How to Assess Process Capability at the Development or Optimization Phase

v9991

Trusted Information Resource
#1
can we calculate process capability from DOE experiments? OR the confirmation runs of the DOE outcome.(design space)?
 
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raghu_1968

Involved In Discussions
#2
Re: How to Assess Process Capability at the Development or Optimization Phase?

Process capability cannot be calculated from the DOE. Process capability deals with Specification limits and Control limits, where as DOE is used for optimization process.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#3
yes you actually can "calculate" capability from a properly designed DoE. In fact this can be the best way to estimate initial capability of your process.

I assume by your use of the phrase "design space" you have performed a DoE that explores the settings of the important input factors and that you have sufficient replication with that DoE (perhaps a response surface DoE) and the confirmation run(s) to know what settings your input factors need to be at to produce in specification results of the output factor(s).

you most likely won't have enough data to calculate a very accurate Cpk value but who ever really does in the early days of a process? Knowing what factors are improtant and what the factor setttings must be are far more insighful and valuable than some random sample used to calculate a capability index...

IF you are able to maintain those input settings, your process will be capable. Of course only time will till tell you if you have captured all of the standard variation (aka common cause variation) in all input factors over time - that is your process performance.

You also will not know all of the assignable causes that create out of control results and excursions (out of spec resutls) but no one knows all of them until they have history with the process...
 

v9991

Trusted Information Resource
#4
I assume by your use of the phrase "design space" you have performed a DoE that explores the settings of the important input factors and that you have sufficient replication with that DoE (perhaps a response surface DoE) and the confirmation run(s) to know what settings your input factors need to be at to produce in specification results of the output factor(s).
Yes. (except for the replications :) )

you most likely won't have enough data to calculate a very accurate Cpk value but who ever really does in the early days of a process? Knowing what factors are improtant and what the factor setttings must be are far more insighful and valuable than some random sample used to calculate a capability index...
so, is there a appraoch/formula for calculating the process capability from DOE trials.

thank you.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#5
well, as you have no doubt figured out, you can't really calculate a standard deviation for the variation from a DoE as your data is VERY chunky; you will have a few points at only a few levels of the input range.

If I were forced to calculate an index, I would determine the minimum and maximum output value that I would expect if I set the inputs at their levels that guranteed in spec results. Then I would calculate a simple ratio of the tolerance range to the max-min output range.
 

v9991

Trusted Information Resource
#6
well, as you have no doubt figured out, you can't really calculate a standard deviation for the variation from a DoE as your data is VERY chunky; you will have a few points at only a few levels of the input range.
Is your assessment of being 'very chunky' dependent on fact that there is no replicates? or is there any other point you are referring to?

btw, its not sombody;s expectation or force to calculate the capability, this is an attempt to get a starting point/indicator of the process capability.

thank you.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#7
you have chunky data, not becuase you have a lack of replicates (although that is a dangerous condition to be in; replication is the foundation of science) but because you only have data at the setpoints of the X and DoE by it's nature has only a few setpoints in the X factor(s). Therefore you while the range of data in your Y will be representative, there are large spaces between the clusters of data where you had no conditions run - therefore you cannot calculate an accurate standard deviation. I have attached a PPT drawing showing what I am talking about...it is a simple case where there is only 1 factor that creates the majority of the variation in Y to illustrate the point. In reality there are often many factors that are imprortant but the drawing then becomes rather complicated.
 

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