Bayesian and non-Bayesian analysis for the lifetime performance index based on generalized order statistics from Pareto distribution

Modern businesses depend on efficient management and evaluation of product quality performance to assure that they are on the right track, and process capability analysis is used to gauge business performance in practice. Consequently, the lifetime performance index (LPI) , where  is the lower specification limit, is used to gauge a process potential and performance. This paper examines distinct estimators of  under Pareto distribution using generalized order statistics (GOS), which is very helpful in a variety of real-world applications. Results for progressive type II censoring (PTIIC) and first-failure censoring are two particular situations. Using symmetric and asymmetric loss functions, the Bayesian estimator was built, then utilized to produce the  hypothesis testing technique. A simulation study and real data analysis have been investigated to study the behavior of different estimates for  under different schemes, namely PTIIC and the progressive first failure censored scheme.