Variable inspection plans for continuous populations with unknown short tail distributions

The ordinary variable inspection plans are sensitive to deviations from the normality assumption. A new variable inspection plan is constructed that can be used for arbitrary continuous populations with short tail distributions. The peaks over threshold method is used, the tails are approximated by a generalized Pareto distribution, their parameters and the fraction defective are estimated by a moment method proposed in a similar form by Smith and Weissman (1985). The estimates of the fraction defective are asymptotically normal. It turns out that their asymptotic variances do not differ very much for the various distributions. Therefore we may fix the variance and use the known asymptotic distribution for the construction of the inspection plans. The sample sizes needed to satisfy the two-point conditions are much less than that for attribute plans.