Bootstrap Interval Estimation of Reliability for Numerical Controlled Machine Tools Considering the Time-censored Data

Abstract

A larger error will be induced due to the lack of time-censored data in the re-sampling process when parametric Bootstrap method is applied to estimate the confidence interval of a reliability index of NC (Numerical controlled) machine tools, and aiming at this problem, a Bootstrap method fully utilizing the time-censored data of the NC machine tools is proposed. Firstly, the relation between the complete and time-censored data in the time-censored test of NC machine tools is analyzed, and the Bootstrap samples are generated based on this relation, solving the problem that the time-censored data can't be utilized in the Bootstrap's re-sampling process. The reliability parameters' point estimators are obtained by the maximum likelihood estimation and the Newton-Raphson. The bias-correction and accelerated method is used to decrease Biased error caused by the maximum likelihood, and then the confidence intervals are estimated. In combination with a real case, the principle of specifying the length of test time T and the number of the initially generated complete datum k are discussed and proved. The results indicates that, under the same confidence level, the length of the confidence interval estimated by the proposed method considering the time-censored data is shorter than those estimated by other interval estimation method, and can be used in the reliability evaluation of NC machine tools.