Abstract
Aiming at the problem that the parameter interval estimation of NC machine tool’s reliability model considering working conditions established by Hongzhou is difficult to implement, given that it has several independent variables, an improved interval estimation method based on Bootstrap is proposed. Firstly, the two-step estimation method was used to calculate the point estimation of NC machine tool’s reliability parameter in test field, based on which B resamplings are generated based on the point estimation. The reliability parameter’s point estimation of the resamplings was obtained by maximum likelihood estimation. Permutation of B point estimations was made in ascending order and the interval estimations were obtained by the α quantile of the permutation. Case study indicated that the location and length of the interval estimation of NC machine tools’ reliability parameter, under different levels of working condition covariates, vary obviously.
Highlights
Aiming at the problem that the parameter interval estimation of NC machine tool’s reliability model considering working conditions established by Hongzhou is difficult to implement, given that it has several independent variables, an improved interval estimation method based on Bootstrap is proposed
Permutation of B point estimations was made in ascending order and the interval estimations were obtained by the α quantile of the permutation
Case study indicated that the location and length of the interval estimation of NC machine tools’ reliability parameter, under different levels of working condition covariates, vary obviously
Summary
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. 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. Aiming at the above problem, a reliability model parameter’s interval estimation method of NC machine tools considering working conditions based on the Bootstrap method is proposed in this paper. The feasibility of the proposed method is validated in the case study
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