 00:50:49.862 --> 00:50:51.770 AUDIENCE: [INAUDIBLE] 00:50:51.770 --> 00:50:53.000 PROFESSOR: Yeah. 00:50:53.000 --> 00:50:54.330 If it has a pattern. 00:50:54.330 --> 00:50:55.220 If it has a trend. 00:50:57.880 --> 00:50:59.560 Things like that. 00:50:59.560 --> 00:51:03.340 If it does improbable things. 00:51:03.340 --> 00:51:04.570 That's the one that I think-- 00:51:04.570 --> 00:51:05.800 obviously, a trend. 00:51:05.800 --> 00:51:09.060 If it starts to go like this. 00:51:09.060 --> 00:51:12.720 If it starts to move up instead of being flat, that's a trend. 00:51:12.720 --> 00:51:18.966 If it goes like this, that's a trend. 00:51:18.966 --> 00:51:21.653 Then those are common trends that we'll talk about. 00:51:21.653 --> 00:51:23.820 There's some ones that are a little bit more subtle. 00:51:26.410 --> 00:51:29.590 Think about confidence intervals. 00:51:29.590 --> 00:51:31.120 OK? 00:51:31.120 --> 00:51:33.440 Let's put some confidence intervals on here. 00:51:33.440 --> 00:51:36.350 Let's just put some lines in here. 00:51:36.350 --> 00:51:40.510 And I'll, just for fun, put three lines 00:51:40.510 --> 00:51:44.077 above the average and three lines below the average. 00:51:44.077 --> 00:51:46.160 And I don't even know if those in the right place. 00:51:46.160 --> 00:51:50.510 But remember, confidence intervals 00:51:50.510 --> 00:51:54.060 that said that I should get 63%-- 00:51:54.060 --> 00:51:54.650 is that right? 00:51:54.650 --> 00:51:58.190 63% in the plus or minus 1 sigma. 00:51:58.190 --> 00:51:59.960 So most of my data should fall in there. 00:52:02.870 --> 00:52:03.950 That one interval. 00:52:03.950 --> 00:52:07.370 Even more of it should fall within the next two intervals 00:52:07.370 --> 00:52:10.100 and the plus or minus 3 sigma. 00:52:10.100 --> 00:52:12.680 And it's very unlikely that I'll get very many points 00:52:12.680 --> 00:52:14.970 in the 2 to 3 sigma. 00:52:14.970 --> 00:52:17.960 A little bit more likely that'll get them within the 1 to 2 00:52:17.960 --> 00:52:18.770 sigma. 00:52:18.770 --> 00:52:20.390 So if I look at this data and I start 00:52:20.390 --> 00:52:26.720 to see a lot of data points up here or down here, 00:52:26.720 --> 00:52:28.250 that's pretty unlikely. 00:52:28.250 --> 00:52:30.520 That shouldn't be happening. 00:52:30.520 --> 00:52:33.610 That's an indication that it's not following the behavior 00:52:33.610 --> 00:52:34.780 that I expected. 00:52:34.780 --> 00:52:37.360 Or what if I-- in fact, I just drew it here. 00:52:37.360 --> 00:52:39.560 But what if, in fact, what I saw-- 00:52:39.560 --> 00:52:40.810 let me get rid of those lines. 00:52:40.810 --> 00:52:42.550 They're distracting. 00:52:42.550 --> 00:52:50.170 What if I saw instead maybe the same data, 00:52:50.170 --> 00:52:53.790 but it looked like this instead? 00:52:53.790 --> 00:52:58.800 I was getting, I don't know, two or three data points in a row 00:52:58.800 --> 00:53:00.890 all in the same band. 00:53:00.890 --> 00:53:03.540 That's pretty unlikely, too. 00:53:03.540 --> 00:53:06.050 So based on these things and actually using things 00:53:06.050 --> 00:53:07.800 like confidence intervals, you can come up 00:53:07.800 --> 00:53:11.390 with some rules on this. 00:53:11.390 --> 00:53:12.470 I'm going to skip this. 00:53:12.470 --> 00:53:14.510 Is covered in the text very nicely, 00:53:14.510 --> 00:53:18.530 but there are ways of calculating 00:53:18.530 --> 00:53:24.470 the sample mean and the sample standard deviation. 00:53:24.470 --> 00:53:28.880 And there's some correction factors because of biases. 00:53:28.880 --> 00:53:33.390 But-- for both the x-bar and the S-chart. 00:53:33.390 --> 00:53:36.290 So what is typically done, and you always hear about this, 00:53:36.290 --> 00:53:39.290 is the plus or minus 3 sigma limit. 00:53:39.290 --> 00:53:41.990 So here's an x-bar chart. 00:53:41.990 --> 00:53:43.670 Historical x-bar chart. 00:53:43.670 --> 00:53:45.530 I've calculated the grand mean. 00:53:45.530 --> 00:53:46.910 Arithmetic average. 00:53:46.910 --> 00:53:50.420 I've calculated plus or minus 3 sigma 00:53:50.420 --> 00:53:53.570 of the grand mean with the correction factors 00:53:53.570 --> 00:53:54.870 and all that. 00:53:54.870 --> 00:53:56.870 And so what do these two lines tell me? 00:53:56.870 --> 00:53:58.830 These, often called control limits. 00:53:58.830 --> 00:54:01.750 What do those lines mean? 00:54:01.750 --> 00:54:10.680 They mean that I expect 99.7% of all the data 00:54:10.680 --> 00:54:12.450 to fall within those two lines. 00:54:12.450 --> 00:54:13.410 That's all it means. 00:54:16.140 --> 00:54:19.890 So a simple SPC thing and one you 00:54:19.890 --> 00:54:21.840 hear about all the time without much thought, 00:54:21.840 --> 00:54:24.960 frankly, is, oh, there's a data point up there or there's 00:54:24.960 --> 00:54:27.820 a data point up there. 00:54:27.820 --> 00:54:28.970 Impossible. 00:54:28.970 --> 00:54:30.550 Shut down the process. 00:54:30.550 --> 00:54:33.430 Everything's wrong. 00:54:33.430 --> 00:54:36.070 So you can see that's a good first order thing to do. 00:54:36.070 --> 00:54:39.880 You know, there's only 3 chances in 1,000 00:54:39.880 --> 00:54:41.410 that one would be out there, would 00:54:41.410 --> 00:54:42.660 be in one of these two limits. 00:54:42.660 --> 00:54:44.560 So that's a pretty good first cut. 00:54:44.560 --> 00:54:51.520 But it's a little bit simplistic because it is possible 00:54:51.520 --> 00:54:54.130 that you'd get a process that's perfectly in control, 00:54:54.130 --> 00:54:56.500 and you'd have one point that's up here. 00:54:56.500 --> 00:54:58.708 It's just not probable, but it's possible. 00:54:58.708 --> 00:55:00.500 So we can do a little bit better than that. 00:55:00.500 --> 00:55:02.050 We can-- and again, we can do the same thing 00:55:02.050 --> 00:55:02.870 with the S-chart. 00:55:02.870 --> 00:55:07.650 We can do upper and lower control limits. 00:55:07.650 --> 00:55:09.720 But the more important thing, I think, 00:55:09.720 --> 00:55:17.610 is not waiting for that one data point that pops up here. 00:55:17.610 --> 00:55:21.460 For example, one of the reasons that might be a problem-- 00:55:21.460 --> 00:55:25.500 what if I have underlying behavior that looks like this? 00:55:25.500 --> 00:55:27.440 And you can see that this is, again, this 00:55:27.440 --> 00:55:29.715 is truly normal data. 00:55:29.715 --> 00:55:31.340 And it's a smaller sample set that it's 00:55:31.340 --> 00:55:33.890 highly improbable I'll get anything near the 3 sigma 00:55:33.890 --> 00:55:35.720 limit. 00:55:35.720 --> 00:55:37.160 And this is what you typically get 00:55:37.160 --> 00:55:38.970 if you had a process that this was in control. 00:55:38.970 --> 00:55:40.220 But what if it was doing this? 00:55:45.880 --> 00:55:47.000 And you eyeball that. 00:55:47.000 --> 00:55:49.930 And would you say, is anything wrong with this process? 00:55:53.650 --> 00:55:54.150 Yeah. 00:55:54.150 --> 00:55:56.130 Look, it's trending up like crazy. 00:55:56.130 --> 00:55:57.270 When did that trend begin? 00:56:01.310 --> 00:56:03.690 Maybe here. 00:56:03.690 --> 00:56:08.490 Now, if all I do is sort of have an alarm when 00:56:08.490 --> 00:56:12.090 I cross over this upper limit, can you 00:56:12.090 --> 00:56:16.860 see that I've been-- something's been wrong for a long time. 00:56:16.860 --> 00:56:18.210 And this could be hours. 00:56:18.210 --> 00:56:21.867 It could be milliseconds, but it could be hours. 00:56:21.867 --> 00:56:23.450 Something going wrong for a long time. 00:56:23.450 --> 00:56:26.150 It would be nice to have something a little bit more 00:56:26.150 --> 00:56:28.820 subtle than just simply waiting for that one 00:56:28.820 --> 00:56:33.120 random, potentially just purely random event. 00:56:33.120 --> 00:56:36.240 So-- although we'll talk about that in just a second. 00:56:36.240 --> 00:56:38.160 So one of the things you can do, as I said, 00:56:38.160 --> 00:56:41.990 is look at the data on the basis of looking at confidence 00:56:41.990 --> 00:56:46.190 intervals on the frequency of getting any sorts of extremes 00:56:46.190 --> 00:56:46.730 and trends. 00:56:46.730 --> 00:56:48.650 And so there are a number of different things. 00:56:48.650 --> 00:56:50.810 Now, there's a text we used to use for the class 00:56:50.810 --> 00:56:55.190 by DeVore, Chang, and Sutherland. 00:56:55.190 --> 00:56:57.230 We stopped using it because it's just 00:56:57.230 --> 00:57:02.770 got some rough edges and theoretical problems. 00:57:02.770 --> 00:57:04.970 Not problems, but lack of-- 00:57:04.970 --> 00:57:06.650 it's theoretically correct, but it's 00:57:06.650 --> 00:57:09.187 got some gaps in the theory. 00:57:09.187 --> 00:57:10.520 So you need another book anyway. 00:57:10.520 --> 00:57:12.380 Montgomery is a little bit more basic on it. 00:57:12.380 --> 00:57:14.463 This is a little bit better on some of the process 00:57:14.463 --> 00:57:18.350 optimization and pragmatic-- these guys are engineers 00:57:18.350 --> 00:57:20.123 and less statisticians. 00:57:20.123 --> 00:57:22.040 But one of the things they did is they came up 00:57:22.040 --> 00:57:23.360 with the so-called eight rules. 00:57:26.030 --> 00:57:30.460 In fact, I'm going to-- let me go past those for just a second 00:57:30.460 --> 00:57:33.190 because-- 00:57:33.190 --> 00:57:35.680 oops. 00:57:35.680 --> 00:57:37.420 OK, never mind. 00:57:37.420 --> 00:57:38.962 I was going to talk about that, but I 00:57:38.962 --> 00:57:40.087 don't know if it's in here. 00:57:40.087 --> 00:57:40.600 OK. 00:57:40.600 --> 00:57:43.180 So the eight rules are based on really just four tests. 00:57:43.180 --> 00:57:44.980 The probability that the data falls 00:57:44.980 --> 00:57:48.120 into one of these confidence interval bands. 00:57:48.120 --> 00:57:49.560 A measure of periodicity. 00:57:49.560 --> 00:57:51.930 You should have no periodicity in the data. 00:57:51.930 --> 00:57:53.790 No regularity in it. 00:57:53.790 --> 00:57:55.920 Linear trends. 00:57:55.920 --> 00:57:59.880 Something that's changing up or down over time. 00:57:59.880 --> 00:58:03.348 And mean shift-- a jump change in the mean. 00:58:03.348 --> 00:58:04.890 All these things are things are going 00:58:04.890 --> 00:58:06.528 to be looking for in the data. 00:58:06.528 --> 00:58:08.070 Now, mean, you're going to hear a lot 00:58:08.070 --> 00:58:10.080 about mean shift throughout the term 00:58:10.080 --> 00:58:12.205 because that's your most-- in some ways, 00:58:12.205 --> 00:58:14.580 you can think of that is as one of the most likely things 00:58:14.580 --> 00:58:15.080 to happen. 00:58:15.080 --> 00:58:18.120 You're making product with a certain batch of material, 00:58:18.120 --> 00:58:20.200 and you change the batch. 00:58:20.200 --> 00:58:21.090 Something changes. 00:58:21.090 --> 00:58:23.310 You have a shift change. 00:58:23.310 --> 00:58:26.100 You have PM on the machine, Preventive Maintenance 00:58:26.100 --> 00:58:27.090 on the machine. 00:58:27.090 --> 00:58:29.010 And the next time you run it, things jump up. 00:58:29.010 --> 00:58:32.880 So the underlying behavior, something in this model, 00:58:32.880 --> 00:58:35.760 just made a step change, and you saw that out there. 00:58:35.760 --> 00:58:37.110 Linear trends, obviously. 00:58:37.110 --> 00:58:38.010 Something. 00:58:38.010 --> 00:58:40.200 Tool wearing. 00:58:40.200 --> 00:58:42.990 Something not-- something changing over time. 00:58:42.990 --> 00:58:44.840 Periodicity. 00:58:44.840 --> 00:58:46.720 It could be temperature changes. 00:58:46.720 --> 00:58:48.850 It could be something that's underlying. 00:58:48.850 --> 00:58:50.670 That sort of thing. 00:58:50.670 --> 00:58:51.570 OK. 00:58:51.570 --> 00:58:53.657 So test for out of control. 00:58:53.657 --> 00:58:54.990 I think this comes out to eight. 00:58:54.990 --> 00:58:57.480 So if you have a set of data and you look at it, 00:58:57.480 --> 00:58:58.950 first thing you might do is say is 00:58:58.950 --> 00:59:02.200 anything outside the plus or minus 3 sigma limits. 00:59:02.200 --> 00:59:03.640 That's really unlikely. 00:59:03.640 --> 00:59:07.500 If I get any extreme points like that, pull the Andon cord. 00:59:07.500 --> 00:59:08.550 Stop the production. 00:59:08.550 --> 00:59:09.330 Something's wrong. 00:59:09.330 --> 00:59:11.910 Let's go out and fix it. 00:59:11.910 --> 00:59:14.030 Improbable points. 00:59:14.030 --> 00:59:16.650 Now, they've quantified this by saying, look. 00:59:16.650 --> 00:59:21.830 If I get 2 out of 3 points, if I look at any triad of points, 00:59:21.830 --> 00:59:25.210 if 2 or 3 of those are in the plus or minus 2 sigma band, 00:59:25.210 --> 00:59:30.140 that's pretty improbable based on confidence intervals. 00:59:30.140 --> 00:59:34.550 4 out of 5 in the plus or minus, outside the plus or minus 1 00:59:34.550 --> 00:59:36.150 band. 00:59:36.150 --> 00:59:37.950 That's pretty improbable. 00:59:37.950 --> 00:59:41.640 Or all the data inside the plus or minus 1 band. 00:59:41.640 --> 00:59:45.850 That shouldn't happen, either, if my process is stationary. 00:59:45.850 --> 00:59:46.350 OK? 00:59:46.350 --> 00:59:47.808 So each of these things you can see 00:59:47.808 --> 00:59:49.590 could indicate that it's not following 00:59:49.590 --> 00:59:51.855 the expected normal behavior. 00:59:54.770 --> 01:00:00.638 Another one is in runs of 8 or more points, am I always-- 01:00:00.638 --> 01:00:01.930 is there a run of eight points? 01:00:01.930 --> 01:00:04.090 That's always above the mean value. 01:00:04.090 --> 01:00:04.900 That's improbable. 01:00:04.900 --> 01:00:08.920 It's supposed to be random on both sides. 01:00:08.920 --> 01:00:10.330 Linear trends, of course. 01:00:10.330 --> 01:00:11.170 Six points. 01:00:11.170 --> 01:00:15.220 And they pick the numbers to trade off between sensitivity 01:00:15.220 --> 01:00:18.060 and resolution. 01:00:18.060 --> 01:00:20.040 Six points in a consistent direction. 01:00:20.040 --> 01:00:22.920 Always heading upwards or downwards. 01:00:22.920 --> 01:00:25.470 And bimodal data. 01:00:25.470 --> 01:00:32.617 You got points-- if I get points outside of the central region, 01:00:32.617 --> 01:00:34.950 that could indicate-- you go back to that picture I had. 01:00:34.950 --> 01:00:36.075 I have a distribution here. 01:00:36.075 --> 01:00:37.290 I have a distribution here. 01:00:37.290 --> 01:00:39.390 It's actually following two different mean values 01:00:39.390 --> 01:00:42.710 on either side of the mean value. 01:00:42.710 --> 01:00:43.670 OK. 01:00:43.670 --> 01:00:48.630 So how would I apply the Shewhart charting concept? 01:00:48.630 --> 01:00:49.130 OK. 01:00:49.130 --> 01:00:51.297 Well, keep in mind, the first thing I've got to do-- 01:00:54.780 --> 01:00:57.997 well, let me back up. 01:00:57.997 --> 01:00:58.830 Not the first thing. 01:00:58.830 --> 01:01:02.840 What I'm trying to accomplish is this. 01:01:02.840 --> 01:01:05.860 I'm in production. 01:01:05.860 --> 01:01:07.330 Let's just look at the x-bar chart. 01:01:07.330 --> 01:01:10.270 I'm in production, and this is now-- 01:01:10.270 --> 01:01:13.150 I've got some data back here. 01:01:13.150 --> 01:01:19.710 This is now-- and I took another piece of data. 01:01:19.710 --> 01:01:21.820 And I want to say, OK. 01:01:21.820 --> 01:01:23.640 Is everything all right? 01:01:23.640 --> 01:01:26.500 Time to take any action? 01:01:26.500 --> 01:01:32.830 I can't do that until I know I have at least done 01:01:32.830 --> 01:01:38.950 my grand mean and I have at least my upper control limit, 01:01:38.950 --> 01:01:43.610 my plus 3 sigma, and my lower control limit. 01:01:43.610 --> 01:01:48.590 So I can't really do SPC until I have these limits. 01:01:48.590 --> 01:01:50.438 Where do they come from? 01:01:50.438 --> 01:01:51.730 They came from historical data. 01:01:51.730 --> 01:01:54.670 They came from the stuff that already happened. 01:01:54.670 --> 01:01:57.275 So this is a little bit of a catch-22. 01:01:57.275 --> 01:01:59.650 What do you do if the process is horribly out of control. 01:02:02.440 --> 01:02:05.345 And back here, it's all over the place. 01:02:05.345 --> 01:02:06.220 And you just say, oh. 01:02:06.220 --> 01:02:09.940 Well, here's the mean value on the standard deviation. 01:02:09.940 --> 01:02:12.760 You can see that these will be totally bogus limits. 01:02:12.760 --> 01:02:14.260 And if it's out of control back here 01:02:14.260 --> 01:02:16.610 and you put those limits on here, guess what? 01:02:16.610 --> 01:02:18.620 It'll appear to be in control here, too. 01:02:18.620 --> 01:02:21.310 It'll stay within these limits. 01:02:21.310 --> 01:02:26.380 So it's a bit of a catch-22. 01:02:26.380 --> 01:02:28.930 But what do you do with these-- 01:02:28.930 --> 01:02:30.655 how would I take these, I don't know, 01:02:30.655 --> 01:02:33.680 25 to 50 points before I actually start doing control? 01:02:33.680 --> 01:02:36.010 How would I take those and say, OK. 01:02:36.010 --> 01:02:37.740 Looks good. 01:02:37.740 --> 01:02:40.050 What kind of things would you do if I 01:02:40.050 --> 01:02:43.780 were taking data to say, yep. 01:02:43.780 --> 01:02:47.740 Looks like I can now apply the chart. 01:02:47.740 --> 01:02:50.440 What am I looking for in the data? 01:02:50.440 --> 01:02:52.382 AUDIENCE: [INAUDIBLE] 01:03:04.157 --> 01:03:06.490 PROFESSOR: That could be very dangerous for a reason I'm 01:03:06.490 --> 01:03:08.920 going to show you in a second. 01:03:08.920 --> 01:03:11.260 But yeah, you have certain expectations for the process. 01:03:11.260 --> 01:03:12.610 Yeah, absolutely. 01:03:12.610 --> 01:03:16.990 But let's say that, again, here's the historical data. 01:03:16.990 --> 01:03:18.380 I've got the historical data. 01:03:21.340 --> 01:03:23.120 I always draw it looking periodic. 01:03:23.120 --> 01:03:26.410 So I've got the historical data. 01:03:26.410 --> 01:03:28.900 I've got to look at that data and say, 01:03:28.900 --> 01:03:30.640 what do I need to say about it to say 01:03:30.640 --> 01:03:33.300 it's useful for charting? 01:03:33.300 --> 01:03:37.130 Number 1, it needs to be normal. 01:03:37.130 --> 01:03:41.980 Number 2, it needs to be stationary. 01:03:41.980 --> 01:03:43.750 Then I can start doing the charting. 01:03:43.750 --> 01:03:50.690 What's the test I would do for it being normal? 01:03:50.690 --> 01:03:53.070 AUDIENCE: [INAUDIBLE] 01:03:54.110 --> 01:03:55.970 PROFESSOR: Yeah. 01:03:55.970 --> 01:03:56.930 Exactly. 01:03:56.930 --> 01:03:58.550 You could do things like-- that's 01:03:58.550 --> 01:04:00.092 one of the reasons we looked at this. 01:04:00.092 --> 01:04:01.870 Do a histogram. 01:04:01.870 --> 01:04:02.500 What else? 01:04:07.790 --> 01:04:08.340 Yeah, yeah. 01:04:08.340 --> 01:04:13.560 You do a QQ or normal distribution plot. 01:04:13.560 --> 01:04:15.450 Really good thing to do. 01:04:15.450 --> 01:04:18.210 That's pretty fast and easy to do. 01:04:18.210 --> 01:04:20.280 Is it following normal distribution? 01:04:20.280 --> 01:04:23.490 If it's not, we got a real problem. 01:04:23.490 --> 01:04:27.660 I just had a student of mine who plotted some measurement data, 01:04:27.660 --> 01:04:31.200 and he plotted on a QQ, plot and it was nowhere near 01:04:31.200 --> 01:04:31.770 following it. 01:04:31.770 --> 01:04:33.160 Didn't make any sense. 01:04:33.160 --> 01:04:34.980 And then I found out that, underlying, 01:04:34.980 --> 01:04:37.980 he'd been doing some very deterministic things 01:04:37.980 --> 01:04:39.480 between measurements. 01:04:39.480 --> 01:04:41.520 Changing things in a very deterministic way. 01:04:41.520 --> 01:04:43.990 And it came out exactly in the data. 01:04:43.990 --> 01:04:45.990 It should have followed the normal distribution, 01:04:45.990 --> 01:04:47.790 and it didn't because of this. 01:04:50.590 --> 01:04:51.090 What else? 01:04:56.380 --> 01:04:58.820 Hayden, what else could we do? 01:04:58.820 --> 01:05:02.320 AUDIENCE: Well, I'm thinking you could get the upper 01:05:02.320 --> 01:05:05.140 and lower control limits there in your specification. 01:05:05.140 --> 01:05:06.490 [INTERPOSING VOICES] 01:05:06.490 --> 01:05:08.680 PROFESSOR: You got to careful of that, though. 01:05:08.680 --> 01:05:10.210 Yeah. 01:05:10.210 --> 01:05:10.780 Good point. 01:05:10.780 --> 01:05:11.890 That's the same issue of, you know, 01:05:11.890 --> 01:05:13.140 here's what I expect it to be. 01:05:13.140 --> 01:05:16.690 But the whole point about process capability, 01:05:16.690 --> 01:05:18.970 which I'm going to get to in the last five minutes, 01:05:18.970 --> 01:05:25.090 is process capability is what you're dreaming of getting. 01:05:25.090 --> 01:05:27.460 This is what you actually get. 01:05:27.460 --> 01:05:29.410 And they can do really far off. 01:05:29.410 --> 01:05:32.140 The reason I ask you is you just put that derivation 01:05:32.140 --> 01:05:33.815 of the kurtosis up there. 01:05:33.815 --> 01:05:35.440 So you could do other tests on the data 01:05:35.440 --> 01:05:36.862 like kurtosis and skewness. 01:05:36.862 --> 01:05:38.320 There are all these different tests 01:05:38.320 --> 01:05:40.180 to see if the data is normal. 01:05:40.180 --> 01:05:41.720 And then that's all well and good, 01:05:41.720 --> 01:05:42.720 but then you have to look at it. 01:05:42.720 --> 01:05:43.840 Is it trending up or down? 01:05:43.840 --> 01:05:45.640 Does it have any of these things? 01:05:45.640 --> 01:05:47.470 Before I ever put a limit on it, can I 01:05:47.470 --> 01:05:49.660 say, yeah, that kind of looks random? 01:05:49.660 --> 01:05:52.240 And even without a limit, you can say, OK. 01:05:52.240 --> 01:05:55.240 The data looks like it's not trending up. 01:05:55.240 --> 01:05:57.310 I don't see any periodicity in the data. 01:05:57.310 --> 01:05:59.380 In the case with my student's data, 01:05:59.380 --> 01:06:01.150 there was this big hump in the data where 01:06:01.150 --> 01:06:02.567 it spent a lot of time doing this, 01:06:02.567 --> 01:06:04.930 and then it came back being [INAUDIBLE].. 01:06:04.930 --> 01:06:10.330 It doesn't-- I may be wrong, but that doesn't look random to me. 01:06:10.330 --> 01:06:11.140 OK. 01:06:11.140 --> 01:06:12.400 So once I've done that-- 01:06:12.400 --> 01:06:14.383 and this is where the art is-- 01:06:14.383 --> 01:06:16.300 then I compute the center lines and the limits 01:06:16.300 --> 01:06:18.520 and I begin plotting and do this. 01:06:18.520 --> 01:06:21.790 And then I start to apply the eight rules. 01:06:21.790 --> 01:06:24.220 Or there are some simpler rules, often called 01:06:24.220 --> 01:06:29.290 the Western Electric rules, that are actually in your text. 01:06:29.290 --> 01:06:31.900 And again, what these rules mean is these are alarm points. 01:06:31.900 --> 01:06:34.840 These mean, to the best of our ability, 01:06:34.840 --> 01:06:39.490 your process is not following a state of statistical control, 01:06:39.490 --> 01:06:41.530 meaning it's not stationary. 01:06:41.530 --> 01:06:43.780 There is some sort of cause on the outside that's 01:06:43.780 --> 01:06:46.853 making a change, and it can be eliminated and identified. 01:06:46.853 --> 01:06:48.520 And these are the Western Electric rules 01:06:48.520 --> 01:06:51.400 that are in your text. 01:06:51.400 --> 01:06:55.330 Any points outside the limit, 2 to 3 points outside 2 sigma 01:06:55.330 --> 01:07:00.250 and 5 points outside 1 sigma, that sort of thing. 01:07:00.250 --> 01:07:01.330 OK. 01:07:01.330 --> 01:07:04.180 So you can see that just reviewing what we said, 01:07:04.180 --> 01:07:05.390 this is in control. 01:07:05.390 --> 01:07:09.850 Here's what the data should look like if it's in control. 01:07:09.850 --> 01:07:14.290 And if you see these types of behaviors in the data, 01:07:14.290 --> 01:07:17.140 it means something like this has happened. 01:07:17.140 --> 01:07:20.920 Mean shift, trends, bimodal, whatever. 01:07:20.920 --> 01:07:24.010 I'm going to skip over this thing on average run length. 01:07:24.010 --> 01:07:26.870 It's very interesting, and it gives you an issue-- 01:07:26.870 --> 01:07:29.245 some idea of what to do about sample sizes. 01:07:31.960 --> 01:07:34.960 And it's very carefully covered in the text. 01:07:34.960 --> 01:07:40.810 And you can play with this beautiful animation that 01:07:40.810 --> 01:07:42.160 was made up a long time ago. 01:07:44.870 --> 01:07:49.690 And let me just summarize this by saying, keep in mind, 01:07:49.690 --> 01:07:52.970 what we're really doing here is hypothesis testing. 01:07:52.970 --> 01:07:56.440 So all the stuff you just had on hypothesis testing 01:07:56.440 --> 01:07:57.740 is exactly what we're doing. 01:07:57.740 --> 01:08:02.350 We're testing the hypothesis that the data is defined 01:08:02.350 --> 01:08:04.450 by a normal distribution. 01:08:04.450 --> 01:08:06.400 And these charts are allowing us to test it, 01:08:06.400 --> 01:08:10.900 but it's sort of testing it as we go along. 01:08:10.900 --> 01:08:14.080 And these issues of alpha and beta probabilities 01:08:14.080 --> 01:08:15.700 all fall into this. 01:08:15.700 --> 01:08:18.967 So the power of the test is important. 01:08:24.700 --> 01:08:26.260 I think I'm getting redundant here. 01:08:35.990 --> 01:08:37.010 OK. 01:08:37.010 --> 01:08:41.840 So again, repeating what I said earlier, 01:08:41.840 --> 01:08:45.620 remodel the process as a normal, independent, random variable. 01:08:45.620 --> 01:08:47.840 By doing sampling the way we did, 01:08:47.840 --> 01:08:49.760 we sort of invoked the central limit theorem, 01:08:49.760 --> 01:08:53.420 and by potentially by spreading the samples out, 01:08:53.420 --> 01:08:57.710 we have a better chance of it being independent, 01:08:57.710 --> 01:08:59.450 even if it's not. 01:08:59.450 --> 01:09:01.460 We say, as a result of it being normal, 01:09:01.460 --> 01:09:04.399 there are only two things I need to know about the distribution. 01:09:04.399 --> 01:09:06.691 That's the beautiful thing about a normal distribution. 01:09:06.691 --> 01:09:08.630 Two parameters, mean and variance. 01:09:08.630 --> 01:09:10.220 So it's completely described by that. 01:09:10.220 --> 01:09:12.000 I only need to know those two things. 01:09:12.000 --> 01:09:15.680 So I estimate those with x bar and S on the data 01:09:15.680 --> 01:09:20.750 and then enforce this concept of stationary conditions. 01:09:20.750 --> 01:09:25.290 So if it's a stationary, normally distributed process, 01:09:25.290 --> 01:09:26.220 everything's fine. 01:09:26.220 --> 01:09:28.189 If it's not, everything's not fine. 01:09:31.300 --> 01:09:31.800 Oh, yeah. 01:09:31.800 --> 01:09:33.526 What happens if it's not right? 01:09:33.526 --> 01:09:34.109 This is great. 01:09:34.109 --> 01:09:36.569 I read this in the statistics book a long time ago. 01:09:36.569 --> 01:09:39.602 If it's not right, you call an engineer. 01:09:39.602 --> 01:09:41.810 So if you're from a purely statistical point of view, 01:09:41.810 --> 01:09:44.270 you're just saying something's not right. 01:09:44.270 --> 01:09:45.380 OK. 01:09:45.380 --> 01:09:48.470 Now, I'm rushing because I did want to mention this. 01:09:48.470 --> 01:09:51.180 I'm sure [INAUDIBLE] will do some more on it. 01:09:51.180 --> 01:09:54.140 But I really wanted to get to this because of some 01:09:54.140 --> 01:09:56.940 of the questions that came up. 01:09:56.940 --> 01:09:59.960 This is our empirical model of the process now. 01:09:59.960 --> 01:10:02.780 It's an empirical, statistical model of the process. 01:10:02.780 --> 01:10:06.980 The real world, our estimate of the real world, 01:10:06.980 --> 01:10:11.490 our underlying model, is this theoretical parent 01:10:11.490 --> 01:10:14.300 normal distribution. 01:10:14.300 --> 01:10:15.840 That's what you get. 01:10:15.840 --> 01:10:16.890 It's not what you want. 01:10:16.890 --> 01:10:19.590 It's what you get. 01:10:19.590 --> 01:10:23.030 So the question is, how good is the process? 01:10:23.030 --> 01:10:24.080 This is what it is. 01:10:24.080 --> 01:10:25.670 Is that good, or bad, or indifferent? 01:10:25.670 --> 01:10:28.370 And that's where you get into the concept of process 01:10:28.370 --> 01:10:29.490 capability. 01:10:29.490 --> 01:10:32.380 So we assume the process is in control. 01:10:32.380 --> 01:10:34.420 We assume it follows that normal distribution. 01:10:34.420 --> 01:10:35.540 Then we compare it. 01:10:35.540 --> 01:10:39.140 Then we compare it to things like tolerances. 01:10:39.140 --> 01:10:41.903 Where do I want my parts to be? 01:10:41.903 --> 01:10:44.070 And there's also this concept of quality loss, which 01:10:44.070 --> 01:10:46.260 is a better way, in some ways of looking 01:10:46.260 --> 01:10:49.270 at design specifications. 01:10:49.270 --> 01:10:51.460 The simplest design specification we can think of 01:10:51.460 --> 01:10:52.660 is an upper and lower limit. 01:10:52.660 --> 01:10:54.220 A tolerance. 01:10:54.220 --> 01:10:57.490 If you can make me a part that falls between these two limits, 01:10:57.490 --> 01:11:00.590 it's a good part. 01:11:00.590 --> 01:11:06.515 So can think of that as a nominal value, 01:11:06.515 --> 01:11:11.210 a target, and then an upper specification limit and a lower 01:11:11.210 --> 01:11:13.920 specification limit. 01:11:13.920 --> 01:11:16.110 Not control limit, but specification limit. 01:11:18.840 --> 01:11:22.220 Tolerances basically say, anything in there 01:11:22.220 --> 01:11:23.030 is a good part. 01:11:23.030 --> 01:11:25.820 Has equal quality, if you will. 01:11:25.820 --> 01:11:29.570 Quality loss, which was introduced by Taguchi 01:11:29.570 --> 01:11:31.925 some time ago, basically said, that's baloney. 01:11:35.070 --> 01:11:37.788 And there's some really good case examples of this, 01:11:37.788 --> 01:11:38.580 but that's baloney. 01:11:38.580 --> 01:11:39.690 He said, look. 01:11:39.690 --> 01:11:43.170 If there's a target value for some specification, 01:11:43.170 --> 01:11:46.650 it's a dimension or a property of something. 01:11:46.650 --> 01:11:48.000 And you can specify that. 01:11:48.000 --> 01:11:49.890 That's the best one. 01:11:49.890 --> 01:11:53.670 Any deviation from that is less good, 01:11:53.670 --> 01:11:58.260 and there is an actual cost associated with that deviation. 01:11:58.260 --> 01:12:01.080 And he said, not knowing anything more about it, 01:12:01.080 --> 01:12:02.920 we'll call it a quadratic loss. 01:12:02.920 --> 01:12:07.200 So the farther you are from the specified value, 01:12:07.200 --> 01:12:09.090 the worse the product is. 01:12:09.090 --> 01:12:13.280 And of course, you should always work your way down this curve. 01:12:13.280 --> 01:12:15.600 And there's a way to calibrate this, 01:12:15.600 --> 01:12:17.000 which basically would say-- 01:12:17.000 --> 01:12:20.890 one way to think of it is-- 01:12:20.890 --> 01:12:24.200 a simple way to calibrate this. 01:12:24.200 --> 01:12:26.720 If I actually have upper and lower specification limits 01:12:26.720 --> 01:12:30.550 here, I can say, what's the cost of scrapping apart? 01:12:30.550 --> 01:12:33.790 And where this curve crosses that, you say, OK. 01:12:33.790 --> 01:12:37.258 That's my calibration constant. 01:12:37.258 --> 01:12:39.050 But again, there's some great case examples 01:12:39.050 --> 01:12:43.970 that show that if you work against quality loss, 01:12:43.970 --> 01:12:45.680 you can actually end up with much-- 01:12:45.680 --> 01:12:48.890 once you combine together parts into the whole thing, 01:12:48.890 --> 01:12:54.440 you actually end up with a much better overall quality. 01:12:54.440 --> 01:12:57.320 But for the moment, let's just look at the tolerances. 01:12:57.320 --> 01:13:01.430 Process capability in it's simplest form is just this. 01:13:01.430 --> 01:13:03.920 I start with my desired. 01:13:03.920 --> 01:13:06.560 I'd like the part to fall between these two limits. 01:13:06.560 --> 01:13:08.810 Once I say that, it doesn't matter what the target is, 01:13:08.810 --> 01:13:09.020 right? 01:13:09.020 --> 01:13:10.340 It's just between the two limits. 01:13:10.340 --> 01:13:12.132 I'd like it to fall between the two limits. 01:13:14.740 --> 01:13:16.660 There's my process. 01:13:16.660 --> 01:13:17.950 That's the real world. 01:13:17.950 --> 01:13:19.730 How did I do? 01:13:19.730 --> 01:13:23.590 What's the likelihood that the part that I make 01:13:23.590 --> 01:13:26.320 will fall inside those limits? 01:13:26.320 --> 01:13:30.080 That's process capability. 01:13:30.080 --> 01:13:32.480 You can, and their numbers-- 01:13:32.480 --> 01:13:34.070 this is the chart. 01:13:34.070 --> 01:13:35.580 You can look at that and say, OK, 01:13:35.580 --> 01:13:37.370 how likely is it that I make a bad part? 01:13:37.370 --> 01:13:40.280 Well, it's the area of that little space right there. 01:13:40.280 --> 01:13:43.150 The way I've drawn this. 01:13:43.150 --> 01:13:46.703 It's that area right there, and it looks like nil here. 01:13:46.703 --> 01:13:48.370 So I could look at that and say, that's. 01:13:48.370 --> 01:13:51.530 The probability that I make a bad part. 01:13:51.530 --> 01:13:55.370 Again, to try and give us a more common basis for this, 01:13:55.370 --> 01:13:57.180 things like this have been defined. 01:13:57.180 --> 01:13:59.600 The CP parameter. 01:13:59.600 --> 01:14:01.680 Process capability, which basically says, 01:14:01.680 --> 01:14:07.540 what's the ratio of the width of that window to my plus or minus 01:14:07.540 --> 01:14:10.150 3 sigma width? 01:14:10.150 --> 01:14:13.570 So is the variability of my process 01:14:13.570 --> 01:14:19.270 similar to or different from the underlying, the desired? 01:14:19.270 --> 01:14:22.510 But it compares ranges only. 01:14:22.510 --> 01:14:24.430 And if you look at this carefully, 01:14:24.430 --> 01:14:28.570 that could say that I could have the following. 01:14:28.570 --> 01:14:34.880 I could have a process where these are my specification 01:14:34.880 --> 01:14:35.380 limits. 01:14:41.070 --> 01:14:44.220 And here's my distribution. 01:14:46.960 --> 01:14:48.840 It's pretty narrow. 01:14:48.840 --> 01:14:51.120 So the width of this, plus or minus 3 sigma, 01:14:51.120 --> 01:14:54.870 is well within this width. 01:14:54.870 --> 01:14:58.830 So this number would actually be pretty large. 01:14:58.830 --> 01:15:01.530 This window is wide compared to the window of this. 01:15:01.530 --> 01:15:04.600 But how many bad parts do I make? 01:15:04.600 --> 01:15:06.640 They're all bad, right? 01:15:06.640 --> 01:15:10.242 So CP is one way of looking at how well you're 01:15:10.242 --> 01:15:11.200 doing with the process. 01:15:11.200 --> 01:15:13.920 But it's really only looking at variability. 01:15:13.920 --> 01:15:15.490 So we come up with this CPK measure, 01:15:15.490 --> 01:15:17.573 and there are a whole pile of these different ways 01:15:17.573 --> 01:15:18.580 of looking at stuff. 01:15:18.580 --> 01:15:24.700 CPK now penalizes deviations from the mean. 01:15:24.700 --> 01:15:25.270 OK? 01:15:25.270 --> 01:15:30.910 So now, this would have either negative or zero CPK. 01:15:30.910 --> 01:15:33.280 And if you do the calculation, this 01:15:33.280 --> 01:15:38.210 is sort of a blend between how well it's centered in here 01:15:38.210 --> 01:15:39.470 and what the deviation is. 01:15:39.470 --> 01:15:42.230 So if it's perfectly centered, then these two numbers-- 01:15:46.610 --> 01:15:48.770 this is actually-- if it was perfectly centered 01:15:48.770 --> 01:15:56.530 and it exactly fits like this, what's CPK going to be? 01:15:56.530 --> 01:16:00.160 So here's the center specification and here's x-bar. 01:16:00.160 --> 01:16:03.810 This is exactly plus or minus 3 sigma. 01:16:03.810 --> 01:16:06.390 This distance here will be 3 sigma. 01:16:06.390 --> 01:16:12.610 So your process capability, CPK, will be 1. 01:16:12.610 --> 01:16:15.010 So let me just end up with this and just say 01:16:15.010 --> 01:16:17.500 that there are a couple ways you can look at this. 01:16:17.500 --> 01:16:20.380 If I have a process perfectly centered 01:16:20.380 --> 01:16:23.650 and exactly plus or minus 3 sigma limits to my upper 01:16:23.650 --> 01:16:28.480 and lower specification limit, both CP and CPK will be 1. 01:16:28.480 --> 01:16:28.980 OK. 01:16:28.980 --> 01:16:32.610 If that's the case, what's my parts 01:16:32.610 --> 01:16:34.920 per million, which many companies will 01:16:34.920 --> 01:16:36.930 use to measure their quality? 01:16:36.930 --> 01:16:38.775 Once my parts per million bad parts? 01:16:44.760 --> 01:16:46.492 AUDIENCE: [INAUDIBLE] 01:16:48.430 --> 01:16:51.730 PROFESSOR: 3 out of 1,000. 01:16:51.730 --> 01:16:53.170 So it's a lot. 01:16:53.170 --> 01:16:53.950 So yeah. 01:16:53.950 --> 01:17:00.320 So CP of 1's not particularly that good. 01:17:00.320 --> 01:17:03.257 Companies like to have it a lot higher than that. 01:17:03.257 --> 01:17:04.340 Here's an interesting one. 01:17:04.340 --> 01:17:05.840 Look at the difference between this. 01:17:05.840 --> 01:17:06.930 CP is 1. 01:17:06.930 --> 01:17:08.420 CPK is 1. 01:17:08.420 --> 01:17:11.150 CP is still 1 because the width of this distribution 01:17:11.150 --> 01:17:13.610 didn't change. 01:17:13.610 --> 01:17:17.870 But the mindshift shift was such that I actually have-- 01:17:17.870 --> 01:17:22.130 half my parts will now be bad, and that, if you calculate, 01:17:22.130 --> 01:17:25.520 gives you CPK of 0. 01:17:25.520 --> 01:17:27.550 Here's another interesting one. 01:17:27.550 --> 01:17:30.410 CP went up to 2 because I narrowed the distribution, 01:17:30.410 --> 01:17:32.370 but it wasn't centered. 01:17:32.370 --> 01:17:35.490 And so I got a CPK of 1. 01:17:35.490 --> 01:17:37.540 This is really good. 01:17:37.540 --> 01:17:39.160 This is really good. 01:17:39.160 --> 01:17:41.450 This is now plus or minus-- 01:17:41.450 --> 01:17:46.490 can you see that's plus or minus 6 sigma out to here? 01:17:46.490 --> 01:17:48.670 So what's the likelihood of making a bad part now? 01:17:51.570 --> 01:17:54.345 A couple per million, I think. 01:17:54.345 --> 01:17:55.970 this-- I don't have time to go into it, 01:17:55.970 --> 01:17:59.720 but this is sort of the origin of the 6 sigma 01:17:59.720 --> 01:18:01.040 revolution of saying, wow. 01:18:01.040 --> 01:18:04.840 If we could do this, we'd never make a bad part. 01:18:04.840 --> 01:18:06.760 There's a little bit more to that, 01:18:06.760 --> 01:18:10.655 but that's process capability. 01:18:10.655 --> 01:18:12.530 There are all sorts of different forms of it. 01:18:12.530 --> 01:18:14.655 But the last thing-- let me just say one more thing 01:18:14.655 --> 01:18:16.940 about process capability. 01:18:16.940 --> 01:18:20.360 All these things, CP, CPK, six sigma, they're all great. 01:18:20.360 --> 01:18:25.670 Keep in mind that, again, if you can do it, 01:18:25.670 --> 01:18:28.100 if you actually have the data to do it, it's useful to do, 01:18:28.100 --> 01:18:28.880 I think. 01:18:28.880 --> 01:18:35.870 What it really says is here's the design, 01:18:35.870 --> 01:18:41.240 and somewhere here is manufacturing. 01:18:46.260 --> 01:18:49.320 And both of these can change. 01:18:49.320 --> 01:18:49.960 OK? 01:18:49.960 --> 01:18:51.370 Both of these can change. 01:18:51.370 --> 01:18:53.070 I can do better manufacturing. 01:18:53.070 --> 01:18:54.420 I can center it. 01:18:54.420 --> 01:18:56.160 I can do worse manufacturing. 01:18:56.160 --> 01:18:57.330 I can buy new equipment. 01:18:57.330 --> 01:19:00.150 I can change this all the ways we've talked about. 01:19:00.150 --> 01:19:05.110 I can also go back to design or start with design and say, 01:19:05.110 --> 01:19:08.470 you know, this part really isn't that important. 01:19:08.470 --> 01:19:11.200 This window can actually be here. 01:19:11.200 --> 01:19:12.710 And if I move the window out there, 01:19:12.710 --> 01:19:15.800 look at how the process capability just changed. 01:19:15.800 --> 01:19:17.690 In case 1, the process capability 01:19:17.690 --> 01:19:20.300 of this distribution against this design is terrible. 01:19:20.300 --> 01:19:23.000 The CPK is almost 0. 01:19:23.000 --> 01:19:29.150 Now, if I opened up the window, CPK now skyrockets. 01:19:29.150 --> 01:19:31.250 I'm great. 01:19:31.250 --> 01:19:36.050 The trend usually is just the opposite, though. 01:19:36.050 --> 01:19:39.320 And this is certainly true in semiconductor manufacturing is 01:19:39.320 --> 01:19:42.140 you might say, here's the inherent underlying capability 01:19:42.140 --> 01:19:45.080 of many of the processes that we've had historically. 01:19:45.080 --> 01:19:50.420 Here were the design specifications back in 1980. 01:19:50.420 --> 01:19:52.860 Line width or something like this. 01:19:52.860 --> 01:19:54.210 Characteristic to mention. 01:19:54.210 --> 01:19:57.730 Here they are now. 01:19:57.730 --> 01:20:00.430 Oops. 01:20:00.430 --> 01:20:03.295 Can't make this product with this process. 01:20:06.530 --> 01:20:08.510 And it was all because-- so you can 01:20:08.510 --> 01:20:10.970 look at how I have to improve my process capability. 01:20:10.970 --> 01:20:13.280 And it's interesting to talk to people who've 01:20:13.280 --> 01:20:16.100 been in the semiconductor industry their whole lives, 01:20:16.100 --> 01:20:18.200 and they'll tell you this exact story 01:20:18.200 --> 01:20:21.260 that, well, we didn't worry about this back when 01:20:21.260 --> 01:20:24.065 the specifications for this wide. 01:20:24.065 --> 01:20:26.190 But all of a sudden, it became much more important, 01:20:26.190 --> 01:20:29.950 so we had to do a lot of things, including not just SPC, 01:20:29.950 --> 01:20:31.910 but some extraordinary things. 01:20:31.910 --> 01:20:32.410 OK. 01:20:32.410 --> 01:20:33.340 Thanks for your patience. 01:20:33.340 --> 01:20:35.290 I ran over, but it was a technical difficulty 01:20:35.290 --> 01:20:36.070 at the beginning. 01:20:36.070 --> 01:20:36.880 OK. 01:20:36.880 --> 01:20:38.620 Bye bye.