1 00:00:02,750 --> 00:00:06,570 In this section, we start looking outside our cube plot. 2 00:00:06,570 --> 00:00:11,110 What happens when we leave that range from minus one to plus one that we've been so 3 00:00:11,110 --> 00:00:11,690 focused on? 4 00:00:13,070 --> 00:00:17,420 We're going to add a new tool to our toolkit that we used to analyze the data. 5 00:00:17,420 --> 00:00:19,709 The concept called Response Surface Methods (RSM). 6 00:00:20,820 --> 00:00:25,630 Now, in the next video, we will consider in depth the case of a single factor. 7 00:00:25,630 --> 00:00:30,080 Most practical systems, though, have two or more factors that affect the outcome. 8 00:00:30,080 --> 00:00:31,510 But if you understand the idea for 9 00:00:31,510 --> 00:00:34,920 one factor, then the subsequent videos will make more sense. 10 00:00:36,110 --> 00:00:39,200 I'll explain what Response Surface Methods are in this video and 11 00:00:39,200 --> 00:00:41,070 why you would want to use them. 12 00:00:41,070 --> 00:00:43,711 And in the remainder of the videos, we'll see them in action. 13 00:00:45,832 --> 00:00:49,752 When I use data to improve a process or a system, in my experience, 14 00:00:49,752 --> 00:00:54,240 I find that I'm inevitably trying to achieve one of these five objectives. 15 00:00:55,320 --> 00:00:58,390 Trying to learn more or increase my knowledge of the system. 16 00:00:58,390 --> 00:01:00,820 Maybe I'm troubleshooting the process. 17 00:01:00,820 --> 00:01:04,170 Or perhaps, I'm using the data to make some form of prediction. 18 00:01:04,170 --> 00:01:07,170 Or maybe I'm trying to optimize the system in some way. 19 00:01:07,170 --> 00:01:11,790 Or finally, I might just be monitoring the process based on the data to make sure 20 00:01:11,790 --> 00:01:15,570 that I'm retaining all those performance gains I've made in the past. 21 00:01:15,570 --> 00:01:19,960 Those of you taking the course and working in a company, you will find that any 22 00:01:19,960 --> 00:01:24,630 project or task you do likely falls into one of these five categories. 23 00:01:24,630 --> 00:01:28,040 Think back about the past few projects you've been working on. 24 00:01:28,040 --> 00:01:31,830 The biggest problem I often encounter is that people don't have 25 00:01:31,830 --> 00:01:34,130 their objectives clearly in mind. 26 00:01:34,130 --> 00:01:38,050 Once you've figured out your objective, picking the simplest approach, and 27 00:01:38,050 --> 00:01:41,740 using the appropriate tools to solve that problem becomes apparent. 28 00:01:42,740 --> 00:01:44,600 In the prior four modules of this course, 29 00:01:44,600 --> 00:01:48,390 we have focused really only on the first three objectives listed there. 30 00:01:48,390 --> 00:01:50,700 We've hinted a little bit at that fourth one, 31 00:01:50,700 --> 00:01:53,640 trying to optimize the process in some way. 32 00:01:53,640 --> 00:01:56,790 For that first objective, we've seen how we can learn 33 00:01:56,790 --> 00:02:00,650 which factors are important and illuminate which are not. 34 00:02:00,650 --> 00:02:03,690 This improves our overall understanding of the system. 35 00:02:03,690 --> 00:02:05,130 To quote George Box: 36 00:02:05,130 --> 00:02:09,750 "discovering the unexpected is more important than confirming the unknown". 37 00:02:09,750 --> 00:02:13,720 Really think about your experimental results and interpret them every time. 38 00:02:14,890 --> 00:02:19,440 The concepts learnt in this course can also be used to troubleshoot a problem. 39 00:02:19,440 --> 00:02:23,720 If your boss comes to you with a problem, you can brainstorm a list of five, six, or 40 00:02:23,720 --> 00:02:26,740 more factors that are potentially the cause. 41 00:02:26,740 --> 00:02:29,820 Use fractional factorial ideas from module four, and 42 00:02:29,820 --> 00:02:34,550 you can quickly identify which factors are actually related to the issue. 43 00:02:34,550 --> 00:02:37,970 And right since video 2A, we've been making predictions based on 44 00:02:37,970 --> 00:02:41,110 our experimental results, so you're very comfortable with that idea. 45 00:02:42,360 --> 00:02:46,340 In this section, we're going to be optimizing our process. 46 00:02:46,340 --> 00:02:50,170 Let's go back to a familiar process, making popcorn. 47 00:02:50,170 --> 00:02:54,550 And it was perfect timing, that there was a great forum posting about that. 48 00:02:54,550 --> 00:02:57,240 It seems many of you love this snack. 49 00:02:57,240 --> 00:03:00,060 Let's say you were simply investigating two factors. 50 00:03:00,060 --> 00:03:04,370 Cooking time as factor A, and the type of oil as factor B. 51 00:03:04,370 --> 00:03:09,280 And I'm going to use the number of unburned popcorn as the outcome variable. 52 00:03:09,280 --> 00:03:11,230 You'll see why I chose this. 53 00:03:11,230 --> 00:03:17,580 Unburned popcorn are those that have popped but not burned, the white popcorn. 54 00:03:17,580 --> 00:03:22,560 We want to maximize this outcome variable, that's the objective of my experiments. 55 00:03:22,560 --> 00:03:24,050 And here are the results on a cube plot. 56 00:03:25,340 --> 00:03:28,790 You're experts at this now, so you can quickly see that factor B, 57 00:03:28,790 --> 00:03:32,580 the type of oil, has almost no effect on the outcome. 58 00:03:32,580 --> 00:03:34,860 Notice that the first objective was used here. 59 00:03:35,860 --> 00:03:40,340 We have learned in our system that the type of oil over this range of 60 00:03:40,340 --> 00:03:44,060 cooking times seems to have little impact on the outcome. 61 00:03:44,060 --> 00:03:46,560 We've learned something new about our process. 62 00:03:46,560 --> 00:03:49,910 It doesn't mean that oil type is totally irrelevant. 63 00:03:49,910 --> 00:03:54,050 It simply says that over the range of A that we've used here, 64 00:03:54,050 --> 00:03:55,940 cooking time seems to have little effect. 65 00:03:56,960 --> 00:03:59,680 Visually, this means we can collapse our square down to 66 00:03:59,680 --> 00:04:01,280 a single line as shown here. 67 00:04:02,360 --> 00:04:07,110 Let's go apply objective three now and build a predictive model for the system. 68 00:04:07,110 --> 00:04:10,500 Y = 90 + 15 x_A 69 00:04:10,500 --> 00:04:12,860 Note that we don't have to include factor B or 70 00:04:12,860 --> 00:04:17,880 the AB interaction in our model because we've determined that B is not useful. 71 00:04:17,880 --> 00:04:18,950 Here is the R code. 72 00:04:19,960 --> 00:04:23,740 And you will get the exact same result with any statistical software. 73 00:04:23,740 --> 00:04:29,420 Just a brief recap on the interpretation of the 15 x_A term in the model. 74 00:04:29,420 --> 00:04:33,700 That says, when we increase the cooking time from -1 to 0, or 75 00:04:33,700 --> 00:04:39,110 from 0 to +1 in coded units, in other words, a one unit increase, then 76 00:04:39,110 --> 00:04:45,260 the number of popped but unburned popcorn increases on average by a value of 15. 77 00:04:45,260 --> 00:04:49,720 Now response surface methods, or response surface optimization, 78 00:04:49,720 --> 00:04:54,340 uses the idea that this model can tell us where to move to next. 79 00:04:54,340 --> 00:04:57,650 We're going to build on our existing experiments over here 80 00:04:57,650 --> 00:05:00,340 to figure out what happens over there. 81 00:05:00,340 --> 00:05:04,560 We've figured out already that factor B does not play an important role in 82 00:05:04,560 --> 00:05:05,580 this system. 83 00:05:05,580 --> 00:05:09,010 So response surface methods are used after you've already completed your 84 00:05:09,010 --> 00:05:10,880 screening experiments. 85 00:05:10,880 --> 00:05:12,370 That's an important point. 86 00:05:12,370 --> 00:05:15,990 Don't include factors in the optimization that have little or 87 00:05:15,990 --> 00:05:17,800 no effect on the outcome. 88 00:05:17,800 --> 00:05:21,250 Then once we build a model based on they important factors, 89 00:05:21,250 --> 00:05:25,270 we can now go use it to tell us where to move to next. 90 00:05:25,270 --> 00:05:28,600 We can see here that we should be moving towards the right, 91 00:05:28,600 --> 00:05:29,950 to increase out objective. 92 00:05:31,040 --> 00:05:34,320 Now we can never expect the model to tell us exactly or 93 00:05:34,320 --> 00:05:39,170 perfectly what will happen over there on the right as we move towards that region. 94 00:05:39,170 --> 00:05:44,000 There is no way that this simple model summarizes all the laws of physics, 95 00:05:44,000 --> 00:05:45,280 heat transfer, and 96 00:05:45,280 --> 00:05:49,950 the complex chemical reactions taking place when popcorn is popping. 97 00:05:49,950 --> 00:05:54,530 This simple model, also referred to by the name of an "empirical model", 98 00:05:54,530 --> 00:05:59,940 is a great approximation, and provides good guidance on where to move to next. 99 00:05:59,940 --> 00:06:03,660 That is what response surface methods (RSM) are about, in a nutshell. 100 00:06:03,660 --> 00:06:08,010 Efficient sequential experiments to reach an optimum, using only 101 00:06:08,010 --> 00:06:11,710 the important factors after you've done a preliminary screening design.