About statman

statman

I''d be happy to take a shot with some feedback, but realize you are asking about a specific situation and you really haven't provided us with enough information to fulfill your specific request. 1. Your quote " We are working with models so standard DOE won't work" does not make any sense to me. Analysis of most DOE's is typically done by entering a model into the fit model platform. 2. You have one variable that you want to test at multiple levels. How did you get to there being only one variable? Did you perform other iterations to filter down to this one variable? What about noise? 3. Testing at 15 levels (I'm not sure what exactly you mean by 15 conditions except you have only 1 variable) is basically trying to pick a winner. What we are typically trying to do is to be able to predict a response variable(s) by developing a mathematical model that is a simplification of what is probably a more complex response surface. Typically these model are developed with some hierarchy of model terms. First order linear effects, second order linear effects,...2nd order non-linear effects (quadratic), etc. Second order non-linear effects can be estimated with 3-levels, third order non-linear effects (cubic) can be estimated with 4-levels, etc. What order effect would you be trying to estimate with 15-levels? This would be virtually useless in the real world. If the 15 means something else, I still would question why 15? 4. It looks like have historically built in either replication or repeats of the "conditions". I can't tell which from your message? The reason for doing replication this is to either form a basis of random un-biased errors to test the significance of treatment effects or to assign the variation in to the noise changing between replicates (if you were doing blocks for example). Why are you doing replication? And why 3 replicates? 5. You mention 2 dozen "systems". What is a system? Why must you test over all of the systems? 6. The attached JMP data table has nothing in it but column labels. 7. A practical argument for reducing runs can be just as valuable as a statistical argument.

statman

A different interpretation of the charts (actually Shewhart's original interpretation). There are 2 charts that Shewhart created. The Range chart and the X-bar chart. These are used together. The range chart assesses the consistency/stability of the within subgroup variation (which is a function of the variables (x's) changing at within subgroup sampling frequency). This is done because the within subgroup variation is the basis for comparison. If the within subgroup variation were inconsistent, then the comparisons would be useless (they would depend on what the within subgroup variables were doing at the time). The X-bar chart is a comparison chart. It does not assess consistency, but instead compares the within subgroup variation (these are the control limits) to the between subgroup variation, the plotted averages (which is a function of the variables changing at the between subgroup sampling frequency). If no points are out-of-control, then the within subgroup variation dominates. This set of x's is where the leverage is. If there are points out-of-control (or other non-random patterns) then the between subgroup variation dominates. In this way, control charts helps point investigators towards the subset of x's that have the greatest leverage. Further sampling or experimentation is necessary to further desegregate the subset of variables to identify the specific causal factors.

statman

Aside from the technical method to do what you want...Could you help me understand why? Not trying to be antagonistic, just enhance my knowledge. I understand the assignable causes for a trend may be different than a point OOC, but the charts are just meant to help identify those, you still need process knowledge to determine what the causes are in any case. AFAIK, Shewhart did not propose differentiating the different tests. These were established by a group at the Western Electric Company in 1956. They were intended to provide guidance and perhaps enhance our ability to identify unusual patterns in the data presented as a time series (over and above the control limits interpretation). I'm curious as to why you would differentiate what "rule" was used to identify unusual patterns as evidence of assignable cause variation? Also the rules often do not apply to 1 point. For example, on a MR chart an OOC condition is a function of 2 data points. A trend is a function of 7 data points...etc.

statman

Trying to interpret your question so I apologize if I misunderstand...Typically you use screening designs (e.g., fractional factorials) to compare lots of factors in the intended design space. After determining which of these factors are significant (both practical significance and perhaps statistical significance) you would likely continue to investigate that subset of factors to find optimum regions. This methodology is what GEP Box calls Response Surface Methodology (not one experiment with factors at >2 levels). It is the use of iteration of experiments to understand the rather complex surface. How many experiments it takes is dependent on your current state of knowledge. And, of course, as new materials and processing technology evolves, so does the response surface...thus continuous improvement.

statman

Is this a different behavior than JMP 14?

statman

Windows or Mac? When you Open an Excel file, do you get the Use Excel Wizard? Have you tried changing Preferences, you can select Third Party Data and Text Data Files for options.

statman

Here are a few of my thoughts: 1. You will need to have the x's (variables during the processing of a batch) and the Y's (response variables characterizing the batch) in the SAME data file. 2. While you suggest there is one sample of the batch that is tested (or that you have a quantitative response for), is that sufficient? Have you considered variation due to the measurement systems in the lab? How is the sample obtained? With one sample from each batch it will be impossible to speared within batch variation from between batch variation. You should develop sampling plans based on hypotheses regarding the effect of x's and sample to understand those relationships. 3. Can you create intermediate response variables? Y's that may be correlated to the Y's measured at the lab, but are measured upstream from the lab? For example, maybe the Y in the lab is molecular weight and a measure of the batch could be viscosity. 4. You might not need all of the continuous data as the batch is being made. Again start with hypotheses as to what relationships you think are of interest. Sample the stream of data to select data of interest to examine relationships in JMP. For example, you might hypothesize that the rate of temperature change impacts the Y. Then you can determine the slope of the line for the rate of temp change in making the batch and use that statistic to investigate the relationship with the Y (using fit model in JMP). 5. Using Analyze>Multivariate Methods>Multivariate look for relations ships between the x's. Reduce the number of x's to include in the data set based on which x's are correlated.

statman

My first thought is to give appropriate advice, more information regarding your situation may be needed. What are the response variables? What are the factors? How far do you need to move the response variables? etc. To reiterate Mark's points, a screening design is meant to give a relative comparison of the factors of interest in the selected design space (which includes level setting and noise). Often the initial screening design will help to prioritize which factors have the largest effect on the response variable(s) of interest and which direction you want to move the design space. The objective being to efficiently move towards the optimum region. Usually, you are not concerned with non-linearity as this occurs within the design space and you are likely to move the space. More than 2-levels is very inefficient. Why create a complex model at the base of the mountain? (an analogy is creating a detailed map of Philadelphia when you are trying to get to Boulder, CO.). What wasn't clear in your first post was this would be run via simulation. Realize in simulation, an algorithm has already been created in your simulation program. You may not know what it is (especially if you bought the simulation from a supplier), but it is already there. Now comes the difficult part....if the algorithm does not contain factors that you want to investigate, the analysis will say those factors have no effect. There are other opinions, my thoughts are simulation has limited utility for screening. In screening, you are investigating many variables that you don't know have an effect, while simultaneously comparing those factor effects to NOISE. How is NOISE simulated? IMHO, this cannot be realistically simulated. Admittedly there are some programs that take a long time to run (e.g., FEA) and therefore to conserve computer runtime fractional factorials may be run, but if computer time is no big deal, run full factorials.

statman

Mark is completely correct. There are a lot of papers on the subject. Fred Spiring, Bartholomew Leung, Smiley Cheng and Anthony Yeung, Bibliography of Process Capability Papers,QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL Qual. Reliab. Engng. Int. 2003; 19:445–460 (DOI: 10.1002/qre.538) lists many of the papers on the subject. Here is another with a good summary of issues: http://www.stats.uwaterloo.ca/~shsteine/papers/cap.pdf

statman

Adding to @markbailey's excellent advice, here are some things to think about: 1. How much of a change in the response variable (Colored Structures) is of practical significance? What is the smallest increment of change you care about or would be of scientific interest? 2. The pictures may be considered components of the measurement system. What is done with the pictures? How is the response quantified from the pictures? 3. Here is a variability plot for the data set: As you can see there is a good deal of variability within slides 4 and 8 (is this measurement error?). This will ultimately have a large affect on any quantitative analysis. This will also likely make it difficult to detect Fermentor-to-fermentor variability.

statman

Some questions for a different perspective...Why are those particular treatment combinations impossible? How do you know they are impossible?Can you provide more context? Are the levels too bold? Are the levels you set for some factors dependent on the levels of other factors (potentially factors nested within others vs. crossed)?

statman

Claire, Some questions for you: 1. I don't see the data set attached, so what is the data set? Is it from an experiment? 2. How many levels are there for the factors in the model? 3. Do you have a way of quantifying "stability"? Perhaps a measure of variability over some time period. 4. If you don't have one, can you create one from your data set? In essence, the response variable you are using is likely providing a model for the mean of the response. What you may be interested in is the variation in the response. If you can create this, then you can use the profiler and interaction plots to determine which factors affect that response variable. What you are looking for is a plateau on the theoretical "response surface". This is a good idea as this is one aspect of robustness.

statman

@DEDuvall, your statement "The fitted regression equations are used to extrapolate time to failure results to end use temperature and internal pressure conditions that are well outside of those employed in the accelerated testing." is a bit confusing. You are saying your accelerated testing does not cover the conditions you are trying to draw conclusions about? Typically, in accelerated testing, aren't the conditions exaggerated to simulate long-term conditions? We shake, bake and sprinkle water on the products to expose failures meant to represent failures in time. How we expose those products and to what conditions is typically an educated guess to start and then over time we refine those acceleration models to match reality. TMK, Lack of fit tests don't really answer whether you can extrapolate the results BEYOND the inference space the study was conducted over. They are used to assess whether the model fits the data in hand.

statman

If your question is: Can JMP calculate lack-of-fit SS, the answer is yes. https://www.jmp.com/support/help/en/15.1/?os=mac&source=application&utm_source=helpmenu&utm_medium=application#page/jmp/lack-of-fit.shtml

statman

The term covariate can be tricky to understand as its interpretation depends on how it is being used (context). In a regression application where the data already exists, covariates are often just a continuous independent variable (and in ANCOVA, the other independent variables are likely categorical). For DOE purposes, the covariate is typically an independent variable that is measured, but not specifically manipulated (often because the covariate is noise, a variable one is unwilling to control). By accounting/assigning the covariate in the model, you increase the precision of detecting the design factor's effects. For example, if you were running an experiment and you were concerned with ambient temperature effects. You are unwilling to manage ambient temperatures, so you take the ambient temp. measurements during each run of the experiment. When you write the model, you add the ambient temp. as a covariate (Typically put the covariate first in the model and use sequential tests (Type 1) for determining its significance. The use partial tests (Type 3) for the remainder of the model effects.). This will account for the effects of ambient temperature (which otherwise would have been captured in the error term). By removing those effects from the error term (reduced MSE), you have increased the precision for testing the factors in the experiment.

statman

If you put the continuous Y value on the Y axis and one of the X's on the X-axis, then choose the other X involved in the interaction and drag it to the Overlay drop zone, you should see the interaction plot. If you post your data, I can use it to show this.

statman · ‎06-15-2020

@moughli, I had some other thoughts about your situation if you'll indulge me. I'm not sure why you are running experiments on factors at more than 2 levels if you are wanting a fractional factorial. You are likely to confound higher order linear effects (2nd+ order interactions) with non-linear effects (quadratic and cubic). Some thoughts: 1. Perhaps you should think of the factors as ratios of each component (if indeed you need all components in the final solution), 2. You might want to think about a mixture design, but only after you have identified, studied and understand the noise, 3. Seems there is likely interaction between the factors and the noise (amount of each ingredient depends on the current soil conditions), so it is paramount that you understand these before optimizing the levels of the controllable factors. 4. I might suggest understanding the first order model for the factors of interest (2 level designs are adequate for this) and identifying noise-by-factor interactions before proceeding with response surface type designs.

statman · ‎06-13-2020

My math might be wrong, but a full factorial for 4^1 x 3^2 = 36 treatments (runs). Replication, or Blocking is used to determine if the results from one replicate repeat over changing noise. The purpose of Blocking is to reduce the amount of noise changing within the Block by holding the noise constant or sampling such that the noise does not change much within the replicate. For an agricultural example, run all of the treatments in a small area of the field over a short time period reducing inherent soil fertility and ambient condition changes thereby increasing the precision of the design. When subsequent Blocks are run, the noise that was constant during the first set of replicates, changes (either by manipulation or sampling). For agricultural example, run the second set of replicates at another location in the field and under different ambient conditions. If you use hypotheses about the effects of noise, you can more efficiently select what noise to study by Blocking.

statman · ‎06-11-2020

To add to @markbailey 's comments, I will say sometimes it is obvious and sometimes not. Here is a simple diagram that shows the continuum between nested and crossed with systematic in the middle. For systematic sampling, you will find different opinions as to how this should be handled.

statman · ‎06-10-2020

Sorry, my italicized must for covariates being continuous was meant to mean there are other options. Even as categorical variables, they are treated as continuous in ANCOVA. I'm not sure what you mean by this: " these noise effects need to be taken up as inputs in the DOE at carefully specified levels the way that accurate estimation and modeling is possible". I have run >100's of experiments successfully using RCBD to estimate noise-by-factor interactions and find factors or levels of factors that are robust to noise. Not sure what you are insinuating from your last comments? I suppose I have outstayed my welcome.

statman · ‎06-09-2020

My thoughts on covariates: 1. You have to consider additional measurement errors 2. Since they are not manipulated, this is more likely evidence of correlation, not causation. In addition, you have multicollinearity issues. 3. You have to choose what "value" to put in for each treatment even though the variables are "wandering around" (you can only put one in). How representative are the values you use compared with the natural variation of the covariate? 4. Potential lag effects must be considered 5. You need to either give up a degree of freedom from the design factors you are manipulating (for each covariate) or run random replicates to accommodate the degrees of freedom for analysis 6. You'll likely miss out on interaction effects 7. You are limited on the number of covariates you can consider at any point in the analysis 8. They must be continuous variables, so not variables like Day or time of day, IMHO. There are a number of what I think are more effective and efficient means of handling noise in experiment situations than covariates. The idea of a block, where noise is somewhat constant within the block and changes between blocks allows you to group or chunk a number of noise variables simultaneously. This is very efficient in the early stages of investigation. For robust design and processes, it is extremely important to be able to assign and understand noise-by-factor interactions. Of course, split-plot designs and cross-product arrays are also quite useful when you have more specifically identified the number of influential noise variables.

statman · ‎06-08-2020

If you have hypotheses as to what is changing between the time periods and why it would effect the response, then by all means keep track of those time periods (at least systematically). To me a random effect is what Shewhart would call unassignable. I believe if you sample it systematically, you can assign it (but not everyone would agree with me). I often assign the block and block-by-factor effects when I am confident I understand what variables are involved and have hypotheses to back them up.

statman · ‎06-08-2020

or randomly select 2 time periods within day and treat that as a random effect.

statman · ‎06-08-2020

Just another thought I had, was do you really need 4 time periods within day? Could you reduce this to 2 (morning and afternoon)? This might be more efficient.

statman · ‎06-08-2020

The key to proper analysis is the model you create. The numbering in @markbailey's post would work for nesting (sequential, non-repeating). The concept of a block is "theoretically" to hold the noise variables constant within the block thereby increasing the precision of detecting factor effects and allow (or manipulate) those noise variables so they change between blocks, thereby increasing the inference space while not negatively effecting the precision. You are in a situation, where some of the noise variables are changing within the block. This "theoretically" will increase the error within the block reducing the precision of detecting factor effects. Can you choose your blocks differently? Is the within day variation in ambient conditions greater than the between day? Some other options: 1. Measure ambient conditions and treat those measurements as a covariate (e.g., dew point) 2. Use a center point treatment (current conditions?) or perhaps an identical treatment combination to replicate over the course of the experiment. Analyze this and use the mean square of this replicated treatment as a basis for statistical tests (error estimate).

statman · ‎06-08-2020

You have an interesting situation. One could argue there is no way the time intervals within a day are crossed with day because the within day time intervals are nested within day. So the numbering is "in question". When you use the coding 1-4, 1-4 for the time intervals (for 2 days), the software recognizes the 1 for time interval for day 1 to be "identical" to the time interval 1 for day 2. While the time interval is similar, it can not be identical. I would call it systematic. I could argue (both ways) the systematic pattern within day is close enough to the same to investigate the interaction or I could argue that it is definitely not the same, hence it is nested. I think it extremely important that you have hypotheses to support the time intervals within day are similar enough to justify the crossed nature of the effects.

statman · ‎06-07-2020

Sorry, I'm a bit confused by your query? Are you dealing with a mixture (where the constraint is due to the fact that when you choose levels for one factor it affects the levels for the other factor as both factors sum to 1)? If you are running an experiment, you, obviously, choose the levels you set. Having F1 at levels: -1 = 250 and 1 = 350 and F2 levels at: -1 = 100 and 1 = 200 easily meets your criteria.

statman · ‎06-06-2020

You want something like this?

statman · ‎06-06-2020

If your model is saturated (all DF's are accounted for in the model), there are no DF's to estimate the error term and therefore there are no tests of significance.

statman · ‎06-05-2020

To add my thoughts to the discussion, repeats capture short-term effects not due to the treatments. This can be useful for being able to analyze measurement error or within treatment variation (due to the sources of variation changing between repeats). This data would need to be summarized to evaluate the treatments as repeats do not increase the degrees of freedom available. Replication is a method to capture (and possibly assign) long-term variation due to "noise" so that you can: 1. determine if the results of the treatments from one replicate repeat for other replicates thereby increasing the inference space of the experiment 2. determine the size of the noise between replicates 3. increase the precision of detecting treatment effects while not compromising inference space 4. determine oil your results are robust to noise.

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