Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution
Mathematisch-Naturwissenschaftliche Fakultät
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.
Files in this item