数控机床的可靠性评估与不完全预防维修及其应用
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摘要
数控机床是先进制造的基础装备,其质量通常包含三个指标:即性能指标、可靠性和维修性指标。其中,性能指标的实现,很大程度上有赖于可靠性和维修性的保障。因此,研究数控机床的可靠性和维修性对于提高其质量具有重要意义。
目前在数控机床可靠性和维修性分析中存在的问题,主要有以下几个方面:
(1)现有的大多数数控机床可靠性评估模型过多的依赖甚至滥用不可修产品的统计分布模型;
(2)缺少针对多故障原因和多故障模式,特别是在使用环境、保养方式、操作水平、维修水平及首次使用时间各异的情况下的可靠性评估技术;
(3)有关可靠性评估指标的区间估计的研究较少或估计精度过低;
(4)针对数控机床的预防维修模型较少。
针对上述问题,本文做了以下工作:
(1)结合Nelson–Aalen和TTT图形检验方法和统计分析检验方法,提出了不同于不可修产品的多台数控机床时间截尾故障数据的综合趋势检验方法。为了确保评估模型的可靠性和准确性,应用该方法对数控机床进行可靠性分析时,需对故障数据按步骤分别进行趋势检验以及更新过程检验。
(2)用自助法和非齐次泊松过程方法分别给出了故障后修复如新和修复如旧的数控机床的可靠性评估结果。当数控机床故障后修复如新时,用自助法给出了可靠性模型的参数估计,包括点估计和区间估计。计算结果显示自助法较之传统的回归法,其所得参数的估计区间、标准差及模型标准残差均小于后者;当数控机床故障后修复如旧时,提出了基于随机点过程的多台NC机床时间截尾的可靠性评估的可修系统方法,建立了故障时间的幂律模型。用Fisher信息矩阵法给出了模型参数的点估计和区间估计,同时也给出了NC机床的累积平均故障间隔时间和累积故障强度在截尾时间的点估计和区间估计。Akaike信息准则(AIC)计算结果表明,对于故障时间具有某种单调趋势的NC机床可靠性评估,可修系统方法优于统计分布方法。模型通过了趋势检验和拟合优度检验。
(3)对于多故障模式和多原因的数控机床可靠性分析,提出了3-参数Weibull多重混合模型。用非线性规划方法解决了混合模型的参数估计难题,该方法以负对数似然函数为优化目标代替求解复杂方程组。采用AIC、Bayes信息准则(BIC)和根均方误差复合准则,优选混合模型重数。通过具体应用,给出了NC机床的可靠性评估结果。结果显示该模型优于单一模型,适合于多故障模式和多原因的数控机床可靠性分析。
(4)基于AIC和BIC信息准则,解决了多台NC机床可靠性评估模型和评估方法的选择问题。用Fisher信息矩阵法给出了模型参数和机床平均寿命的可靠度及给定可靠度的工作保证时间的区间估计,用Monte Carlo仿真法扩大少样本数据的样本容量,提高了区间估计的精度。结果显示,平均寿命的可靠度及可靠度为90%时的工作保证时间的区间估计长度分别减少了93%、95%。
(5)给出了Kijima型广义更新过程不完全维修恢复因子的数值解法。推导了Kijima型广义更新过程故障时间的抽样公式,用Monte Carlo方法验证了所提方法的有效性和正确性。结果表明,在可修系统可靠性分析中,广义更新过程模型因考虑了系统的恢复因子,所以其评估结果较普通更新过程模型和幂律非齐次泊松过程模型更接近真实的维修环境,后两者只是广义更新过程模型的特殊情况。
(6)对处于磨损阶段的设备,在考虑可靠度的情况下,提出了系统任意维修质量的不完全顺序预防维修的混合模型,该模型综合考虑了修复因子和故障率增加因子的影响,并且假设修复因子和故障率增加因子均为服从均匀分布的随机变量,用迭代的方法给出了顺序预防维修时间,以平均费用为目标函数,给出了最佳的维修次数,分析了费用参数对目标函数的影响。结果显示为了满足高可靠性的要求,在预防维修中考虑可靠性是必要的和值得的。
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.
目前在数控机床可靠性和维修性分析中存在的问题,主要有以下几个方面:
(1)现有的大多数数控机床可靠性评估模型过多的依赖甚至滥用不可修产品的统计分布模型;
(2)缺少针对多故障原因和多故障模式,特别是在使用环境、保养方式、操作水平、维修水平及首次使用时间各异的情况下的可靠性评估技术;
(3)有关可靠性评估指标的区间估计的研究较少或估计精度过低;
(4)针对数控机床的预防维修模型较少。
针对上述问题,本文做了以下工作:
(1)结合Nelson–Aalen和TTT图形检验方法和统计分析检验方法,提出了不同于不可修产品的多台数控机床时间截尾故障数据的综合趋势检验方法。为了确保评估模型的可靠性和准确性,应用该方法对数控机床进行可靠性分析时,需对故障数据按步骤分别进行趋势检验以及更新过程检验。
(2)用自助法和非齐次泊松过程方法分别给出了故障后修复如新和修复如旧的数控机床的可靠性评估结果。当数控机床故障后修复如新时,用自助法给出了可靠性模型的参数估计,包括点估计和区间估计。计算结果显示自助法较之传统的回归法,其所得参数的估计区间、标准差及模型标准残差均小于后者;当数控机床故障后修复如旧时,提出了基于随机点过程的多台NC机床时间截尾的可靠性评估的可修系统方法,建立了故障时间的幂律模型。用Fisher信息矩阵法给出了模型参数的点估计和区间估计,同时也给出了NC机床的累积平均故障间隔时间和累积故障强度在截尾时间的点估计和区间估计。Akaike信息准则(AIC)计算结果表明,对于故障时间具有某种单调趋势的NC机床可靠性评估,可修系统方法优于统计分布方法。模型通过了趋势检验和拟合优度检验。
(3)对于多故障模式和多原因的数控机床可靠性分析,提出了3-参数Weibull多重混合模型。用非线性规划方法解决了混合模型的参数估计难题,该方法以负对数似然函数为优化目标代替求解复杂方程组。采用AIC、Bayes信息准则(BIC)和根均方误差复合准则,优选混合模型重数。通过具体应用,给出了NC机床的可靠性评估结果。结果显示该模型优于单一模型,适合于多故障模式和多原因的数控机床可靠性分析。
(4)基于AIC和BIC信息准则,解决了多台NC机床可靠性评估模型和评估方法的选择问题。用Fisher信息矩阵法给出了模型参数和机床平均寿命的可靠度及给定可靠度的工作保证时间的区间估计,用Monte Carlo仿真法扩大少样本数据的样本容量,提高了区间估计的精度。结果显示,平均寿命的可靠度及可靠度为90%时的工作保证时间的区间估计长度分别减少了93%、95%。
(5)给出了Kijima型广义更新过程不完全维修恢复因子的数值解法。推导了Kijima型广义更新过程故障时间的抽样公式,用Monte Carlo方法验证了所提方法的有效性和正确性。结果表明,在可修系统可靠性分析中,广义更新过程模型因考虑了系统的恢复因子,所以其评估结果较普通更新过程模型和幂律非齐次泊松过程模型更接近真实的维修环境,后两者只是广义更新过程模型的特殊情况。
(6)对处于磨损阶段的设备,在考虑可靠度的情况下,提出了系统任意维修质量的不完全顺序预防维修的混合模型,该模型综合考虑了修复因子和故障率增加因子的影响,并且假设修复因子和故障率增加因子均为服从均匀分布的随机变量,用迭代的方法给出了顺序预防维修时间,以平均费用为目标函数,给出了最佳的维修次数,分析了费用参数对目标函数的影响。结果显示为了满足高可靠性的要求,在预防维修中考虑可靠性是必要的和值得的。
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.
引文
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