Inference on the Weibull distribution with heavily censored data

Abstract

It is common and difficult to analyze the reliability based on heavily censored data in engineering application. For this problem, an improved method is proposed in this paper under the Weibull distribution based on the Bayesian theory and non-linear regression method with heavily censored data. First, prior distributions for failure probability at each time in sample are set using the Bayesian theory. Next, the hyper-parameters are determined when the information entropy of prior distribution is maximized to compute the Bayesian estimation of failure probabilities at the time in sample. Then, the Weibull parameters are estimated through the distribution curve fitting directly with the non-linear regression method using the data pairs of times in sample and corresponding failure probability estimations. Finally, after the comparison with existing methods by a Monte Carlo simulation study and the illustration of a real data example, the proposed method is proved to be accurate and robust.