From: Stan Hilliard
Date: 24 Jul 2003
Time: 00:50:50
Chris,
I understand that you do not want a plan for the purpose of accepting/rejecting the lots, but rather to estimate the quality of each lot based on a sample of wheels.
About the EMAT and PET data -- when you test a wheel, do they come up with a single number that can be compared to a nominal value to deternine if the wheel is defective? Or is the judgement more complex?
You mention binomial and hypergeometric distributions, which are for go/no-go attribute data. If your data is such that you classify each sampled wheel measured by EMAT or PET as either defective or non-defective, you can use the binomial distribution to calculate the upper and lower confidence limits for fraction defective of each lot. No decision necessary.
In your case, you don't have to be concerned about binomial versus hypergeometric because the binomial merges into the hypergeometric for large lot size. (N/n greater than 10.)
You could increase the sample size in steps until the confidence interval is narrow enough.
One of out programs will calculate and print a confidence limit report -- Audit Sample Planner (ASP). $245.
www.samplingplans.com/programasp.htm
Using only the fact that there were n wheels, X of which were defective, ASP will generate a report containing the interval estimate of the lot fraction defective. It uses the percent confidence that you specify. This report is intended to be an overall summary of findings of the quality of lots. It also shows the assumptions made in the calculations.