Bayesian zero-failure reliability modeling and assessment method for multiple numerical control (NC) machine tools

Abstract

A new problem that classical statistical methods are incapable of solving is reliability modeling and assessment when multiple numerical control machine tools (NCMTs) reveal zero failures after a reliability test. Thus, the zero-failure data form and corresponding Bayesian model are developed to solve the zero-failure problem of NCMTs, for which no previous suitable statistical model has been developed. An expert-judgment process that incorporates prior information is presented to solve the difficulty in obtaining reliable prior distributions of Weibull parameters. The equations for the posterior distribution of the parameter vector and the Markov chain Monte Carlo (MCMC) algorithm are derived to solve the difficulty of calculating high-dimensional integration and to obtain parameter estimators. The proposed method is applied to a real case; a corresponding programming code and trick are developed to implement an MCMC simulation in WinBUGS, and a mean time between failures (MTBF) of 1057.9 h is obtained. Given its ability to combine expert judgment, prior information, and data, the proposed reliability modeling and assessment method under the zero failure of NCMTs is validated.