Reliability Assessment And Imperfect Preventive Maintenance For NC Machine Tools And Their Applications

NC machine tools are basic equipments of advanced manufacturing, their quality usually consist of three indices including performance, reliability and maintainability index. Among them, the completeness of performance index partly depends on the guarantee of reliability and maintainability indices. Therefore, it is very important to study the reliability and maintainability of NC machine tools to improve their quality. At present, the main problems of reliability and maintainability analyses of NC machine tools are as follows:(1) Many existing models for reliability assessment of NC machine tools are much more rely heavily on or even abuse the statistical distribution model of non-repairable items.(2) Lacking of the solution to multiple failure modes and causes, especially to the different operation environment, types of maintenance, skills of maintenance and operation and the first service time.(3) Study on interval estimation of reliability assessment indices is still shortage or the accuracy of interval estimation is too low.(4) There exist few preventive maintenance models for NC machine tools.Aiming at the problems mentioned above, the following work is done:(1) Combing Nelson-Aalen and TTT graphical testing methods and statistical method together, a comprehensive trend testing method for failure data of multiple NC machine tools with time truncation is proposed. This method is different from one for non-repairable items. To guarantee the reliability and accuracy of estimated models of reliability analyses for NC machine tools, one should test failure data with trend testing and renewal process testing, respectively.(2) By using bootstrap method and non-homogeneous Poisson process method, reliability assessment for NC machine tools are presented when machine tools are restored to‘as good as new'and‘as bad as old'states after a repair, respectively. When machine tools are in‘as good as new'state, a bootstrap method of parameter estimation for reliability model is proposed and the estimators of point and interval are presented, respectively. The proposed method is validated by an application example, it is shown that this method is feasible and effective and the model has a smaller error and higher precision than traditional method; While machine tools are in‘as bad as old'state after a repair, based on stochastic point process, a repairable system approach of reliability evaluation for multi-NC machine tools with time truncation is proposed, and a power law model of failure times is presented. The point and confidence interval estimators of model parameters and reliability indices, such as cumulative MTBF and failure intensity at truncated time, are all given by FM method. The values of AIC show that repairable system approach performs advantage over statistical distribution method when failure times of NC machine tools have monotonic trend in reliability analyses. The proposed model is passed by trend testing and goodness-fit-test, respectively.(3) To analyze the reliability of NC machine tools, a 3-parameter Weibull mixture model is proposed. Negative log-likelihood function is used as an optimal objective instead of solving complex system of equations, the problem of parameter estimation of mixture model is solved by a nonlinear programming method. A comprehensive criteria, which includes Akaike information criterion, Bayesian information criterion and root mean squared error, is presented for selecting the number of components of mixture model. The field failure data of 3 NC machine tools are analyzed and the results of reliability assessment, such as the reliability, maintainability and availability etc., are all presented. The results show that the mixture model of 3-parameter Weibull distribution, with advantages over other Weibull models, is suitable for modelling failure data of multiple NC machine tools with multiple failure modes and causes.(4) Based on Akaike information criterion (AIC) and Bayesian information criterion (BIC), the problem of model selection and parameter estimation for time-between-failure of multiple NC machine tools with time truncation is solved. Confidence intervals of model parameters, the reliability of mean time between failure (MTBF) and warranty time with 90% reliability are all presented by Fisher Information Matrix method. Monte Carlo simulation method is used to enlarge size of small sample data and improve the accuracy of interval estimation. The results show that interval length of reliability given MTBF and operational time with 90% reliability are all reduced by 95% and 93%, respectively.(5) The sampling formulas of failure times for the generalized renewal process (GRP) I and II model are derived and the effectiveness of the proposed method is validated with Monte Carlo simulation method. The results show that the GRP model is superior to the ordinary renewal process and the power law non-homogeneous Poisson process model.(6) To determine the optimal maintenance number for a system with random maintenance quality in infinite time horizon, a sequential imperfect preventive maintenance model considering reliability limit is proposed. The proposed model is derived from the combination of the Kijima type virtual age model and the failure rate adjustment model. Maintenance intervals of the proposed model are obtained through an iteration method when both failure rate increase factor and maintenance restoration factor are random variables with a uniform distribution. The optimal maintenance policy is presented by minimizing the long-run average cost rate. A real numerical example for the failures of NC equipment is given to demonstrate the proposed model. Discussion is presented to show how the optimal average cost rate depends on the different cost parameters. The results show that in order to satisfy the practical requirements of high reliability, it's necessary and worthwhile to consider the system's reliability limit in preventive maintenance practice.