Response Surface Method

[Music] welcome to complexity made simple my name is Paul Alec the subject of today's video newsletter well I've had a request from a viewer who like me to cover response surface methodology so so do a technique it's often known as RSM response surface RSM and it is a subject that it's still referred to today it's still used today but this is quite an this is quite an old-fashioned technique and we're going to talk about why it was why it was developed when it was developed and essentially how it was used back in the 1950s 1960s especially and why actually a lot of the methodology today isn't really needed that's partly because today we have computers to do what RSM was designed to do okay so let's talk about what we what our response surfaces in your DOA normally when we think about understanding a process let's say we're gonna we're going to understand what time does to a process we're gonna go from 10 seconds up to a hundred seconds we're gonna see what the effect is on the let's say it's the strength of let's take the spent on a molded part and this is cooling time we could but so what wheeler cause do is we would test in different places and we would get this response now this diagram this diagram is 2-dimensional it's just a flat it's just a flat picture and of course is very easy to understand you know I could almost buy I say well if I set the result to 50 you could almost read that off just by using the diagram it's very it's very easy to understand you don't really need any mathematics you know you're gonna have some simple y equals MX plus C equation that represents that a straight line is very simple to understand but even so the diagram is very useful the diagram is very useful and the response surface using essentially the same thing except it's not two-dimensional it's three-dimensional because if you if you were to understand now if I were to test time in this direction there's the response going in that direction time in that direction but we've also got temperature in this direction so imagine now this line starts to go backwards so instead of it being a flat a flat line it's now a plane it's going to look like this so if you imagine if you imagine this is the straight line obviously I'm looking straight at it but if I just if I just tilt my head I can now see this effect going in this direction which is caused by the temperature now this plane is known as the response surface and it's really difficult to draw these things in three dimensions I can't really do it I'm just going to kind of draw something very simple you would get a three-dimensional response surface and the reason why these response surface is unneeded of course is when we start talking in two dimensions or three dimensions or indeed these these surfaces are twisted in shape so they are curves in shape and things like that it becomes almost impossible to understand what the hell's going on and we and as I said earlier these were invented George Parkes is credited with inventing response surface methodology and he invented it in the 1950s and the 1960s in the chemical industry why did he do it he didn't have a computer to understand his process so he needed some simple pictures to help you so he invented this technique called a response surface methodology now I'm going to show you a computer-generated one of these this this diagram here look this is an interaction plot exactly what you're seeing for time and temperature here it's an interaction plot and you can see that the the surface is twisted in nature it's not it's not a straight plane like I showed you with that that white sheet of paper just it's a it's twisted and it's showing you an interaction plot and if I show you the two-dimensional interaction plot so here's the two-dimensional interaction plot and if I indicate look this line on the interaction plot is the front edge of this response surface so this line here in red represents this line here in red if I go back to my interaction plot the two-dimensional version this straight line that's now been highlighted in black is this line on the response surface also being highlighted in black and of course you can see that we're looking at the three-dimensional version of that and those two lines are opposing one another so the plane twists in space and that's known as a that's known as a surface plot a three-dimensional thing that you're looking at there the idea of response sir his methodology is known as I surf his plot so these pictures were drawn to be able to understand where the top of the curve was so why did why did box do this number one he wanted to understand how to optimize the process model in other words he wanted to know where the peak of that curve would sit and just by looking at the maths it wasn't obvious where the peak might be especially with the interactions in a model and this was very difficult to do in your head it was very difficult to do mathematically but if you look at the diagram and you want to go to the highest point on this surface for example and often curves were part of the problem in Gorge boxes processes so this curved shape box wants to know how to get to the peak of that curve shape and the best way to do it is to draw the picture and he can see where the settings would be so if I if I follow the scales down this diagram for example it would tell me to set one variable to this point and it would tell me to set one variable to this point and he can see we know computer how to optimize his process that's reason one why we draw these things reason two though is to find a sweet spot for multiple responses so again today the computer does this so one of the reasons why we don't need this much today the computer will find an optimized spot today so I can just say to the computer please take me to the highest place in this model and he will do that also the computer if you have mini tab for example Minitab will do this if you ask you to hit two targets at the same time it'll tell you where the sweet spot is or it will tell you the sweet spot do exist well the technique for hitting the sweet spot was to use a response surface now it wasn't used the three-dimensional diagram that we've just looked at they were gone and look at something called a contour plot so the contour plot let's imagine here we're playing with this this molding process again time and temperature we want to get the strength correct but we'd also like to get the white correct so we want to make the molding as light as possible we'd like to make the molding as strong as possible so we would draw one of these diagrams which would show us the weight we would also draw a diagram then that would show us the strength so we would draw two diagrams the diagram we would use though he's known as a contour plot a contour plot how the contour plot is flat and he's got contour lines on it just like a map so you would draw a contour plot you would have time and temperature on this contour plot this would be the strength contour plot you would have time and temperature on this contour map something slightly different so it makes a bit more sense so they draw something that looks okay so this contour plot wouldn't be showing strength this would be showing the weight and we would have a target strength which could be in this region here so the center of that region would be the absolute nominal that we're trying to hit the size of the box might be the tolerances that we're able to be in and then for the weight same thing we might have a target and we might have a tolerance what they would do is they'd pick this up and they put them over the top and they would look for the point where these two regions will lap one another so maybe if I impose the white box on here and there is the point where they overlap that's the sweet spot when I can get closest to the strength and closest to the weight and so they used to draw these on an acetate they would do it by hand they would draw a contour plot you can see the contour plot here the computer is drawn in the contour plot for me today so here's the contour plot of this three dimensional space you can see the contour lines there to represent the shape of the hillside just like looking at an Ordnance Survey map what we do is we lay those two contour plots over the top of one another we look for the sweetspot region and that is the point where we can hit both targets at the same time now this technique and this technique today we now need them the computer does the work for us so the computer will tell me whether whether the peak of this curve is so this diagram here look although I can see it on the the surface plot and I can see the hillside and the top of the hillside and where the two settings would be actually I can also just go to the software and say take me to the maximum and he will do that the same with this problem here of looking for the sweet spot I can ask the optimizer to hit the two targets and it will tell me whether that's possible or not so this technique in response service methodology it isn't really needed anymore because today the software does the work the one thing that I do use the response surface for he's on the interaction plots the interaction plots tell me where the flat spot is now software typically won't do this but what I'm looking for let me just show you just get some space here when you get curvature I'm gonna draw it just as though a two-dimensional diagram for a second again let's say that this is time this is strength yeah look this region here I can move time backwards and forwards what happens to my response well it moves almost imperceptibly that is a region of robustness so these areas of the flat spot it doesn't always have to be the maximum or the minimum by the way in twisted Plains sometimes the flat spot is in the middle in terms of the highest response value and the lowest response value the robust region is actually in the middle but what we're looking for is when these surfaces when these surfaces go flat they are regions of robustness so I could set my time here my tolerance could be nice and white and I would get an impossible effect here on my my output of interest however look if I take that same tolerance and I drop it here and I'd said time there well now look if I allowed time to move backwards and forwards Wow the same tolerance battalion the same tolerance pertain here it has no effect here it has a massive effect now the software can't do it but the response surfaces can show you when the when the sign of the response starts that go upwards and gets steep the incline gets very steep that is a region of sensitivity keep away from it where the surface goes flat that is a region of robustness use that set your tolerances around that set your settings around that if you can okay so that is what you would use response surface methodology for today you wouldn't use it for these two things because the software will do the work now one final thing response surface methodology has become associated with particular types of do E's so often in Minitab for instance the central compositor so the central composite design central composite often also called the CCD central composite design can only be found on Minitab on the response surface menu so this DOA was generated to generate these diagrams it's effectively there to spot curvature the central composite design is there to see curvature so if you think you have curvature in your responses forget the response of his methodology necessarily you need the CCD just to capture the curvature in your models then you can find flat spots by looking at the diagrams you don't have to do this anymore because the software will find the optimised regions but that's we use response service methodology it was invented in the 1950s by a wonderful British mathematician called George box in his day it was absolutely vital that he had these tools you need to optimize and understand complex systems today we use software to do the same thing we've got fine robust areas that's the use of response service methodology today well if you use response services if you find regions of robustness like this your tolerances will be wider you'll please the customer in a much cheaper and easy to achieve way basically you'll make more money response surface methodology [Music]

Channel: Paul Allen

Views: 12,958

Rating: 4.8762889 out of 5

Keywords: RSM, George Box, Response Surface Methodology, Central Composite Design, CCD, Full Factorials, Axial points, Juran, Deming, Shewhart, Taguchi, L12, L18, Kevin Dunn, https://www.youtube.com/watch?v=id71dS8b8EA, nptelhrd, https://www.youtube.com/watch?v=sIRl1xWrViY, Design of Experiments, Gemba Academy, SPC, MSA, Dr. Bharatendra Rai, https://www.youtube.com/watch?v=vSFo1MwLoxU

Id: LBVPxeqirpE

Length: 18min 15sec (1095 seconds)

Published: Tue Apr 21 2020