Classical and generalized inference for a process capability index from a bounded lifetime population under censoring

Process capability indices (PCIs), essential in manufacturing, engineering, and quality management, quantify process performance, ensuring specification compliance and facilitating continuous improvement. While traditional PCI analysis assumes normality, industrial quality processes often exhibit bounded characteristics violating this assumption. For such scenarios, statistical inference is considered for the PCI given quality characteristics following a bounded lifetime distribution. Classical likelihood-based estimation is discussed under Type-II censoring; the existence and uniqueness of the model parameters are established. For comparison, alternative generalized approach are further proposed to estimate the PCI using constructed pivotal quantities. Finally, extensive simulation studies are conducted to compare the performance of different methods, and two real-life examples are also presented for illustration. The results demonstrate that the proposed generalized methods outperform traditional classical approach in general.