Imprecise Reliability Analysis for Lifetime Modeling Based on Four-parameter Weibull Distribution

Abstract

Weibull distribution is one of the most classical distributions in the field of reliability applications. In order to improve the capability to fit various failure data, a number of extended forms of Weibull distribution have been proposed. In this paper, we will focused on the four-parameter Weibull distribution. It is difficult to estimate the parameters of fourparameter Weibull model accurately under limited failure data, but we can treat the parameter as a random variable and use the gamma distribution as a prior distribution to get the imprecise ones. From the view of impreciseness and Bayesian theory, we proposed a novel imprecise reliability analytical method named the Four-parameter Weibull-Gamma model which used for incomplete life data. The upper and lower bounds of the cumulative density function, the reliability function and the hazard function can also be obtained. Aiming at two cases that the hazard function is monotonically increasing or a bathtub shape, the experiments demonstrate the fitting effect of the proposed model, and the modeling capability of components or systems for different hazard function. Furthermore, it also verifies the multi-parameter of the proposed model can increase the adjustable flexibility of the distribution.