Understanding Operating Characteristic Curves in Quality Control Sampling
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This document explores the parameters of Operating Characteristic (OC) Curves, focusing on the differences between Type A and Type B curves. It discusses key concepts such as lot size, sample size, acceptance numbers, and risks associated with production and consumption quality. The relationship between Average Outgoing Quality (AOQ) and non-conforming product percentages is clarified, along with the implications of producer's and consumer's risks. Additionally, it emphasizes the significance of the Acceptable Quality Level (AQL) in determining satisfactory sampling outcomes.
Understanding Operating Characteristic Curves in Quality Control Sampling
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Presentation Transcript
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.
