Reliability analysis for q-Weibull distribution with multiply Type-Ⅰ censored data

摘要

The widely used Weibull distribution could be generalized to be q-Weibull distribution. To fill out the gap in existing literature, the reliability is studied for q-Weibull distribution with multiply Type-I censored data, which is the general form of Type-I censored data. The point estimates and confidence intervals (CIs) for q-Weibull parameters and reliability parameters such as the reliability and remaining lifetime are all focused on. The maximum likelihood estimates (MLE) are obtained by maximizing the likelihood function and transforming it to an unconstrained optimization problem. The least-square estimates (LSEs) are proposed by minimizing the single-variable profile error function derived from reducing the previous multivariable error function. These improvements could make the computation of point estimates efficient. Concerning the CIs, the asymptotic normality of log-transformed MLE is used to guarantee they fall into the value ranges. Particularly, the closed form for the Fisher information matrix is derived using the missing information principal and is combined with the delta method to construct the CIs for reliability. Besides, the bias-corrected and accelerated (BCa) bootstrap method is also applied. Further, a Monte Carlo simulation study is conducted to compare different point estimates and CIs. Finally, an illustrative example is presented to show the application of the study in this paper.