Applying Weibayes to Attribute sampling

Came across an interesting application of Weibayes. For a time based attribute specification, testing for a greater time than the specification time was used to derive reduced attribute sample sizes.

For example, say desired confidence of 0.95 and desired acceptance of 0.95. Traditional attribute techniques using the binomial distribution gives 59 samples. If the test involves a P/F acceptance criteria to a desired spec time (say 20 seconds), using the weibayes formula, assuming no failures, and a test time of 60 seconds, shape factor =1.

n = ln(1-alpha)/(ln[Acceptance]*(Test time/spec time)^weibull shape parameter))

you arrive at n = 19.47 ~ 20 samples.

This is known as "Weibayes extended success testing"

Thoughts on this application? Essentially if you know and understand your shape factor (failure rate, mode, and time) you can extend the test time which results in reduced sampling.

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