Abstract
The existing methods of determining testing period do not consider the effect of working condition covariates on reliability testing period of Numerical Control (NC) machine tools, which may lead to high-cost testing or low-precision assessment. Aiming at the problem, a new method of determining the testing period considering working condition covariates is proposed. The change rate of interval estimation of Mean Time between Failures (MTBF) is used as the criterion for determining the length of testing period. The reliability model of NC machine tools is established by the Cox proportional hazards model, and the two-step estimation method is used to estimate parameters of the baseline failure rate function and the coefficients of working condition covariates. The Bootstrap resamples are obtained by the Bootstrap resampling method. And then the parameters of the baseline failure rate function and the coefficients of working condition covariates are estimated simultaneously by maximum likelihood method, and thus interval estimations of MTBF under each covariate are obtained. The change rate models of MTBF interval estimation under each covariate level are established by Power function, and the testing periods under each covariate are obtained. Case study indicates that the testing periods under each covariate obtained by the proposed method are more accurate than those obtained by the others, when the same criterion and confidence level 1-α are set.
Highlights
Field reliability test is the basic method of reliability assessment for Numerical Control (NC) machine tools
The existing methods of determining testing period do not consider the effect of working condition covariates on reliability testing period of Numerical Control (NC) machine tools, which may lead to high-cost testing or low-precision assessment
The change rate models of Mean Time between Failures (MTBF) interval estimation under each covariate level are established by Power function, and the testing periods under each covariate are obtained
Summary
Field reliability test is the basic method of reliability assessment for NC machine tools. Mchane determined the number of test pieces and test period based on the width of interval estimation of pivot, when Time between Failures (TBF) of the product followed logarithmic position-scale model [2]. Zhou implemented the reliability assessment process of abrasion units and overloading units using Bayesian methods [10] It can be deduced from the above studies that the worse the working conditions are, the shorter the testing period is. The parameters of the baseline failure rate function and the coefficients of working condition covariates are estimated simultaneously by maximum likelihood method, and interval estimations of MTBF under each covariate are obtained. The change rate models of MTBF interval estimation under each covariate level are established by Power function, and the testing periods under each covariate are obtained.
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