Modeling And Estimating Methods For The Failure Process Of Machine Tools Considering Multivariate Impacts

Numerical control machine tools play a crucial role in many manufacturing industries,and their reliability directly affects production efficiency and maintenance costs.An accurate reliability assessment is necessary to realize reliability design,reliability growth,and maintenance strategy optimization.The machine tool constitutes a complex repairable system,whose time between failures generally does not obey the same distribution.Therefore,in the reliability analysis,we should pay more attention to the change of time between continuous failures with age(referred to as the failure process).Compared with simple repairable systems,the failure process of machine tools is more complicated due to the impacts of maintenance and working conditions.Furthermore,the constraints of time,cost,human and equipment,make the data quality uneven.Different data quality affects the evaluation results.However,these characteristics have not been deeply explored in the existing research.Because of the above problems,this paper takes "model-estimation-evaluation-selection" as the main line,relies on the stochastic process theory,considers the impacts of maintenance,operating conditions,and data on the failure process,to analyze the reliability of machine tools.The main work is as follows.(1)A failure process model considering maintenance effects is proposed.Two problems motivate us to systematically study the impact of maintenance on age,scale and age-scale.First,the failure process of machine tools after repairs is not independent and identically distributed.Second,the maintenance strategies study requires a real repair model.Hence,we propose some virtual age models,scale models,and virtualage-scale models to evaluate the effects of corrective maintenance,preventive maintenance,and the both.Following that,a general expression of failure intensity covering various maintenance effects is established.Combining different maintenance effects and effect formulas can simplify this general expression into various specific failure intensity functions.(2)A failure process model considering the effects of working conditions is proposed.The failure process of machine tools under different working conditions is not the same and may not be monotonic(such as a bathtub curve).To better explain this problem,we discuss the multiplicative effect and cumulative effect of working conditions.A general expression of failure intensity considering the effects of maintenance and working conditions is established.Suppose the initial failure intensity obeys the Weibull distribution.In that case,a model in which the Weibull scale and shape parameters change with the working conditions and virtual age is further proposed.The diversity of fault intensity curves under different effects of maintenance and working conditions is verified by simulation analysis.(3)A point and interval estimation method and estimation process are proposed considering the influence of random window censored data.As for machine tools,the collected field data probably has a random window censoring problem,which may cause the estimating deviation and overfitting.To better estimate such data,we propose a conditional expectation likelihood function.Following that,a point and interval estimation method for model parameters,reliability function and cumulative failure intensity is proposed.In the process of parameter point estimation,three regularization techniques are introduced to prevent the estimation from overfitting.Besides,a general estimation process and pseudo-code framework are designed to facilitate the estimation of different models.(4)A model evaluation and selection method is proposed considering the influence of maintenance,working conditions and data.Since some evaluation indicators under the influence of random window-censored data do not obey a uniform distribution,the existing evaluation indicators are revised.Then,an appropriate pool of evaluating indicators is established.Furthermore,a new model optimization framework is proposed by borrowing the idea of stepwise regression to modify the existing framework which cannot select factors' effects.Finally,the above methods are applied to three real cases in the reliability analysis of machine tools.The proposed model and estimation methods are helpful for researchers to accurately obtain the reliability level of machine tools under different service conditions,thereby providing precise information for subsequent reliability design,reliability growth and maintenance strategy optimization.