Statistical inference of Weibull distribution based on generalized progressively hybrid censored data

Abstract

Weibull distribution and generalized progressive hybrid censoring scheme(GPHCS) have been used widely in reliability engineering. The GPHCS can improve the efficiency of statistical inference by allowing experimenters to observe a pre-assigned number of failure samples within a proper testing period. In this paper, we consider maximum likelihood, least squares (LS), weighted least squares (WLS) and maximum product of spacings (MPS) estimates for two-parameter Weibull distribution under the assumption that samples are generalized progressively hybrid censored. The maximum likelihood estimation (MLE) of unknown parameter is obtained using Newton–Raphson algorithm and expectation–maximization(EM) algorithm. The asymptotic normality of the MLE and bootstrap method are used to construct approximate confidence intervals. A parametric bootstrap goodness-of-fit(GOF) testing is proposed for the Weibull distribution with generalized progressively hybrid censored sample. Extensive Monte Carlo simulations are conducted to assess the proposed methods. Finally, one real data set is analyzed for illustrative purposes.