Comparison between Bayesian Method and LSE in Estimating MTBF of NC Machine Tools

Aiming at the large bias of LSE (Least Squares Estimation) in estimating MTBF (mean time between failures) under a small sample of data, a Bayesian MTBF estimating method is proposed for NC (numerical control) machine tools. To solve difficulty in directly presenting the prior distributions of Weibull parameters, an expert-judgment method which incorporates prior information is developed to indirectly obtain Weibull parameters' prior distributions. Aiming at the problem that analytic solutions to Weibull parameters' posterior distributions and estimators are impossible to obtain, a Metropolis algorithm is developed. The iteration procedure of the algorithm is presented, the posterior distribution of each parameter is simulated, and the parameter estimators and MTBF are obtained. Given the actual MTBF as standard value, the proposed method and LSE are applied to the same real case respectively. The results indicate that when sample size n≤10, relative errors of the proposed method lie between 4.43% and 7.19%, which are smaller than those of LSE. The proposed Bayesian MTBF estimating method is better than LSE and suitable for NC machine tools under small samples.