Quality Engineering Report III
OC-curve
A single sampling plan for a population (N) of 1,000,000, a sample size (n) of 250, and number successes (c) in the sample of 4. The producers risk is 0.5% and a rejectable quality level of 4%. This process allows for responsibility for quality to be placed on the process rather than on inspection, it's economical, and can be upgraded from piece to piece decisions to entire lots. However, it takes more time and effort in planning and training for sampling, there is less information about lots when it is completer, and there is no assurance the entire lot will conform to specifications. There is also the producer and consumer risks involved, meaning producers will risk losing good product and consumers will risk receiving faulty products.
The data to the left shows the proportion nonconforming (p) and the number nonconforming (np). Excel was then used to calculate the poisson, binomial, and hypergeometric distributions.
The operating characteristic (light blue line) chart compare the proportion nonconforming (p) to the probability of acceptance.  shows where The probability of acceptance can be represented using either the poisson, binomial, or hypergeometric distributions. As the number of accepted product decreases the curve becomes steeper thus signifying there is more producer risk. Since the producers risk (yellow line) is 0.5%the spot where it intersects the curve corresponding np value, in this case 1, divided by the sample size is the Acceptance quality level (green line), which equals 0.004. The rejection quality level (Blue line), at 4%, can be used to find the consumer risk (dark blue line), 0.004, by looking at where the rejection quality line intersects the operating characteristic curve.
