Process capability indices (PCIs) are useful measures to evaluate the performance and capability of a process when it is under control. Assuming the specification variable is distributed from a normal population, several PCIs are derived by the researchers. Also, many scientists have worked on these indices when data are contaminated with outliers as well as in the homogenous case. But, in almost all studies, they evaluated the effect of outliers on the PCIs nonparametrical and used robust methods. Here, the parametric model of outliers is considered and introduced the PCIs based on the outliers model. Therefore, these indices are estimated based on the maximum-likelihood and moment estimator of the unknown parameters of the normal distribution contaminated by outliers. Finally, the performances of these measures as well as their parametric and nonparametric estimators are discussed by using simulation studies and several numerical examples. It has been seen that parametric estimation has better performances than a nonparametric method.

中文翻译：

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存在异常值的正态分布过程能力指数

过程能力指数 (PCI) 是评估过程在受控情况下的性能和能力的有用指标。假设规格变量是从正常人群中分布的，研究人员会推导出几个 PCI。此外，当数据被异常值以及同质情况污染时，许多科学家都在研究这些指数。但是，在几乎所有研究中，他们都评估了异常值对 PCI 非参数的影响，并使用了稳健的方法。这里考虑了异常值的参数模型，并介绍了基于异常值模型的 PCI。因此，这些指标是基于被异常值污染的正态分布的未知参数的最大似然和矩估计值来估计的。最后，通过使用模拟研究和几个数值示例，讨论了这些措施的性能以及它们的参数和非参数估计量。可以看出，参数估计比非参数方法具有更好的性能。