Reliability Analysis of Repairable Systems With Dependent Component Failures Under Partially Perfect Repair

Existing reliability models for repairable systems with a single component can be well applied for a range of repair actions from perfect repair to minimal repair. Establishing reliability models for multi-component repairable systems, however, is still a challenge problem when considering the dependency of component failures. This paper focuses on a special repair assumption, called partially perfect repair, for repairable systems with dependent component failures, where only the failed component is repaired to as good as new condition. A parametric reliability model is proposed to capture the statistical dependency among different component failures, in which the joint distribution of the latent component failure time is established using copula functions. The model parameters are estimated by using the maximum likelihood method, and the maximum likelihood function is calculated based on the conditional probability. Based on the proposed reliability model, statistical hypothesis testing procedures are developed to determine the dependency of component failures. The developed methods are illustrated with an application in a cylinder head assembling cell that consists of multiple stations.

[1]  Hoang Pham,et al.  Optimal (τ, T) opportunistic maintenance of a k‐out‐of‐n:G system with imperfect PM and partial failure , 2000 .

[2]  S. Osaki,et al.  Optimal replacement policies for a two-unit system with shock damage interaction , 2003 .

[3]  Ling Wang,et al.  A condition-based replacement and spare provisioning policy for deteriorating systems with uncertain deterioration to failure , 2009, Eur. J. Oper. Res..

[4]  Ả. Svensson,et al.  Asymptotic estimation in counting processes with parametric intensities based on one realization , 1990 .

[5]  Philip A. Scarf,et al.  Block replacement policies for a two‐component system with failure dependence , 2003 .

[6]  P. X. Song,et al.  Multivariate Dispersion Models Generated From Gaussian Copula , 2000 .

[7]  Hassan Zahedi,et al.  Repairable Systems Reliability: Modeling, Inference, Misconceptions and Their Causes , 1989 .

[8]  R. Rebonato,et al.  The Most General Methodology to Create a Valid Correlation Matrix for Risk Management and Option Pricing Purposes , 2011 .

[9]  Yong Chen,et al.  Monte Carlo Methods for Reliability Evaluation of Linear Sensor Systems , 2011, IEEE Transactions on Reliability.

[10]  Yili Hong,et al.  Failure Profile Analysis of Complex Repairable Systems With Multiple Failure Modes , 2012, IEEE Transactions on Reliability.

[11]  T. Nakagawa,et al.  Optimal replacement policies for a two-unit system with failure interactions , 1993 .

[12]  Yada Zhu,et al.  Availability optimization of systems subject to competing risk , 2010, Eur. J. Oper. Res..

[13]  D. N. P. Murthy,et al.  Study of a multi-component system with failure interaction , 1985 .

[14]  Zhengqiang Pan,et al.  Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes , 2011, Reliab. Eng. Syst. Saf..

[15]  Axel Lehmann.  Joint modeling of degradation and failure time data , 2009 .

[16]  Qingyu Yang,et al.  Sensor system reliability modeling and analysis for fault diagnosis in multistage manufacturing processes , 2009 .

[17]  Yaping Wang,et al.  Modeling the Dependent Competing Risks With Multiple Degradation Processes and Random Shock Using Time-Varying Copulas , 2012, IEEE Transactions on Reliability.

[18]  Yong Chen,et al.  Reliability of Coordinate Sensor Systems Under the Risk of Sensor Precision Degradations , 2010, IEEE Transactions on Automation Science and Engineering.

[19]  Ralf A. Wilke,et al.  A copula model for dependent competing risks , 2009 .

[20]  Shey-Huei Sheu,et al.  Optimal age and block replacement policies for a multi-component system with failure interaction , 2000, Int. J. Syst. Sci..

[21]  Yaping Wang,et al.  A Multi-Objective Optimization of Imperfect Preventive Maintenance Policy for Dependent Competing Risk Systems With Hidden Failure , 2011, IEEE Transactions on Reliability.

[22]  Christophe Bérenguer,et al.  On the inspection policy of a two-component parallel system with failure interaction , 2005, Reliab. Eng. Syst. Saf..

[23]  Bo Henry Lindqvist,et al.  Statistical Modeling and Analysis of Repairable Systems , 2006, 0708.0362.

[24]  Antoine Grall,et al.  A maintenance policy for two-unit parallel systems based on imperfect monitoring information , 2006, Reliab. Eng. Syst. Saf..

[25]  David W. Coit,et al.  Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes , 2010 .

[26]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[27]  Shey-Huei Sheu,et al.  Optimal replacement of a k-out-of-n system subject to shocks , 1992 .

[28]  Hoang Pham,et al.  Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks , 2005, IEEE Trans. Reliab..

[29]  Ivan Žežula,et al.  On multivariate Gaussian copulas , 2009 .

[30]  Vladimir K. Kaishev,et al.  Modelling the joint distribution of competing risks survival times using copula functions , 2007 .

[31]  Helge Langseth,et al.  Competing risks for repairable systems : A data study , 2006 .

[32]  Loon Ching Tang,et al.  Bivariate constant stress degradation model: LED lighting system reliability estimation with two‐stage modelling , 2009, Qual. Reliab. Eng. Int..

[33]  R. Nelsen.  An Introduction to Copulas , 1998 .

[34]  Lei Jiang,et al.  Reliability and Maintenance Modeling for Dependent Competing Failure Processes With Shifting Failure Thresholds , 2012, IEEE Transactions on Reliability.