Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution

Abstract

The ordinary variable inspection plans rely on the normality of the underlying populations. However, this assumption is vague or even not satisfied. Moreover, ordinary variable sampling plans are sensitive against deviations from the distribution assumption. Nonconforming items occur in the tails of the distribution. They can be approximated by a Generalized Pareto distribution (GPD). We investigate several estimates of their parameters according to their usefulness not only for the GPD, but also for arbitrary continuous distributions. The Likelihood Moment estimates (LME) of Zhang (2007) and the Bayesian estimate (ZSE) of Zhang and Stephens (2009) turn out to be the best for our purpose. Then we use these parameter estimates to estimate the fraction defective. The asymptotic normality of the LME (cf. Zhang, 2007) and of the fraction defective are used to construct the sampling plan. The difference to the sampling plans constructed in Kössler (1999, 2015) is that we now use the new parameter estimates. Moreover, in contrast to the aforementioned papers, we now also consider two-sided specification limits. An industrial example illustrates the method.