Reliability Estimation of Weibull Distribution with Zero-Failure Data

Abstract

This paper focuses on the reliability estimation of Weibull distributions with zero-failure data. Since no product failure occurred in the tests, the conventional maximum likelihood method was not applicable. Recent methods ignore the estimation of location parameter and tend to be conservative. This study developed a new estimation technique to address these problems. A prior model between the life dispersion boundary and shape parameter is constructed by considering the historical failure data of similar high-reliability products. The failure probabilities for all samples were inferred using the E-Bayesian method, after which the reliability was estimated. Afterward, a confidence interval for reliability was obtained based on the bootstrap confidence interval and modified maximum likelihood method. A Monte Carlo simulation study demonstrated that the proposed method is satisfactory in terms of point estimates, confidence intervals, coverage probabilities, and computational efficiency. Finally, a real engineering example is introduced to illustrate the application of this method.