The Process Capability Index of Pareto Model under Progressive Type-II Censoring: Various Bayesian and Bootstrap Algorithms for Asymmetric Data

It is agreed by industry experts that manufacturing processes are evaluated using quantitative indicators of units produced from this process. For example, the (Formula presented.) process capability index is usually unknown and therefore estimated based on a sample drawn from the requested process. In this paper, (Formula presented.) process capability index estimates were generated using two iterative methods and a Bayesian method of estimation based on stepwise controlled type II data from the Pareto model. In iterative methods, besides the traditional probability-based estimation, there are other competitive methods, known as bootstrap, which are alternative methods to the common probability method, especially in small samples. In the Bayesian method, we have applied the Gibbs sampling procedure with the help of the significant sampling technique. Moreover, the approximate and highest confidence intervals for the posterior intensity of (Formula presented.) were also obtained. Massive simulation studies have been performed to evaluate the behavior of (Formula presented.). Ultimately, application to real-life data is seen to demonstrate the proposed methodology and its applicability.