Interval Estimation of the Common Shape Parameter and Coefficient of Variation of Several Weibull Populations under Progressive Censoring

Abstract: The Weibull distribution is one of the most flexible continuous probability distributions used to model various failure rates and skewed data in reliability engineering, industry, weather studies and cancer studies. It is a common scenario in statistical inference that several Weibull populations share the same shape parameter, which also implies that they have the same coefficient of variation. While the inferential study of the common shape parameter is often considered for complete samples, the presence of censored data requires a separate investigation that has not received enough attention in the existing literature. Therefore, the focus of this article is on a comparative study of interval estimators for the common shape parameter and the common coefficient of variation under progressive type-II censoring using frequentist methods based on large-sample theory, variance estimates recovery, generalized pivots, and Bayesian inference. An optimal censoring scheme is also proposed to enhance the robustness of interval estimation. Numerical data analyses using a simulation study and a real carbon fiber strength data example are carried out for comparison, and the results recommend the intervals based on Bayesian and variance estimates recovery methods for their satisfactory performance.