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stats question

Posted By: W Womack
Date: Wednesday, 22 June 2011, at 5:41 p.m.

In Response To: stats question (Christian Munk-Christensen)

This is a basic acceptance sampling type problem and you can apply the binomial distribution to answer your question. There is a nice online binomial calculator at http://stattrek.com/Tables/Binomial.aspx. Excel also contains a binomial calculator (not sure if it is in the core or one of the add-ons) but you can use this to create curves showing the probabilities of a success at different sample sizes and probabilities of single success. In Quality Assurance these types of curves are called operating characteristic curves and are used to determine the level of risk associated with various attribute sampling plans, i.e. the risk of accepting a "bad" lot or rejecting a "good" lot (assuming a good lot allows some number of defective items).

So to answer your original question if there is 1 bad item in the 1400 the probability of success on a single trial is 1/1400=.0007. If you apply the binomial distribution to this you will find that the probability of 0 successes (a success here being finding a bad item) in 30 trials is .9792, so you have very little chance of finding the defect.

If there are 1% defects in the lot the probability of finding a defect on a single trial is 0.01, and the probability of getting 0 in 30 trials is .7397.

At 2% defects it is .5454, at 4% it is .2938

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