Minitab factorial plots - A DOE Tutorial

[Music] welcome to complexity made simple my name is Paul Allen and the subject of today's video newsletter well we are going to take a look at Minitab again today and I'm going to request specifically to do a DOA analysis to do some factorial plots and to do an interaction plot as well so we're going to do some analysis on some data that someone's sent to me and I'm going to just demonstrate where to get these where to get these plots from so that's that that's the story of today's newsletter before we start because we're covering do-e today my new book design of experiments for 21st century engineers great practical text really simple keep the mathematics light keep the money-making procedures to the max design of experiments for 21st century engineers just published you can get it from lulu.com so please go on please go on by that text straight after this video so let's let's all look we're gonna do do e we're gonna use be neater let's be clear it's a two to the three full factorial I'm going to create a regression model I'm gonna create a factorial plot interaction plot and a surface pot okay so simple software tutorial covering off those do-e points let's get into this let's get into this example right now okay here's the here's the dataset that we go into that we're going to analyze as I mentioned earlier it's a two to the three full factorial you could see currently I've got this set in Excel and the reason for that is because I like to see it as a table and this would be the normal way I would analyze it so we'd normally use some Excel based software but I'm going to show you Minitab today but I just want to show you just practical let's keep this practical a lot of DEA and things like that it's very statistical that the mathematicians and the statisticians want to teach you all the numbers and the r-squared values and things like that but one of the things I like to do is to keep this very very practical and having the data in a table like this is part of it being very practical and so you can think sensibly about what's going on so the the actual do a itself course is in this array here on the left hand side my data is in the yellow fields and you could see four columns of data which means that what I did was I collected four data points for each setup so if I look across the row here setup number one I collected eight nine point two fourteen point two and ten point six as the four results and as I said this is a good way to look at the data Minitab is going to put this data in a different orientation but I want to see it as a table before I let Minitab half of the data so let me just show you what I'm doing with this data before we start and then I'll tell you what Minitab is going to do when we set that up so the reason why I want to do is because I want to look across the row of the four data points and I want to look at them all together now if you look at the four on the first row I do have a concern you've got eight you've got nine point two you've got ten point six but then you got fourteen point two there now that's a strange data point I'm not particularly happy with that but by the way this isn't the worst data that's on this page just look the next one down 26:33 28 on the far side but then in mixed in with them is 40 which is well away from the other results now this is a sign maybe things were going wrong in the do a maybe I've got measurement system problems so this is a little bit of a red flag to me when I get spurious data points by the way this could be something simple like a typographical error so you might have typed in 40 when you meant to type in 34 and so that's the other reason why you want to see these data points you're just simply checking for simple errors like have I have I typed all the right numbers in as well so I like to look across the row to see if there's any any nonsense in there the other thing I like to do is I want to check that the process got moved around remember the variables that you chose over here should have been variables that with your your engineering knowledge with your knowledge of the physics these variables do something to the process they move the process around now one of the key points about the DOA is that these values should be a little bit extreme so you can see on the infill look the person has given me this dataset they've gone from 5 to 100 that's a nice extreme setting now think about it if you're moving these important variables to extreme places then what you should see across the data table these lots of different results so for instance look on row one whit as low as 10 but the next row down we're up at 32 then we go to 15 then we go to 44 30 point 9 25 16 42 now that's a nice data set what it's telling me is the process got moved around by the three variables on the left-hand side and that's also a good thing to see so we want to do before we start doing any statistical analysis and and you could do some statistical analysis to get the same information that I've just done by eye but use your common sense first get attached to the dataset don't just let the maths run away with the the analysis without you thinking clearly about what you're doing now let's talk about what Minitab is going to do with this data because it isn't going to put it in a table like that so let me draw you a diagram and what Minitab is going to do for you so what Minitab is going to do you're going to have the this is what I've got currently I've got the array and of course I've got these four columns which are the replicants for replicants across the row now by the way if you happen to do use the Taguchi do he's of course in Minitab this is exactly the way Minitab will present the data to you but if you happen to choose classical's if you go to the factorial menu which is we're going to use today what he's going to do is this look when you tell it how many replicates you have it will repeat the array four times down the spreadsheet down the worksheet and then against the second repetition of the array comes data set two then it'll put replicate three in there and finally of course and I'll put replicate four in there so what you end up with is all the data in one column so you can't do what I just said which is look across the row and look for signals for each setup because the arrays at all are all mixed up on there on the column and this would be even more true if you decided to randomize all of this which is the other choice in Minitab I'm not going to randomize today but that's how Minitab is going to set the the donor up and then we're going to analyze we're going to analyze the data from from there so let's put this information into Minitab and and then let's let's generate a model and let's do the interaction graphs let's do the surface plot and we can show you where to find those and how to do them okay so here we are in Minitab now and the first thing we want to do is to set the do a pattern up it's full factorial so we're gonna go stat do a factorial create factorial design and you can see they're like two level factorial and number of factors where we've got three factors it then says designs so let me take a look at the one I've got a half fraction or a full factorial the half fraction resolution three it is a do e I would never ever use it is not necessary to do things like that today way too risky lots of alias in that you really don't want so I'm gonna pick the full factorial I'm just doing a straight to level do each I'm now sent two points are needed number of replicates so of course it was for I'm gonna need leave the blocks at one I'm gonna click OK now the other menu items appear so let's take you through them I'm gonna look at the options first and the key point about the options I'm gonna switch off the randomization just to make it a little bit more easier to see what's going on then what I'm going to do I've got to tell it the factor names and I've got to tell you the levels so the first one that we're going to do and I put the nozzle in its numeric so this is nozzle diameter not 0.2 to one millimeter then we're going to do orientation again it's numeric noir degrees to 90 degrees then we're going to do infill and infill is 5 to 100 now just before I click off this the more eager lined amongst you will notice that I've put these three variables in in the opposite order to what they would in my Excel spreadsheet and that's because the pattern as it comes up in my software is the other way around the columns are in the reverse order so I've put these in reverse order so that all the data will make sense when we paste into the worksheet so click ok to that now and so I put the factors in let's take a look at the results it's just giving me some options there's some things I might want I don't I don't change any of those things I don't use this particular menu at all so click OK and then we can click OK and it will give us the pattern let's show you it's telling you look all terms of free from aliasing well you would expect that because this is a full factorial so now you can see here's the pattern and it's been multiplied and say look 32 rows it's been multiplied 4 times down the table so now what I have to do is to paste the results into I'm going to paste them into c9 I'm just gonna call them y1 in this case so I'm just going to take them out of Excel and wanted to tell you I can just paste the columns below one another like that so you'll see me finish that off now and then we'll do the analysis so that date is typed in now so it's in this column format as I as I mentioned to you earlier and now what we're going to do is now we're going to do some analysis so let's go out the DL we and let's do some analysis on this so factorial and now you can see that some of the other menu items are alive you can see that the way Minitab works things like factorial plots I can't do a factorial plot effectively until I've done a model so I'm gonna have to do some mathematical analysis on this so I'm gonna have to go analyze factorial design I obviously need to tell it that the response is in y1 and then we can go take a look at what we do in here so here are the terms that I can analyze so because it's a full factorial I've got the main effects all the two ways under the three way I'm going to leave that as it is because I want to do a full analysis now let's go across this there's some certain things here that I don't use the covariates I don't use let's look at the options transforming the data don't want to do that that's fine the graphs well the purrito of the effects is a useful little chart that's the only that's the only thing I'm going to ask you to really do I'm not going to change anything there on the results you want the results I'm going to turn most of this off so it's an everything off except the coefficients now what that's going to do basically is just show me a regression equation now you'll notice I didn't switch the regression equation on there's a very strange thing in Minitab it builds a bit of a weird regression equation that's not very easy to read whereas the coefficients table it's very easy to read you can see the model from the coefficients table so that's the only thing I asked for in the results feature don't do an over again the certain things you could do is this is kind of an analysis which is for the people with much more deeper understanding analyzing the residuals looking for leverage no leverage by the way is based on that thing I was looking at earlier so practically I was looking at outlying data points but you can do a mathematical calculation for leverage you can also do something called cooks distance cooks D that also looks at leverage and so those two analyses could do a mathematical version of using your common sense but initially I like to use me common sense I'm not gonna switch any of those on because it's kind of a little advanced things I'm gonna leave that and now we're just going to click okay and if I just get the data out of the way okay now here is now the coefficient column that's the model so that's the regression model so this particular dataset another way I haven't told you what the process is this is a client's data set so I'm not being too specific about what the process is and what we're trying to achieve but the the targets in the coefficient look the targets can be hit by the equation that says twenty four point nine plus ten point nine nozzle plus four point five orientation minus point six infill etc so you can just read the equation off the column there now obviously we've got P values that allows us to model build and really infill should be taken out of the model infill orientation two way should go out of the model so those two terms should go out of the model so should nozzle an orientation so using the P values I would normally reduce the model down to remove terms that really shouldn't be there and let's take a look at the Purita below so the Pareto look is showing us the important terms so the things that I just said to take out the three way being fill and the the be seen are action they should be removed because that below that red line you see that two point zero six that value there that that value is there helping you to decide what terms should be removed from the model what term should stay in the model so terms they should stay in the model or the a the B the a B interaction and the AC so that's that perrito is quite a nice little [Music] tool to use again use common sense you can easily see that I the nozzle diameter is having the biggest effect on this particular process and if you look at the standardized effect down here on the scale it's moving the process by twenty odd units units whatever you were moving the process in by the way so if you look at that if you look at the coefficient look ten point nine that is whatever units you were measuring so if you were measuring millimeter so you're trying to hit a millimeter target then this particular variable nozzle diameter is moving the results not just by ten point nine millimeters but by twice ten point nine millimeters that's why the burrito is up at twenty odd because two to ten point nine and up to twenty one point something 21.8 you can say look it's in the effect here actually there's the value there look so there's the model and you can reduce the model down but the reason I wanted to do this little example was to show you the plots so let me go stat do e factorial now you can see look the factorial plots are available now that we created a now that we've created a model so let me go click on that menu item there mm-hmm and it says well okay what factorial plots would you like so normally you'd want all three of the main effects and at the moment look it says terms to display only the model terms and you could ask for all terms well at the moment that is the same thing as I'm taking any terms out of the model I'm removed anything into the model yet so of course if I ask for this it's going to give me all the main effects and it's going to give me all the to Wayne or action graphs as well I think but I have to go and ask for them it's gonna have a look at the graphs and he says what would you like main effects plot interaction plot so I could switch the interaction plots off if I didn't want to see this if it was a slightly bigger do-e where there's lots and lots of interaction plots I might switch this off and then just ask for one or two interaction plots specifically later but I'm going to ask for everything because it's just a two to the three full factorial there's not too many diagrams in this case so I click OK click OK again and now look what do I get well I get some pop that it main effects plot there it is so again look it's telling me the longest line on this diagram is the most important variable you can see the nozzle diameter which we've already talked about is moving the result over 20 units and you can see look if we look at the data point down at the bottom which is a point at it give me a value zero fourteen point fourteen point out one all the way up to thirty five point eight it's out you know it's over twenty points that it's getting moved around the longer the line the more influential the variable is so that's the main Affleck effects plot below that I'm gonna get the interaction plots so you can see the three the three interaction plots the nozzle and the orientation probably is the one that's are more interested in this is the BC interaction which is also a term that would remain in the model so the BC interaction is definitely happening you can see the interaction plot there which is super useful again if you click on this it'll pop it out can you make it fullscreen I think you can yeah so it's a lot easier to take a look at there now I'm also to look at the three-dimensional version of that two-way interaction nozzle orientation so I'm gonna get it to draw me the surface plot so if I go back do a factorial now the surface plot is a separate request here look so surface plot okay so nozzle orientation now that's the way the interaction plot is drawn up in that top left-hand corner nozzle orientation so I'm gonna leave it as not I could put it the other way around by the way I could put it orientation nozzle and it will give me a give me a different looking picture you know it's some that the diagrams not shown here but it's a different way of looking at the data set even though the interaction is the same so just a tip for you go and have a look at these diagrams play around put orientation in the first one and nozzle in the second one see how it changes the picture of the data that you're getting so let's just have a look what the the menu items do for us the first one now this is quite a useful one because obviously you're plotting two variables out there the three and the infill has got to be somewhere now in this case the infill is being left at the midpoint but you could put the in filter 100 you could put the infield amplify even put the infill at any level you wish to do now we'll talk about that in a second but I think the first thing you'd want to do is just leave the infill where it is at the midpoint and then we'll take a look at the diagram and we'll talk about how you can change the infill and what it will do to the diagram that we've created options well that's just a title I'm not going to give it a title in this case and I'm not going to look at the I don't need to look at the model so just gonna click OK so there we go now what what this is this is a three-dimensional diagram of that interaction plot so okay I've taken the diagram out and I've put it into PowerPoint and that just allows me to make a sketch so if you looked at the the interaction plot the interaction plot sort of looks something like this didn't it okay so that diagram this one over here on the left that's a three-dimensional version of that interaction plot so one of those lines so number one will be the slightly flatter slope this edge here the second light line two is the back edge this is the one that's slightly more upright but now what you can see is the complete plane of all the results you could get for moving orientation and nozzle diameter now this technique was invented by George box back in there back in the 1950s and one of the reasons he did this was to to assume that this this diagram is actually part of a hill so if you imagine a hill maybe maybe doing this and what you're trying to do is to get to the top of the hill maybe you're your ultimate achievement is to try and find the maximum point in your system and at this point you've done an initial test in an initial design space so you've gone from here to here so you've gone from on the nozzle diameter point to to one millimeter and you've gone on the orientation you've gone naught to 90 degrees and that was your initial thought somewhere you'd like to gather information but of course you didn't know what you were going to when you've gathered this information well now what this is telling you look look at this picture it's saying if you want to go higher that's the direction you need to travel in in other words you need to get the orientation above 90 degrees and you need to get the nozzle diameter above 1 millimeter now this is the easiest way to see this piece of information you can use models the model if you look at it and you kind of understand it a little bit you can use the model to try and understand this but this is the best way to see where the next deal we might take place so what you might do now is do a designed experiment over in hover in this region and see if you capture that see if you capture that maximum so if you capture that maximum point so it's the idea of being able to visualize your your route up the mountain or even take down the mountain if you're looking for the minimum if you're looking for the minimum value so that's what these surface plots are for and today they are still really useful for this type of thing in the days when they were trying to optimize they were trying to find an optimum point they would also find these techniques very useful when they were trying to do manual calculations today we don't need to use them for this technique because today the software will find an optimized point for you so we use software today where we'd use diagrams back in the 50s and the 60s but the idea of where's the next deal we got to be where is my next area of interest is one of the great uses for the surface plots now I mentioned earlier that we'd we'd fix the infill to 52.5 and I said well we might change that later now you'll notice look this is almost like sitting in a this is like a lift shaft almost think of it like a lift shaft if I change that 52.5 what would I have done well there's a good chance that this plane would move up the lift shaft or if I wound the infill in the right direction this lift shaft this plane would move down the lift shaft so there might be a higher value but 50-odd maybe I don't know where it might go if you move the infill but that's why I've said the first thing you want to do is just leave the infill at the midpoint and maybe you can come back and adjust it later if you want to move this plane up and down in the column where it's sitting but take your time with these things if you move too many things too much you sort of lose the plot of what's happening I usually start very simple I take the midpoint I have a look at what the interaction is telling me I have a look of maybe whether it's telling me there's a new region to test etc there might also be robust settings robust settings is when these diagrams go flat so in the diagram the line goes flat here like this this would be known as a robust robust setting so these diagrams can be really useful but there's the there's the surface plot if we go back to Minitab there's the interaction plot and of course above the interaction plot was the factorial plots which is a pictorial representation of what you're seen in the model effectively so there's the latest Minitab tutorial obviously I'd be creating a better model and be taking terms out of the model etc but I like to just show you these tech takes a piece of the time because often if you learn the full process of correcting the DLA doing the DLA reducing the model creating the diagrams using the diagrams finding robot settings etc etc etc it could be a one hour one hour 20 video you're probably not gonna watch it and even if you do watch it you're probably not going to remember it so I like to do pieces that's the main effects plot the factorial interaction plots and the surface plot using Minitab okay well I hope you enjoyed that little Minitab tutorial if you've got any comments any questions please leave the comments below remember design of experiments for 21st century engineers keeps it really simple and practical and get you into one of the best money making tools you can ever use in any engineering situation so there's your software of choice there Minitab there's the book that helps you with other parts of the subject as well I would love for you to get into day away because it really is a money-making monster you [Music]

Channel: Paul Allen

Views: 5,187

Keywords: Minitab, SPC XL, DOE Pro, Six Sigma, DOE, Shewhart, Juran, Taguchi, L12, Full factorial, SPC, MSA, FMEA, Gemba academy, RA Fisher, Half fraction, Interaction plots, Surface plots

Id: 0EdR119g6XI

Length: 33min 57sec (2037 seconds)

Published: Wed Jun 10 2020