Maintenance Policy for a System With Stochastically Dependent Failure Modes With Shock-Accumulation Effect

In this paper, a stochastic failure model for a system with two dependent failures is proposed and a maintenance policy for such system is studied. The system can fail due to two causes of failure: the failure due to accumulated wear and that due to the catastrophic failure. We analyze the dependence structure of the two competing failure modes. Based on these properties, we develop a maintenance strategy for such system and study the optimal maintenance policy which minimizes the long-run average cost rate.

[1]  J. Rice.  On generalized shot noise , 1977, Advances in Applied Probability.

[2]  Ling-Yau Chan,et al.  Maintenance of continuously monitored degrading systems , 2006, Eur. J. Oper. Res..

[3]  J. Cha,et al.  A stochastic failure model with dependent competing risks and its applications to condition-based maintenance , 2015 .

[4]  Khac Tuan Huynh,et al.  Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks , 2012, Eur. J. Oper. Res..

[5]  Nader Ebrahimi.  MULTIVARIATE AGE REPLACEMENT , 1997 .

[6]  J. Cha.  On a better burn-in procedure , 2000, Journal of Applied Probability.

[7]  T. Aven,et al.  A general minimal repair model , 2000, Journal of Applied Probability.

[8]  Antoine Grall,et al.  A sequential condition‐based repair/replacement policy with non‐periodic inspections for a system subject to continuous wear , 2003 .

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

[10]  H. Saunders,et al.  Probabilistic models of cumulative damage , 1985 .

[11]  Axel Lehmann.  Degradation-Threshold-Shock Models , 2006 .

[12]  Terje Aven.  Condition based replacement policiesa counting process approach , 1996 .

[13]  F. G. Badía,et al.  Optimization of inspection intervals based on cost , 2001, Journal of Applied Probability.

[14]  Y. S. Sherif,et al.  Optimal maintenance models for systems subject to failure–A Review , 1981 .

[15]  Khac Tuan Huynh,et al.  A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events , 2011, Reliab. Eng. Syst. Saf..

[16]  E. Lehmann.  Some Concepts of Dependence , 1966 .

[17]  Chanseok Park,et al.  Stochastic degradation models with several accelerating variables , 2006, IEEE Transactions on Reliability.

[18]  Soumaya Yacout,et al.  Replacement Models with Minimal Repair , 2011 .

[19]  J. Cha.  Burn-in procedures for a generalized model , 2001, Journal of Applied Probability.

[20]  Henk C. Tijms,et al.  A First Course in Stochastic Models: Tijms/Stochastic Models , 2003 .

[21]  C. Cuadras.  On the Covariance between Functions , 2002 .

[22]  Inmaculada Torres Castro,et al.  A condition-based maintenance for a system subject to multiple degradation processes and external shocks , 2015, Int. J. Syst. Sci..

[23]  Richard M. Feldman,et al.  A survey of preventive maintenance models for stochastically deteriorating single-unit systems , 1989 .

[24]  Inmaculada Torres Castro,et al.  A condition-based maintenance of a dependent degradation-threshold-shock model in a system with multiple degradation processes , 2015, Reliab. Eng. Syst. Saf..

[25]  Austin J. Lemoine,et al.  On failure modeling , 1985 .

[26]  Antoine Grall,et al.  Continuous-time predictive-maintenance scheduling for a deteriorating system , 2002, IEEE Trans. Reliab..

[27]  Ji Hwan Cha.  A further extension of the generalized burn-in model , 2003, Journal of Applied Probability.

[28]  Nozer D. Singpurwalla,et al.  Survival in Dynamic Environments , 1995 .

[29]  K. S. Chaudhuri,et al.  An EOQ model for items with weibull distribution deterioration, shortages and trended demand: an extension of philip's model , 1998, Comput. Oper. Res..

[30]  M. Ciampoli.  Time dependent reliability of structural systems subject to deterioration , 1998 .

[31]  Hongzhou Wang,et al.  A survey of maintenance policies of deteriorating systems , 2002, Eur. J. Oper. Res..

[32]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[33]  Jie Mi.  BURN-IN AND MAINTENANCE POLICIES , 2008 .

[34]  J. Shanthikumar,et al.  Multivariate Stochastic Orders , 2007 .

[35]  M. Bagnoli,et al.  Log-concave probability and its applications , 2004 .

[36]  Austin J. Lemoine,et al.  Technical Note - A Note on Shot-Noise and Reliability Modeling , 1986, Oper. Res..