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 (LMEs) of Zhang (Aust N Z J Stat 49:69–77, 2007) and the Bayesian estimate (ZSE) of Zhang and Stephens (Technometrics 51:316–325, 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 that of the fraction defective are used to construct the sampling plan. The difference to the sampling plans constructed in Kössler (Allg Stat Arch 83:416–433, 1999; in: Steland, Rafajlowicz, Szajowski (eds) Stochastic models, statistics, and their applications, Springer, Heidelberg, pp 93–100, 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.

中文翻译：

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未知分布的任意连续种群的双向可变检查计划

普通的变量检查计划依赖于基础人群的正常性。但是，这种假设是模糊的，甚至不能满足。而且，普通的变量抽样计划对与分布假设的偏差很敏感。不合格项出现在分布的尾部。它们可以通过广义帕累托分布（GPD）近似。我们根据其参数不仅对GPD的有效性，而且对任意连续分布的有效性，研究了几种参数估计值。事实证明，张的似然矩估计值（LMEs）（Aust NZJ Stat 49：69–77，2007）和张和斯蒂芬斯的贝叶斯估计（ZSE）（Technometrics 51：316–325，2009）证明是最适合我们的目的。然后，我们使用这些参数估计来估计缺陷分数。LME（参见Zhang 2007）的渐近正态性和缺陷分数的渐近正态性被用于构建抽样计划。与Kössler（Allg Stat Arch 83：416-433，1999; in：Steland，Rafajlowicz，Szajowski（eds）随机模型，统计数据及其应用，Springer，Heidelberg，第93-100页，2015年构建的采样计划的差异）是我们现在使用新的参数估算值。此外，与上述论文相比，我们现在还考虑了双面规范限制。工业示例说明了该方法。Heidelberg，第93-100页，2015年）是我们现在使用新的参数估算值。此外，与上述论文相比，我们现在还考虑了双面规范限制。工业示例说明了该方法。Heidelberg，第93-100页，2015年）是我们现在使用新的参数估算值。此外，与上述论文相比，我们现在还考虑了双面规范限制。工业示例说明了该方法。