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.

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。