In order to obtain distribution parameter estimates, points ( τ i, p i ) first need to be obtained, and then a distribution curve based on the points needs to be assigned. Thirdly, improve the original weighted least square method with a new weight function, which consider the number of failed samples. Secondly, we use the unevenness of the distribution function and the function characteristics to determine the value range of the failure probability. Firstly, based on the E-Bayesian estimation and the distribution curve method, we develop a confidence interval method. In order to overcome the above problems, we propose a new reliability assessment method based on the E-Bayesian. Furthermore, in the process of solving the distribution parameters by using the distribution curve, the weight of the weighted least square method used does not consider the role of the failure sample, which makes the obtained reliability higher. In addition, most E-Bayesian estimation methods assume that the range of failure probability is (0, 1), it does not consider the relationship between the failure probability of each truncation time, which causes the range of failure probability values to be too large, and affects the accuracy.
If the calculation method of confidence interval estimation is different from point estimation, the credibility of the results will reduce. The current E-Bayesian estimation methods mainly focus on point estimation of parameters, which do not solve the problem of confidence interval estimation. Jia proposed an improved method based on the Bayesian inference and least-squares method, and the four existing methods were com-pared with this method in terms of applicability, precision, efficiency, robustness, and simplicity. Compared with the hierarchical Bayesian method, the E-Bayesian estimation method simplifies the mathematical model and improves the calculation efficiency. Based on the modification of the hierarchical Bayesian estimation method, the E-Bayesian estimation method was proposed. The hierarchical Bayesian method generalizes the current Bayesian method to provide the ability to perform parameter point estimation and confidence interval estimation at the same time, which effectively improves the credibility of the results. It can effectively avoid the aggressive phenomenon of reliability estimation results. Li proposed a reliability assessment method with revised confidence limits. Han reviewed the reliability assessment methods under zero-failure data conditions, and summarized the corresponding advantages, disadvantages and application ranges. Jiang developed a hybrid censoring index to quantitatively describe censoring characteristics of a data set, proposed a novel parameter estimation method based on information extracted from censored observations, and evaluated the accuracy and robustness of the proposed method through a numerical experiment. Jiang studied the problem of reliability estimation with zero failure data, in which the Bayesian prior distribution model was constructed by using the “kernel” idea. Denecke, Tan and Krishnamoorthy studied the method of solving lower confidence limit for Weibull distribution. Wang, Joarder and Kundu proposed MLE methods for Weibull parameters. Wang proposed a new inference for constant-stress accelerated life tests with Weibull distribution.
Many studies show that the life distribution of most mechanical products approximately follows Weibull distribution. In addition, by adjusting the shape parameters, Weibull distribution is also capable of describing the normal distribution approximately. The introduction of shape parameters makes it more accurate than the exponential distribution model in describing the products whose failure rate increases or decreases with time. The Weibull distribution model can be regarded as a generalization of the exponential distribution model. Weibull distribution was first proposed by Swedish scientist Weibull. Among them, Weibull distribution is the most flexible one. Normal distribution, exponential distribution and Weibull distribution are often used to describe the life distribution of products. The reliability evaluation method of the product is essentially a mathematical statistical method of specific censored data under specific distribution occasions.
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