From: Stan Hilliard
Date: 13 Aug 1999
Time: 00:13:39
You do not have to know anything about the actual quality of production to calculate the probabilities of acceptance (Pa) for sampling plans. They depend only on a sampling plan's specific decision rule - the sample size and acceptance limit(s). You can calculate these probabilities even before the factory is designed and built to manufacture the product.
Statistically, the probability of acceptance is a "conditional probability" because each value of Pa depends upon a hypothesized quality level of the lot or process. The Pa is calculated at each of several different possible quality levels and it is plotted versus quality level. This is the Operating Characteristic Curve (OC-Curve, Pa=f(quality)).
You can use OC Curves to evaluate whether the specific decision rules are suitable for your purpose of accepting some quality levels and rejecting others.
You perform this evaluation by repeatedly choosing a point on the oc curve and saying to yourself: "if the true quality level of a lot is X, then the probability that a sample will satisfy the acceptance rule is Y. Is this the way I want the decision to go?" You should want the oc-curve to be "steep" enough to discriminate between suitable and unsuitable quality levels.
For further discussion of oc curves, see www.samplingplans.com/usingoccurves.htm.
You can find a more detailed explanation in the tutorial, which can be printed from www.samplingplans.com/modern3.htm.
To simplify the procedure, software can perform the calculation of the probabilities and plotting of the oc curves. See it here: www.samplingplans.com/software.htm
Stan Hilliard shilliard@samplingplans.com