How to look for optimum mean with low variation from DOEHi All,
May i know what is the method that we can do in order to find the optimum mean from our DOE which has the lowest possible variation?
Rgrds
Irfan
Re: How to look for optimum mean with low variation from DOEI no longer have JMP 5 installed on my computer so I cannot run through an example in parallel with you. I will do my best to answer your question in spite of that deficiency.
So it looks like you found the Loglinear Variance personality in the drop-down menu in the upper right corner of Fit Model launch dialog - good! It also looks like you don't have two tabs for the linear predictor, as we would with the current version of JMP, but instead you select a term in the Effects list and apply the LogVariance attribute. That way is correct! You can enter the same term twice, once for the mean model and again for the variance model. JMP won't let you enter the same term twice, though, so in the case that you want to estimate the same effect in both models, enter it, add the LogVariance attribute for the variance model, then add it again for the mean model. A bit clumsy but that is why they changed the interface in a later version! It works.
In your example, you have the MoldTemp, Screw Speed, and their interaction effects in the linear predictor for the mean model and only the HoldTime effect in the linear predictor for the variance model. (Note again that you can have any combination of effects for either model.)
Based on these predictors, the results indicate that all of the terms in the linear predictor for the mean model are significant. The LRT for Equal Variance report for the variance model serves the same purpose as the ANOVA report for the mean model: is the proposed model (active variance effects) significant compared to the reduced model (constant variance). We reject the null hypothesis (constant variance) in this case because the p-value is very small.
Furthermore, the t-test for the Variance Parameter Estimates indicates that the Hold Time estimate has has a large t-ratio. You an also use the interval exp(Estimate) to exp(2|Estimate|) to evaluate the significance. If this interval excludes 1, then the estimate is significant. (This last statement is from distant and often faulty memory, so take it with 'a grain of salt.')
Hint: if you select Tools > Help (?) and then click on a table of results in a report (e.g. parameter estimates), JMP will go directly to the explanation of that information!
Re: How to look for optimum mean with low variation from DOEHi Mark,
Here is a screenshot of my jmp interface as you can see i can't select both the standard least squares and loglinear variance personality together, it only works with one of these two options
After constructing the model based on the above factors combination here is what i got, how do i interpret the data for the variance table
Another thing using this jmp version how do I do the analysis that you did to determine which factors has a strong impact on the variance and which factors has a strong impact on the mean.
If I want to run the loglinear variance model then I have to add in the logvariance effect from the attributes option
Let me know if my question is not clear and thanks in advance for your help
Rgrds
Irfan
Re: How to look for optimum mean with low variation from DOEFirst, save the picture. macOS and Windows both include utility apps for screen capture. Each is sufficient for this purpose. Then click the Photos button in the menu bar for your reply. A small dialog opens. Click Choose Files to select the file with the image. Wait until the Done button in the lower right corner is active, then click it.
As to the problem, I don't know what you mean. The linear predictor for the mean and the variance are separate. You can independently enter any terms you like for each one.
Re: How to look for optimum mean with low variation from DOEDear Mark,
Thank you for the continous support, but unfortunately after selecting the personality and selecting the loglinear variance option, when I tried to add in all the factors into the contruct model effects i have to put in the logvariance effects attributes for all the 7 factors.
Variance Parameter Estimates
Term Estimate Std Error t Ratio exp(Estimate) exp(2|Estimate|)
Intercept 5.1223121 0.31623 16.1982 167.723 28130.9
MoldTemp&Variance -0.143491 0.35355 -0.4059 0.86633 1.3324
Screw Speed&Variance 2.3306542 0.35355 6.5921 10.2847 105.774
Hold Time&Variance 0.5258412 0.35355 1.4873 1.69188 2.86246
Gate Size&Variance -0.278257 0.35355 -0.7870 0.7571 1.74458
Cycle Time&Variance -0.458603 0.35355 -1.2971 0.63217 2.50229
Moisture&Variance -0.312123 0.35355 -0.8828 0.73189 1.86684
Pressure&Variance 0.311134 0.35355 0.8800 1.36497 1.86315
btw is there a way for me to paste a picture in this discussion so that I can show what am I getting
Re: How to look for optimum mean with low variation from DOEThe key is to change the fitting personality. Click the Standard Least Squares button in the upper right corner of the Fit Model launch dialog and select Loglinear Variance for the personality. You should see two tabs now for effects. The first one is for the terms in the linear predictor for the mean and the second is for the variance. You need to separately specify the linear predictor for both.
Let me know if there is still some confusion about how to set it up.
Re: How to look for optimum mean with low variation from DOEDear mark, i was trying to replicate your analysis using JMP 5.1.2 but I'm not sure which model did you use to do this, are you able to show how you do this. When i tried to use the standard least square model the effect tests indicate that only 2 factors have a signficant main effects.
Effect Tests
Source Nparm DF Sum of Squares F Ratio Prob > F
MoldTemp 1 1 770.0625 12.7571 0.0038
Screw Speed 1 1 5076.5625 84.0998 <.0001
Hold Time 1 1 3.0625 0.0507 0.8256
Gate Size 1 1 7.5625 0.1253 0.7295
Cycle Time 1 1 0.5625 0.0093 0.9247
Moisture 1 1 0.5625 0.0093 0.9247
Pressure 1 1 95.0625 1.5748 0.2334
How do you run the variance effect likelihood ratio test in JMP 5.1.2, is this feature available in my JMP version
Re: How to look for optimum mean with low variation from DOEI honestly can't say. It is not my example. I am only stating my conclusions based on the logvariance model and analysis that I did with this example data table. I hope that the steps I showed (and direction to the JMP guide) will help you with your own analysis.
Re: How to look for optimum mean with low variation from DOEHi Mark,
Thanks for the elaboration on the subject, any reason in the example it actually states that the hold time is the factor that will affect the variance?Or its just for example purpose only
Rgrds
IrfanRe: How to look for optimum mean with low variation from DOEI am using the latest version of JMP (13.1.0) but it won't matter for your question. I fit the main effects only linear predictor against the Shrinkage response. Here is the Fixed Effect Tests report for the model of the mean response:
You can see that five of the seven factors have significant main effects. That is, there is strong evidence that they affect the mean response.
Here is the Variance Effect Likelihood Ratio Tests report for the model of the variance of the response:
So it appears that none of the factors affect the variance of the response. This result means that the ordinary least squares regression with a model that includes normally distributed errors with constant variance is sufficient.
This result also means that none of these factors can be used to reduce the variability of the Shrinkage.
Re: How to look for optimum mean with low variation from DOEHi mark, my company is still using JMP 5.1.2, from the loglinear example it shows that an example from the injectionmolding datasets. According to the example it was determined from the screening design example 'Preliminary investigation determined that the mean response only seemed to vary with the first two factors, Mold Temperature, and Screw Speed, and the variance seemed to be affected by Holding Time', then the question I have is how does the screening design able to show this responseRe: How to look for optimum mean with low variation from DOEI don't know if we have a video demonstrating the Loglinear Variance Model but the documentation has a good example.
Re: How to look for optimum mean with low variation from DOEDear Mark,
Any webcast showing how to use the loglinear varianceRe: How to look for optimum mean with low variation from DOEYou can always used the log-linear variance model through the Fit Model dialog for this purpose. Change the fitting personality to Loglinear Variance. Then you define the linear predictor for the Main Effects (mean) and another for the Variance Effects as you normally would for a multivariate linear model. This way you also have a profiler for each. You can save the fitted models as column formulas and then use them in other platforms outside of the fitting.
You do not need replicates for this model, but they help. You do need a large number of degrees of freedom for the error.
Read more about it in Help > Books > Fitting Linear Models. Chapter 10 is devoted to this platform.
Re: How to look for optimum mean with low variation from DOEMyers et. al. give a good overview of simultaneously modeling mean and variance in this reference:
http://amstat.tandfonline.com/doi/abs/10.1080/00031305.1992.10475869?src=recsys
Essentially it's no different than modeling two responses...of course you'll need replication within your design to estimate the variance for each treatment combination. All the usual co-optimization, simulation tools in the Fit Model platform, for the specific modeling personality you choose, will come into play.
On the simulation side of things one path is within the JMP Prediction Profiler (which I assume you'd use, since you can fit a model of your experimental results) you can use the Simulator from the Profiler framework to assign target values for each predictor variable, distributional forms for each variable, and estimates of mean and variance for predictors. Add other sources of noise as you see fit. You can even run a simulated experiment with the assumed mean and variance for each factor setting within the Profiler...so lots of different ways to go at this from a simulation point of view.
Re: How to look for optimum mean with low variation from DOEMay i know what is the JMP version that Robert Anderson is using in his webcast?Re: How to look for optimum mean with low variation from DOEHi Peter, do you have any example of how we do model the mean and also the variance of the response?Since for the variance we need multiple data from the same condition runs. Are you able to elaborate on the simulation approach what do you mean by thisRe: How to look for optimum mean with low variation from DOEAt a high level, there are any number of possible ways to arrive at a solution which I like to call 'on aim, with minimum variability'. Using DOE you could take a purist Taguchi style approach and use his signal to noise ratios (lots of reasons to avoid this method...but I don't want to turn this thread into a Taguchi vs. Classical methods discussion). Another approach is to model the mean and variance of the response as two separate and distinct responses...then using JMP's co-optimization capability to help balance deviation from target with minimum variance. A third approach is through simulation.
Re: How to look for optimum mean with low variation from DOE(I'm assuming that you have already collected your data).
You could view the second video (by Robert Anderson, 'Using historical production data to identify manufacturing process improvements') at this link (SAS profile required). It uses observational data, but the mechanics of how to use JMP are the same.
