Application of power law model in reliability evaluation of machine tools by considering working condition difference

The influence of working condition difference has not been considered in the traditional reliability modeling of numerical control (NC) machine tools. To solve the problem, a reliability evaluation method based on mixture variable parameter power law model (MVPPLM) is proposed in this study. First, the scale parameter of the PLM is obtained by multi-dimensional exponential distribution. Second, a proportional relation of failure rate function between each working condition and reference working condition is established. The proportion coefficient is solved using the partial likelihood function. Working condition factors with a significant influence on reliability levels are selected through the chi-squared test. Third, reliability evaluation models under different working condition levels are established through mixture distributions. The mixture weight coefficient is calculated by the standard deviation of working condition covariates. The maximum likelihood estimation method is used to estimate parameters. Finally, results of a case analysis based on the data of NC machine tools in the user field tracing test show that the MVPPLM has higher precision than the traditional method. Therefore, reliability evaluation that considers working condition difference is valuable for engineering application.