Imprecise Bayes Analysis of Component Reliability Based on Four-parameter Weibull Distribution

The reliability function, distribution function, hazard function and probability density function of component life are the basis of component reliability research. However, when the sample data is lacking, the precise point probability cannot be obtained according to the law of large numbers, and the probability distribution information of component life is presented as an imprecise interval probability. To solve this problem, this paper firstly chooses the four-parameter Weibull (FPW) distribution with multiple parameters and more flexible and adjustable curve as the research object. Then, starting from the imprecise Bayesian theory, according to the scale parameters that obey gamma distribution and the lifetime of random variation that obey FPW distribution, the upper and lower bound expressions of reliability function and hazard function are carried out by imprecise probability inference. Finally, the validity of the proposed method is verified by finite lifetime samples of a component of electronic device.