Parametric Estimation of the Asymmetric Loss Based Process Capacity Index Spk′′ Under Progressive Type‐II Censored Scheme

ABSTRACT This paper examines the estimation of the process capability index for the normal distribution based on progressively Type‐II right‐censored samples (PTIICS). Three estimation paradigms are explored: maximum likelihood estimation (MLE), maximum product of spacings (MPS), and Bayesian inference. Within the Bayesian framework, both likelihood‐based and product‐spacing–based formulations are employed under two loss functions‐the squared error loss and the linear exponential (LINEX) loss‐assuming a normal prior for the shift parameter and an inverse gamma prior for the scale parameter. In addition to point estimation, interval estimation is performed by constructing approximate confidence intervals using classical methods and percentile bootstrap confidence intervals for the model parameters, and by comparing these intervals with highest posterior density (HPD) credible intervals obtained from Bayesian procedures. A comprehensive Monte Carlo simulation study is conducted to assess the finite‐sample performance of the proposed estimators in terms of absolute bias, mean squared error, coverage probability, and average interval length. Moreover, the optimal design of the PTIICS is systematically determined using multiple optimality criteria to ensure efficient and reliable estimation. Finally, the practical applicability of the proposed methodologies is illustrated through the analysis of two real‐life datasets from the electronic industry. The results demonstrate that the proposed estimation techniques provide effective and reliable assessments of process capability under complex censoring schemes.