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What Sample Size Should I Use for My DOE?

Six Sigma – iSixSigma Forums General Forums Methodology What Sample Size Should I Use for My DOE?

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  • #55474

    Behs
    Participant

    Hi all,
    I am planning to conduct a DOE with failure rate as my response. I need to determine which samples size I should use for each run.

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    #200127

    Robert Butler
    Participant

    The issue isn’t so much one of a sample size for a DOE as it is one of sample sizes needed to see a failure rate. Before anyone can offer much of anything in the way of advice you will need to tell us the followins:

    1. What is the current failure rate?
    2. What kind of an improvement in the failure rate would be considered a physically meaningful (i.e.if you made an improvement would it translate into something better/cheaper/faster that would justify the changes you might propose to make)?

    If you can provide an answer to these two questions perhaps I or someone else could offer some additional thoughts.

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    #200128

    Sergey
    Participant

    Type of design, amount of factors used will be helpful as well

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    #200129

    MPBatista
    Participant

    Hi,

    I have a similar problem. I will run a factorial experiment(2^k) for a current inspection. We’re trying other method of measurement/inspection. However, we can’t apply a hypothesis test because we have other factors.

    We have 3 factors(Method of inspection, Winding Temperature and Equipment) and I’m also using failure rate as my response. I have many familys of products. I’m thinking to run a DoE for each family which has a high failure rate.

    Thanks

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    #200130

    Behs
    Participant

    Hi Robert and Sergey

    Regarding current failure rate; as a reference failure rate I have 9 observations with a pooled failure rate of 1%. One observation with failure rate 8/20= 40% (note the small sample size), one observation is 3/200 =1.5% and the remaining 7 observations are 0%.

    I do not have any specific target for improvement, I just want to find out which parameters cause this extremely high failure rate of 40%.

    DOE will be with 3 parameters, 2 continues factor and 1 categorical on two levels.

    According to a DOE software package (Design Expert), the minimum sample size for a DOE with Fraction Defective Response can be calculated as:

    2*n/Number of runs, where n >p/5 ( or in best case n>p/10). Unfortunately, the software doesn’t provide the mathematical calculation/ justification for this equation.

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    #200137

    Sergey
    Participant

    For my mind, DOE is not a tool for problem solving. What is actual situation is you have 3 hypothesis that some factors may influence defect rate. 1 proportion test to calculate sample size versus current defect level might be used to define amount of trials needed to see the effect of factors on defect rate. It should be mentioned that sample size is much more bigger than observations you already have.

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    #200147

    MPBatista
    Participant

    Hi Sergey,

    Can I use 1 proportion test for 3 factors? Is there any problem to use failure rate as my response in DoE?

    Thanks!

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    #200148

    Robert Butler
    Participant

    It sounds like what you are saying is that you set up some kind of process conditions and made a run of size 20 and found 8 failures, then you set up some other kind of process conditions and ran 200 samples and found 3 failures. Finally you set up a third condition – ran 7 items and decided you had 0 failures.

    If the above is a fair description of what you did then I guess we are to assume that either the changes you made in the system involved just the three variables you listed or that, based on some other work, you have decided these three variables are the most likely suspects with respect to failures.

    If this is the case then, based on what you have described and your prior data, it would seem that testing 20-40 samples per experimental condition should provide enough discrimination with respect to changes in the failure rates. Obviously this is an opinion and not one based on sample size calculations but it is an opinion based on the data you have provided.

    I can think of a number of questions to ask about the whys and wherefores of the sampling method you did use – particularly the decision to stop testing after 7 samples did not exhibit failure – but I’ll assume there were valid reasons and your experience with the process is such that you a comfortable with the samples you did take and the results you derived from them.

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