Reliability Evaluation of NC Machine Tools considering Working Conditions

Abstract

Reliability evaluation is the basis for reliability design of NC machine tools. Since traditional reliability evaluation methods do not consider the working conditions’ effects on reliability, there is a great error of a result of a traditional method compared with an actual value. A new reliability evaluation model of NC machine tools is proposed based on the Cox proportional hazards model, which describes the mathematical relation between the working condition covariates and the reliability level of NC machine tools. Firstly, the coefficients of working condition covariates in the new reliability evaluation model are estimated by the partial likelihood estimation method; secondly, the working condition covariates which have no effects on the reliability of NC machine tools are eliminated by the likelihood ratio test; then parameters of the baseline failure rate function are estimated by the maximum likelihood estimation method. Thus, the reliability evaluation model of NC machine tool is obtained under different working conditions and the reliability level of NC machine tools is obtained. Case study shows that the proposed method could establish the relation between the working condition covariates and the reliability level of NC machine tools, and it would provide a new way for the reliability evaluation of NC machine tools.

Reliability Parameter Interval Estimation of NC Machine Tools considering Working Conditions

“…For convenience, the failure rate function of NC machine tools considering working conditions in [1] is expressed as follows:…”

“…Point estimations, includinĝ,̂, and̂, of the shape parameter , the scale parameter , and coefficients of working condition covariates are calculated by two-step interval estimation in [1], according to the fault information and the working conditions corresponding to fault information obtained from the test field.…”

“…The parameter interval estimations are made according to the test data in [1] which is shown in Table 1 for convenience to discuss.…”

“…The reliability model of NC machine tools considering working conditions was established in [1], and the point estimations of the shape parameter, scale parameter, and the coefficients of working condition covariates were obtained by the two-step estimation method. To make NC machine tool's reliability evaluation more accurate, the interval estimations of the shape parameter, scale parameter, and the coefficients of working condition covariates should be made.…”

“…Each of the above interval estimation methods usually establishes, respectively, the interval estimation formula with only one independent variable. However, there are several independent variables of the reliability model in [1], including Time between Failure (TBF) and working condition covariates, which make it difficult for the above methods to calculate the model parameters' interval estimation.…”