Process Analysis Sampling Plans - Fixed Sampling Plans

To construct a simple sampling plan, we would first decide on a sample size, based on the means under H0/H1 and the particular Alpha and Beta error probabilities. Then, we would take a single sample of this fixed size and, based on the mean in this sample, decide whether to accept or reject the batch. This procedure is referred to as a fixed sampling plan. Process Analysis allows you to "play around" with the different parameters that determine the sample sizes, or to enter a sample size and to estimate the resultant Beta error probability.

Operating characteristic (OC) curve
The power of the fixed sampling plan can be summarized via the operating characteristic curve. In that plot, the probability of rejecting H0 (and accepting H1) is plotted on the y-axis, as a function of an actual shift from the target (nominal) specification to the respective values shown on the x-axis of the plot. This probability is, of course, one minus the Beta error probability of erroneously rejecting H1 and accepting H0; this value is referred to as the power of the fixed sampling plan to detect deviations. Also indicated in this plot are the power functions for smaller sample sizes.