Virtual age models with time-dependent covariates: A framework for simulation, parametric inference and quality of estimation

Abstract A repairable system faces some failures and imperfect maintenances throughout its lifetime. If several identical and independent systems are considered together, some differences may arise between the systems, such as the geographical location or the maintenance team for example, which are constant information, or the weather conditions, which vary with time. This observed heterogeneity will influence more or less the failure process. In this paper, we include these data in a generalized virtual age model with the use of covariates. Then we estimate simultaneously the effect of the maintenances, that of the covariates, and the intrinsic wear of the systems. We also propose two simulation methods as well as a numerical estimation procedure. Then we assess the quality of the estimation of the parameters with a thorough simulation study.

[1]  B. Davis,et al.  Bayesian regression model for recurrent event data with event-varying covariate effects and event effect , 2018, Journal of applied statistics.

[2]  Jingyuan Shen,et al.  Periodic preventive maintenance planning for systems working under a Markovian operating condition , 2020, Comput. Ind. Eng..

[3]  Mouna Akacha,et al.  Sensitivity analyses for partially observed recurrent event data , 2016, Pharmaceutical statistics.

[4]  Laurent Doyen,et al.  On geometric reduction of age or intensity models for imperfect maintenance , 2015, Reliab. Eng. Syst. Saf..

[5]  Christophe Bérenguer,et al.  Simulation and Parameter Estimation for Virtual Age Models with Time-Dependent Covariates: Methodology and Performance Evaluation , 2019 .

[6]  Shaomin Wu,et al.  Decline and repair, and covariate effects , 2015, Eur. J. Oper. Res..

[7]  Marek Balazinski,et al.  Estimating the remaining useful tool life of worn tools under different cutting parameters: A survival life analysis during turning of titanium metal matrix composites (Ti-MMCs) , 2016 .

[8]  Odd O Aalen,et al.  Dynamic Analysis of Recurrent Event Data Using the Additive Hazard Model , 2006, Biometrical journal. Biometrische Zeitschrift.

[9]  Qiang Zhou,et al.  Remaining useful life prediction of individual units subject to hard failure , 2014 .

[10]  M. Kijima.  SOME RESULTS FOR REPAIRABLE SYSTEMS WITH GENERAL REPAIR , 1989 .

[11]  Qiang Zhou,et al.  Prediction of hard failures with stochastic degradation signals using Wiener process and proportional hazards model , 2018, Comput. Ind. Eng..

[12]  L. Fisher,et al.  Time-dependent covariates in the Cox proportional-hazards regression model. , 1999, Annual review of public health.

[13]  Ralf Bender,et al.  Generating survival times to simulate Cox proportional hazards models , 2005, Statistics in medicine.

[14]  Jean-Yves Dauxois,et al.  Statistical Inference in a Model of Imperfect Maintenance With Arithmetic Reduction of Intensity , 2018, IEEE Transactions on Reliability.

[15]  Laurent Doyen,et al.  Classes of imperfect repair models based on reduction of failure intensity or virtual age , 2004, Reliab. Eng. Syst. Saf..

[16]  Laurent Doyen,et al.  Parametric Bootstrap Goodness-of-Fit Tests for Imperfect Maintenance Models , 2016, IEEE Transactions on Reliability.

[17]  Olivier Gaudoin,et al.  Semiparametric inference for an extended geometric failure rate reduction model , 2019, Journal of Statistical Planning and Inference.

[18]  Jianwen Cai,et al.  Multiplicative rates model for recurrent events in case-cohort studies , 2019, Lifetime data analysis.

[19]  Shanshan Li,et al.  Recurrent event data analysis with intermittently observed time‐varying covariates , 2016, Statistics in medicine.

[20]  Yanyan Liu,et al.  Analysis of multivariate recurrent event data with time-dependent covariates and informative censoring. , 2012, Biometrical journal. Biometrische Zeitschrift.

[21]  L. Bordes,et al.  Semiparametric estimate of the efficiency of imperfect maintenance actions for a gamma deteriorating system , 2020, Journal of Statistical Planning and Inference.

[22]  Deng Pan,et al.  Analysis of a fixed center effect additive rates model for recurrent event data , 2017, Comput. Stat. Data Anal..

[23]  Yves Le Gat,et al.  Integration of time-dependent covariates in recurrent events modelling : application to failures on drinking water networks , 2014 .

[24]  P. Novák.  Regression Models for Repairable Systems , 2015 .

[25]  Edsel A. Peña,et al.  Asymptotics for a class of dynamic recurrent event models , 2014, Journal of nonparametric statistics.

[26]  Qiang Zhou,et al.  Remaining useful life prediction for hard failures using joint model with extended hazard , 2018, Qual. Reliab. Eng. Int..

[27]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[28]  Rui Peng,et al.  A two-phase preventive maintenance policy considering imperfect repair and postponed replacement , 2019, Eur. J. Oper. Res..

[29]  Li Li,et al.  A Bayesian semiparametric regression model for reliability data using effective age , 2014, Comput. Stat. Data Anal..

[30]  Mitra Fouladirad,et al.  Statistical inference for imperfect maintenance models with missing data , 2016, Reliab. Eng. Syst. Saf..

[31]  Sophie Mercier,et al.  Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system , 2019, Eur. J. Oper. Res..

[32]  Lin Ma,et al.  Mixed arithmetic reduction model for two-unit system maintenance , 2017, 2017 Second International Conference on Reliability Systems Engineering (ICRSE).

[33]  Maurizio Guida,et al.  Repairable system analysis in presence of covariates and random effects , 2014, Reliab. Eng. Syst. Saf..

[34]  Sy Han Chiou,et al.  Joint Scale-Change Models for Recurrent Events and Failure Time , 2017, Journal of the American Statistical Association.

[35]  Yutao Liu,et al.  Joint analysis of recurrent event data with additive–multiplicative hazards model for the terminal event time , 2018 .

[36]  Weiwen Peng,et al.  Reliability analysis of repairable systems with recurrent misuse-induced failures and normal-operation failures , 2018, Reliab. Eng. Syst. Saf..

[37]  Xiao Liu,et al.  Analysis of Large Heterogeneous Repairable System Reliability Data With Static System Attributes and Dynamic Sensor Measurement in Big Data Environment , 2020, Technometrics.

[38]  Bo Henry Lindqvist,et al.  Nonhomogeneous Poisson process with nonparametric frailty and covariates , 2017, Reliab. Eng. Syst. Saf..

[39]  Annamraju Syamsundar,et al.  Imperfect Repair Proportional Intensity Models for Maintained Systems , 2011, IEEE Transactions on Reliability.

[40]  L. Yeh.  Nonparametric inference for geometric processes , 1992 .

[41]  Per Kragh Andersen,et al.  Modeling marginal features in studies of recurrent events in the presence of a terminal event , 2019, Lifetime Data Analysis.

[42]  D. Cox.  Regression Models and Life-Tables , 1972 .

[43]  Liuquan Sun,et al.  A semiparametric additive rates model for the weighted composite endpoint of recurrent and terminal events , 2020, Lifetime data analysis.

[44]  Xianghua Luo,et al.  Semiparametric regression analysis for alternating recurrent event data , 2018, Statistics in medicine.

[45]  Julio Mulero,et al.  A modelling approach to optimal imperfect maintenance of repairable equipment with multiple failure modes , 2019, Comput. Ind. Eng..

[46]  Hoang Pham,et al.  A quasi renewal process and its applications in imperfect maintenance , 1996, Int. J. Syst. Sci..

[47]  Sharareh Taghipour,et al.  Modeling Failure Process and Quantifying the Effects of Multiple Types of Preventive Maintenance for a Repairable System , 2017, Qual. Reliab. Eng. Int..