Bayesian Reliability Assessment Method for Single NC Machine Tool Under Zero Failures

Abstract

Reliability modeling and assessment for a single numerical control (NC) machine tool with zero-failure is a new problem that cannot be solved using classic statistical methods. Thus a Bayesian method is proposed aiming at this problem. In combination with the two-parameter Weibull distribution, the Bayes model of zero-failure problem for a single NC machine tool is built. The method of building the Weibull parameters’ prior distributions is presented. The theoretical formula for the parameter vector’s posterior distribution is derived. In software WinBUGS, the Markov chain Monte Carlo (MCMC) simulation is developed to simulate each parameter’s posterior distribution, solving calculation difficulties in high-dimensional integration and parameter estimation. The proposed method is applied to real data, obtaining the parameter estimators and meant time between failures (MTBF). The result is in consistent with the engineering reality. Given the fact that the actual MTBF cannot be achieved by any means, the proposed method achieves the fusion of the expert experience, multi-source prior information and data. The proposed method is advocated to be a standard solution to the zero-failure reliability assessment for NC machine tools.