DOE for binary response

[#1]

Hello,

I have a binary response F/P. The current failure rate is 15%. There are 3 factors we like to experiment with X1, X2, and X3. There is also a blocking factor L with 3 levels, i.e. line 1, line 2 and line 3. X1 and X2 are continuous with two levels. X3 is also continuous bust since it's settings cannot be set accurately, we consider it as two level categorical with low level with values in the range (a, b) and high values in the range (c, d).

I like to design an experiment to minimize the failure rate. Not sure how to use JMP to do this.

[#2]

There is not enough context to provide any specific advice so here are my initial thoughts/questions:

1. I assume F and P are fail and pass.   Fail and pass what?  Is it a specification?  Can you make it a continuous measurement?  Or can you develop a measurement that will quantify the "phenomena" better? The reason I say this is because attribute/discrete categorical response variables are inefficient. They require more experimental units to detect changes and assign cause.  They also have  the flaw of being aggregate of potentially many failure modes/mechanisms.  Have you studied the measurement system that is categorizing F/P?  Is the 15% consistent?

2. I also want to point out a distinction...Are you trying to explain why failures occur or are you trying to predict failures?  Sampling may be a more effective way to explain failures.

3.  Are you trying to understand causal structure or "pick a winner"?  Do you plan on  iterating?

4. The question about level setting suggests you to consider the assumptions.  In DOE, it is "assumed" that if you set at factor at level 1 and change it to another level and then set it back to level 1 again, that is set to the identical level as the first time.  Now reality says that is impossible as variation exists in everything, so one way to reduce the impact of this handicap is to ensure the levels are set boldly different (bold but reasonable).  And of course, the boldness  across multiple factors is about the same (unbiased).

5. Not sure you need to block on all 3 lines.   Why are the lines different? (hypotheses) Can you pick 2 lines that are most different as a starting point?  Do you care about whether the factor effects from one line are different from another line (RCBD)?  Or do you just want to quantify the effect of line and increase the precision of the design (BIB)?

6.  Are there other "noise" variables that need to be accounted for?   For example, raw material lots or operator technique.

[#3]

Thank you statman!
F/P are fail/pass as you guessed. We manufacture widgets. Coming out of each line, they are either defective(F) or not (P). Unfortunately there is not a way to make it continuous. For now assume only one failure mode, as this is the observed one. The 15% is consistent +/- 2%. Sometimes we get higher than expected but reasons are known.
The purpose of the DOE is to find the best settings of the parameters to minimize the failure rate ... hopefully lower than 15% significantly (say to 10%). if by iteration, you mean replication, yes we can effort replicates of runs, but if you mean repeat the experiment after initial DOE, well maybe depending on availability of resources. We can just limit to two lines. We do care about differences in lines, but believe the factor effects should be similar among lines.

There are other noise factors such as operators. Management likes to keep this DOE very economical within reason of course.

I hope I was able to address your questions/comments.

Thanks again

[#4]

Thanks for the follow-up, but there is still too much information/context missing to provide advice.  What makes a widget defective?  I do not mean replicates, although this is essentially what you are doing by including lines in your study (i.e., replicates =blocks) and this is a good idea. I did imply iteration from the first design space to the next.  "Management likes to keep this DOE very economical within reason of course". If they economize by restricting inference space that is a BAD idea.  It means your conclusions are limited to those noise conditions.  If the noise changes, then all of the results from the experiment may be for naught (that is not economical)! You want to maximize inference space and increase precision of the design factors simultaneously.  This requires using strategies to handle noise appropriately.  Restricting the noise is usually NOT a good idea.

If you must stick to the discrete categorical response variable (and you only have 1 response variable), I suggest you read:

Bisgaard, Søren, Howard Fuller, "Analysis of Factorial Experiments with Defects or Defectives as the Response", June 1994, Report #119, Center for Quality and Productivity Improvement, University of Wisconsin.

[#5]

Hi @MarkovVaribles1,

@statman did a great response to initiate the discussion and start thinking about your problem and objective(s).

I'm still struggling to understand exactly the level of complexity of your design/model you're trying to achieve, which might depend on your objective, the number of factors you're investigating, any constraint(s), and a specific (and reasonable ?) limit on the number of experiments possible/allowed.

Do you already have historical data you could use to analyze the cause of defects (root cause analysis to identify factors of interest), and possibly leverage these data to Augment your data into a design (using the Augment Design platform), with possibly larger factors ranges to expand the inference space ?

If not, I think the Custom Designs platform might work for your case, as it can handle a large variety of factors types and constraints (blocking, numerical constraints, etc...).

You might also find this presentation from @DonMcCormack about "How to Design and Analyse Experiments with Pass/Fail Responses" really instructive, as it gives some idea on how to analyze this type of Pass/Fail responses.

Hope this answer might help you,

[#6]

Hi Victor_G,

We are not looking for root cause analysis here. We have these process parameters, X1, X2, X3 that can be controlled. If the response was continuous, this would be simply factorial DOE or a variation of it. Since the response is binary, JMP does not have the option of response being binary. I was wondering how I can design this in JMP.
I hope this helps explain the problem.

[#7 · Accepted solution]

The design is agnostic to the response type. It's the modeling technique that is influenced by the response type. There are several that are amenable to binary responses...starting with logistic regression.

[#8 · Accepted solution]

As @P_Bartell suggests, the response will not influence the design.
So you can create several designs, compare them, select one, and then add new column or change the data and modeling type of your original response column to be able to use a binary response.
You can look at my previous post to see how to analyze such response with the presentation from @DonMcCormack.

[#9]

Thank you all!