Narrow Results

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.

An experiment was conducted using the bootstrap maximum entropy method for reliability evaluation under the poor information condition. The analysis results were derived using the bootstrap maximum entropy method and compared with the results from the Bayesian statistics method. The bootstrap maximum entropy method did not rely on any prior information about the possibility distribution, which was proven to be scientific and reasonable when evaluating the reliability using small data samples.

This article introduces a new method, named M-Bayesian credible limit method, to estimate systems reliability derived from binomial distribution, in the case of zero-failure data. Firstly, the definition of M-Bayesian lower credible limit is provided. Moreover, formulas of M-Bayesian lower credible limits are provided. Secondly, properties of M-Bayesian lower credible limits is discussed, we will see that the M-Bayesian lower credible limit method is superior to the corresponding classical lower confidence limit method. Finally, the new estimation method is applied to a numerical example. Through the example the efficiency and easiness of operation of this method are commended.