Modeling And Assessment Of Reliability Of NC Machine Tools In Service Stage Considering The Effect Of Repair Actions

In traditional assessment methods of reliability,the influences of repair and other factors on the reliability of machine tools are usually not considered,and the Weibull distribution,exponential distribution and lognormal distribution are usually used to estimate the reliability of machine tools under the assumption of “as good as new”.In fact,numerical control(NC)machine tools is a typical repairable system in its service cycle,repair actions run through the whole process of use,and the influence of different repair actions on system reliability are different.Repair actions often can bring the system to one of the following states: “as bad as old”,or “better than old,but worse than new”,that is “minimal repair” and “imperfect repair” assumptions are more realistically,therefore,according to the specific characteristic of the fault and repair of NC machine tools in different service stage,the effect of repair actions should be considered during the course of modeling,thus estimating the reliability of NC machine tools accurately and effectively.Aim at the problems and difficulties in the assessment of reliability of NC machine tools when considering the effect of repair actions,the assessment framework of reliability for NC machine tools in different service stage is constructed by taking the theory of stochastic point process as the core of technology and taking the immune clone selection algorithm and Bayesian theory as the supplementary means,and the assessment technology of reliability of NC machine tools in early failures stage,deterioration stage and the whole service stage are mainly studied,which can provide a theoretical reference and support for making a reasonable maintenance decision and improving the reliability of NC machine tools.The main contents of this paper are as follows:(1)The whole in-service stage of NC machine tools is divided and the specific characteristic of the fault and repair in each stage are analyzed.Then the critical problems in reliability assessment of NC machine tools under different maintenance conditions and in different in-service stage are proposed.To solve these problems and difficulties,the assessment framework of reliability for NC machine tools in the service stage is constructed.(2)Based on improved power law process model I and II,the assessment method of reliability of NC machine tools experiencing degradation phenomena in minimal repair is given,and aiming at the solving problem of model parameters and reliability indices,the immune clone maximum likelihood estimation method is proposed for solving the reliability model parameters.Convert the parameter estimation into an optimization issue with constraints,Perform optimization through setting the minimum negative logarithmic likelihood function as the objective function with the clone selection process by simulating biological immune system to obtain the optimal maximum likelihood point estimation and interval estimation of model parameters and reliability indices.The example verification indicates that the algorithm is feasible and effective.This algorithm also applies to solve reliability model parameters with four or more parameters and provides an effective new method for parameters estimation of reliability model.(3)A new continuous proportional intensity model with closed-form solutions is proposed base on the theory of bounded intensity process.The characteristics of the model are discussed,the formula of point maximum likelihood estimators for model parameters,as well as the important reliability indices such as the conditional reliability at given time,the s-expected number of failures,and the cumulative mean time between failure are all derived,the interval estimators of model parameters and reliability indices are given by using the Fisher information matrix method and delta method,then the assessment criterion of model is provided based on Akaike information criterion and the index of goodness-of-fit test.An example of real failure data from NC machine tools is taken to prove the proposed method,the results show that the closed-form solutions and confidence intervals of reliability indices for NC machine tools are obtained and the method is found very well uses in practical applications.(4)In minimal repair,in order to describe the failure process of NC machine tools experiencing both early failures and deterioration phenomena,and operating so long that the intensity function approaches a finite asymptote as the system operating time grows,a new four-parameter non-homogeneous Poisson process model is proposed.The characteristics of the model are discussed,and the physical meaning of its parameters is given,calculating formula of point estimation for model parameters and reliability indices such as the minimum intensity value and the time of minimum intensity are all derived,then a method of model selection for reliability assessment of two NC machine tools is provided based on the likelihood ratio statistic,and the model evaluation criterion is given based on the index of goodness-of-fit test.Finally,the real failure data of two NC machine tools are analyzed by using the proposed method,the results show that this method can quantitatively evaluate the machine tools' lasting time of early failure period,it is suitable for describing the failure process of NC machine tools with bounded and bathtub shaped failure trend,and can provide a theoretical basis for optimizing reliability test and eliminating as much early failures as possible before the NC machine tools leave the factory.(5)Based on deviance information criterion,Brooks-Gelman-Rubin diagnosis principle,Monte Carlo simulation error and the interval length of posterior estimate for model parameters and reliability indices,the comprehensive evaluation method for Bayesian reliability model of NC machine tools was proposed.The posterior distributions of power law process model used for Gibbs sampling under different priors were given,and the Bayesian point and interval estimate of model parameters and reliability indices were obtained by using Markov Chain Monte Carlo simulation.Finally,Bayesian reliability of NC machine tools in early failures stage and deterioration stage are analyzed respectively by using two real engineering examples,the results of each evaluation index show that the power law process model is better than Weibull model,and when the prior distribution of shape parameter ? is Beta distribution or Gamma distribution,the obtained analysis result are more close to the practical situation.