Classical versus Bayesian risks in acceptance sampling: a sensitivity analysis
Assuming a beta prior distribution on the fraction defective, \(p\), failure-censored sampling plans for Weibull lifetime models using classical (or average) and Bayesian (or posterior) producers and consumers risks are designed to determine the acceptability of lots of a given product. The average risk criterion provides a certain assurance that good (bad) lots will be accepted (rejected), whereas the posterior risk criterion provides a determined confidence that an accepted (rejected) lot is indeed good (bad). The performance of classical and Bayesian risks are analyzed in developing sampling plans when the lifetime variable follows the Weibull distribution. Several figures and tables illustrate the sensitivity of the risks and optimal sample sizes for selected censoring levels and specifications according to the available prior information on \(p\). The analysis clarifies the distinction among the different risks for a given sampling plan, and the effect of the prior knowledge on the required sample size. The study shows that, under uncertainty in the prior variance of \(p\), the designs using Bayesian risks are more appropriate.
producers and consumers risks weibull distribution average and posterior risks reliability sampling plans acceptable and rejectable quality levels beta prior model