Conditional inspection and maintenance of a system with two interacting components

In this paper we consider the inspection and maintenance of a two-component system with stochastic dependence. A failure of component 1 may induce the defective state in component 2 which in turn leads to its failure. A failure of component 1 and a defect in component 2 are detected by inspection. Our model considers a conditional inspection policy: when component 1 is found to have failed, inspection of component 2 is triggered. This opportunistic inspection policy is a natural one to use given this stochastic dependence between the components. The long-run cost per unit time (cost-rate) of the conditional inspection policy is determined generally. A real system that cuts rebar mesh motivates the model development. The numerical examples reveal that when the ratio of the cost of corrective system replacement, that is on failure, to the cost of preventive system replacement is large there exists a finite optimum policy in most cases. Moreover, for the studied system wherein inspections of component 2 are expensive relative to those of component 1, having a reliable indicator of the defective state in component 2 is a good strategy to avoid costly failures of component 2, particularly when its time to failure is short.

[1]  D. N. P. Murthy,et al.  Study of two‐component system with failure interaction , 1985 .

[2]  P. Scarf,et al.  On the development and application of maintenance policies for a two-component system with failure dependence , 1998 .

[3]  Rommert Dekker,et al.  Optimal maintenance of multi-component systems: a review , 2008 .

[4]  María Dolores Berrade,et al.  Optimum inspection under competing risks with proportional hazards , 2002 .

[5]  María Dolores Berrade,et al.  Maintenance policy for multivariate standby/operating units , 2002 .

[6]  Joseph Mathew,et al.  Rotating machinery prognostics. State of the art, challenges and opportunities , 2009 .

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

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

[9]  María Dolores Berrade,et al.  A bivariate delay-time model , 2013 .

[10]  Xiaofei Lu,et al.  Optimizing the Periodic Inspection Interval for a 1-out-of-2 Cold Standby System Using the Delay-Time Concept , 2012, Qual. Reliab. Eng. Int..

[11]  A. H. Christer.  Delay-Time Model of Reliability of Equipment Subject to Inspection Monitoring , 1987 .

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

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

[14]  Shaomin Wu,et al.  A condition-based maintenance policy for degrading systems with age- and state-dependent operating cost , 2017, Eur. J. Oper. Res..

[15]  Wenbin Wang,et al.  A multi-component and multi-failure mode inspection model based on the delay time concept , 2010, Reliab. Eng. Syst. Saf..

[16]  Sofia Panagiotidou,et al.  Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures , 2014, Eur. J. Oper. Res..

[17]  Philip A. Scarf,et al.  Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives , 2010, Eur. J. Oper. Res..

[18]  Min-Tsai Lai,et al.  Optimal periodic replacement policy for a two-unit system with failure rate interaction , 2006 .

[19]  Rommert Dekker,et al.  A review of multi-component maintenance models with economic dependence , 1997, Math. Methods Oper. Res..

[20]  Shey-Huei Sheu,et al.  Age replacement policy for a two-unit system subject to non-homogeneous pure birth shocks , 2013 .

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

[22]  Philip A. Scarf,et al.  On reliability criteria and the implied cost of failure for a maintained component , 2005, Reliab. Eng. Syst. Saf..

[23]  Mahmut Parlar,et al.  A survey of maintenance models for multi-unit systems , 1991 .

[24]  Francisco Germán Badía,et al.  Optimal inspection and preventive maintenance of units with revealed and unrevealed failures , 2002, Reliab. Eng. Syst. Saf..

[25]  Wenbin Wang,et al.  Subjective estimation of the delay time distribution in maintenance modelling , 1997 .

[26]  Lin Ma,et al.  Failure analysis of engineering systems with preventive maintenance and failure interactions , 2009, Comput. Ind. Eng..

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

[28]  Dragan Banjevic,et al.  Periodic inspection optimization model for a complex repairable system , 2010, Reliab. Eng. Syst. Saf..

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

[30]  Wenbin Wang,et al.  An overview of the recent advances in delay-time-based maintenance modelling , 2012, Reliab. Eng. Syst. Saf..

[31]  Donghua Zhou,et al.  Remaining useful life estimation - A review on the statistical data driven approaches , 2011, Eur. J. Oper. Res..

[32]  María Dolores Berrade,et al.  Some Insights Into the Effect of Maintenance Quality for a Protection System , 2015, IEEE Transactions on Reliability.

[33]  Hamid Reza Golmakani,et al.  Periodic inspection optimization model for a two-component repairable system with failure interaction , 2012, Comput. Ind. Eng..

[34]  Ruud H. Teunter,et al.  Condition-based maintenance policies for systems with multiple dependent components: A review , 2017, Eur. J. Oper. Res..