Robust Confidence Intervals for Process Capability Index Based on Cost and Loss Functions With Bootstrap Enhancement

Process capability indices (PCIs) are commonly used to evaluate a process's performance in relation to the standards. Greater PCIs do not necessarily translate into lower rejection rates, even though they do indicate a higher level of process quality. Thus, a loss‐ and cost‐based PCI is a better way to measure process capability. This article looks at the PCI, which is based on the tolerance cost function and the asymmetric loss function (i.e., linear exponential) for normal process. Under the presumption of pure data, may perform well based on standard sample mean and variance estimates. However, these estimates are quite vulnerable to data contamination due to their zero breakdown point, which can affect both and produced confidence intervals (CIs). In this work, we offer robust estimators and robust CIs for in order to mitigate this sensitivity. Through statistical power and receiver operating characteristic (ROC) curve evaluation, we demonstrate the superiority of our methodologies over conventional methods, particularly in cases where data contamination is present. Furthermore, we utilize the bootstrapping technique to calculate the PCI's CIs and illustrate how bias in these hypothesis testing procedures can be decreased by implementing the recommended bootstrap methodology. Last, the effectiveness of the proposed indexing and estimating methodologies is demonstrated through a reanalysis of two datasets from the electronic industries.