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Classical and Bayesian estimation of the index Cpmk and its confidence intervals for normally distributed quality characteristic
Journal of Statistical Computation and Simulation ( IF 1.1 ) Pub Date : 2021-02-16 , DOI: 10.1080/00949655.2021.1879079
Sanku Dey 1 , Chunfang Zhang 2 , Mahendra Saha 3
Affiliation  

In this article we consider the process capability index (PCI) $C_{pmk}$ which can be used for normal random variables. The objective of this article is four fold: first we address the different classical methods of estimation of the PCI $C_{pmk}$ from frequentest approaches for the normal distribution and compare them in terms of their biases and mean squared errors. Second, we compare three bootstrap confidence intervals (BCIs) of the PCI $C_{pmk}$. Third, we consider Bayesian estimation under symmetric and asymmetric loss functions. Fourth, we have incorporated a tolerance cost function in the index $C_{pmk}$ to develop a new cost effective PCI $C_{pmkc}$. A Monte Carlo simulation study has been carried out to compare the performance of the classical BCIs and highest posterior density credible intervals of PCIs $C_{pmk}$ and $C_{pmkc}$ in terms of average width and coverage probability. Finally, two real data sets have been analyzed for illustrative purposes.



中文翻译:

指数 Cpmk 的经典和贝叶斯估计及其正态分布质量特征的置信区间

在本文中,我们考虑可用于正常随机变量的过程能力指数 (PCI) $C_{pmk}$。本文的目标有四个方面:首先,我们从正态分布的最常用方法中解决了估计 PCI $C_{pmk}$ 的不同经典方法,并比较它们的偏差和均方误差。其次,我们比较了 PCI $C_{pmk}$ 的三个自举置信区间 (BCI)。第三,我们考虑对称和非对称损失函数下的贝叶斯估计。第四,我们在指数 $C_{pmk}$ 中加入了容差成本函数,以开发新的具有成本效益的 PCI $C_{pmkc}$。进行了蒙特卡罗模拟研究,以在平均宽度和覆盖概率方面比较经典 BCI 的性能和 PCI $C_{pmk}$ 和 $C_{pmkc}$ 的最高后验密度可信区间。最后,为了说明的目的,分析了两个真实的数据集。

更新日期:2021-02-16
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