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Dive into the world of OC curves and review parameters like lot size, sample size, acceptance and non-acceptance numbers, and more. Learn the differences between Type A and Type B curves, producer's and consumer's risk, and the significance of average outgoing quality in quality control processes.
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Recitation 8 • OC CURVES • AOQ
Review of parameters • N:Lot size • n1: Sample size on the first sample • c1: Acceptance # on the first sample • r1: Non-acceptance # on the first sample • n2: Sample size on the second sample • c2:Acceptance number for both samples • r2: Non-acceptance number for both samples
100 Pa: Percent of Lots accepted. • 100Po: Percent non-conforming • Procedure: One value 100Po assumed and the other calculated.
Difference between two types of curves:TYPE A AND TYPE B • TYPE B Curves: Lots come from a continouos stream of product, therefore the calculations are based on infinite lot size. (Binomial for evaluating, but approx. To poisson) • TYPE A: Probability of accepting an isolated lot. (Hypergeometric used to calculate the acceptance probabilities)
OC Curve - Operating Characteristic CurveThe OC curve shows how the probability of acceptance (y-axis) depends on the quality level (bottom axis).
Producer’s Risk • Producer’s risk :α= Probability of non-acceptance of a conforming lot. • Refelected on the OC curve as Pa=1- α • AQL(Acceptable Quality Level): Max. Percent of nonconforming that can be considered satisfactory for the purposes of accepting sampling.
Consumer’s Risk • β: • Probability of accepting a non-conforming lot. Usually given as Probability of acceptance. • Usually given as 0.10.
Average Outgoing Quality: 100*po(Pa) • Quality that leaves the inspection operation. • Without rectification: AOQ same as incoming quality • In rectification: Average outgoing quality is always better than the incoming quality.
