Reliability Parameter Interval Estimation of NC Machine Tools considering Working Conditions

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.

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A Reliability Analysis of NC Machine Tools Based on the Weibull Distribution

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.741.763 ◽

2015 ◽

Vol 741 ◽

pp. 763-767

Author(s):

Hui Liang Li

Keyword(s):

Weibull Distribution ◽

Machine Tool ◽

Machine Tools ◽

Interval Estimation ◽

Point Estimation ◽

Numerical Control ◽

Control Machine Tool ◽

Failure Data ◽

Nc Machine ◽

Nc Machine Tools

In this paper, a series of numerical control machine tool truncated failure data collect.The data are assumed to be two parameter weibull distribution and related parameters is obtained and relevant inspection and test of hypothesis, it is concluded that the mathematical model of batch of nc machine tool failure interval time distribution.Relevant indicators to determine the reliability of nc machine tools, machine tool's observations, Machine tool observations, point estimation and interval estimation index value provide a theoretical basis for the research on reliability of machine tool.

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Reliability Analysis Based on Improved Bayes Method of AMSAA Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.482-484.2336 ◽

2012 ◽

Vol 482-484 ◽

pp. 2336-2340

Author(s):

Yang Qiang ◽

Lei Zhang ◽

Zhi Li Sun ◽

Yi Liu ◽

Xue Bin Bai

Keyword(s):

Reliability Analysis ◽

Machine Tools ◽

Interval Estimation ◽

Point Estimation ◽

Life Data ◽

Failure Data ◽

Amsaa Model ◽

Nc Machine ◽

Nc Machine Tools ◽

Five Axis

Aiming at the defects that failure samples of five-axis NC machine tools is small, traditional reliability analysis is not accurate, this paper presents reliability analysis mode based on improved Bayesian method for AMSAA model. Firstly, we obtain the failure model of NC machine tools meets the AMSAA model according to goodness-of-fit test, and in order to meet the requirements of simplifying engineering calculations, this paper adpots a method of Coefficient equivalent which converts failure Data into index-life data; then using Bayesian methods to estimate reliability parameters for the Index-life data; for the last we proceed point estimation and interval estimation for the MTBF of the machine. Take High-speed five-axis NC machine tools t of VMC650m for example, the result proved that the method can take advantage of a small sample of the equipment to proceed point estimation and interval estimation for MTBF failure data, and provide a reference for the optimization of maintenance strategies and Diagnostic work of the NC machine tools.

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Reliability Evaluation of NC Machine Tools considering Working Conditions

Mathematical Problems in Engineering ◽

10.1155/2016/9842607 ◽

2016 ◽

Vol 2016 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

Hongzhou Li ◽

Zhaojun Yang ◽

Binbin Xu ◽

Chuanhai Chen ◽

Yingnan Kan ◽

...

Keyword(s):

Working Conditions ◽

Machine Tools ◽

Working Condition ◽

Evaluation Model ◽

Estimation Method ◽

Likelihood Estimation ◽

Reliability Evaluation ◽

Reliability Level ◽

Nc Machine ◽

Nc Machine Tools

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.

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Design of Testing Period for Reliability Assessment of Numerical Control Machine Tools Considering Working Conditions

Mathematical Problems in Engineering ◽

10.1155/2018/1962064 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8

Author(s):

Li Hongzhou ◽

Sun Lixia

Keyword(s):

Machine Tools ◽

Working Condition ◽

Interval Estimation ◽

Rate Function ◽

Numerical Control ◽

Failure Rate Function ◽

Change Rate ◽

Testing Period ◽

Nc Machine ◽

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. 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.

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