Condition-based maintenance policies for a multi-unit deteriorating system subject to shocks in a semi-Markov operating environment

Abstract In this paper, we consider k out of n identical parallel unit systems experiencing deterioration due to random shocks in semi-Markov environments. It is assumed that the occurrence rate of random shocks and the corresponding failures probability are both affected by dynamical environment conditions. We discuss how the semi-Markov environment process can be converted to a Markov process. The systems are maintained through inspections and replacements under some new maintenance policies. The long-run availability and the average cost of the proposed systems are formulated. Finally, we illustrate our results using numerical examples and simulations.

[1]  Zhuoqi Zhang,et al.  Optimal maintenance policy for multi-component systems under Markovian environment changes , 2013, Expert Syst. Appl..

[2]  Shey-Huei Sheu,et al.  Extended optimal replacement policy for a system subject to non-homogeneous pure birth shocks , 2013, Comput. Ind. Eng..

[3]  Min Xie,et al.  Condition-based maintenance for long-life assets with exposure to operational and environmental risks , 2020, International Journal of Production Economics.

[4]  Shahrul Kamaruddin,et al.  An overview of time-based and condition-based maintenance in industrial application , 2012, Comput. Ind. Eng..

[5]  Harry G. Perros.  Queueing Networks with Blocking: Exact and Approximate Solutions , 1994 .

[6]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[7]  C. Richard Cassady,et al.  Optimal maintenance policies for systems subject to a Markovian operating environment , 2012, Comput. Ind. Eng..

[8]  Antonio Puliafito,et al.  Principles of Performance and Reliability Modeling and Evaluation , 2016 .

[9]  Esther Frostig,et al.  Availability of inspected systems subject to shocks - A matrix algorithmic approach , 2009, Eur. J. Oper. Res..

[10]  中川 覃夫,et al.  Maintenance theory of reliability , 2005 .

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

[12]  Steven M. Cox,et al.  Stochastic models for degradation-based reliability , 2005 .

[13]  Mitra Fouladirad,et al.  Condition-based maintenance policies for a combined wear and shock deterioration model with covariates , 2015, Comput. Ind. Eng..

[14]  Jeffrey P. Kharoufeh,et al.  Evaluating failure time probabilities for a Markovian wear process , 2005, Comput. Oper. Res..

[15]  L. Breuer.  Introduction to Stochastic Processes , 2022, Statistical Methods for Climate Scientists.

[16]  C. D. Meyer,et al.  Generalized inverses of linear transformations , 1979 .

[17]  Jeffrey P. Kharoufeh,et al.  Semi-Markov models for degradation-based reliability , 2010 .

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

[19]  Ravishankar K. Iyer,et al.  Measuring and Understanding Extreme-Scale Application Resilience: A Field Study of 5,000,000 HPC Application Runs , 2015, 2015 45th Annual IEEE/IFIP International Conference on Dependable Systems and Networks.

[20]  Ling-Yau Chan,et al.  Maintenance models for a continuously degrading system , 2010, Comput. Ind. Eng..

[21]  Gang Li,et al.  Shock model in Markovian environment , 2005 .

[22]  Esther Frostig,et al.  M out of n inspected systems subject to shocks in random environment , 2009, Reliab. Eng. Syst. Saf..

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

[24]  Leonardo P. Santiago,et al.  A condition-based maintenance policy and input parameters estimation for deteriorating systems under periodic inspection , 2011, Comput. Ind. Eng..

[25]  Lirong Cui,et al.  Availability and optimal maintenance policy for systems degrading in dynamic environments , 2019, Eur. J. Oper. Res..

[26]  Philippe Delsarte,et al.  On the optimal scheduling of periodic tests and maintenance for reliable redundant components , 2006, Reliab. Eng. Syst. Saf..

[27]  Miklós Telek,et al.  Phase Type and Matrix Exponential Distributions in Stochastic Modeling , 2016 .

[28]  Pierre-Etienne Labeau,et al.  Reliability of a multi-state system subject to shocks using phase-type distributions , 2013 .

[29]  Dustin G. Mixon,et al.  On a Markov‐modulated shock and wear process , 2009 .

[30]  Jeffrey P. Kharoufeh,et al.  Explicit results for wear processes in a Markovian environment , 2003, Oper. Res. Lett..

[31]  Mitra Fouladirad,et al.  Condition-based inspection/replacement policies for non-monotone deteriorating systems with environmental covariates , 2010, Reliab. Eng. Syst. Saf..

[32]  Tom Burr,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 2001, Technometrics.

[33]  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.

[34]  Yisha Xiang,et al.  A review on condition-based maintenance optimization models for stochastically deteriorating system , 2017, Reliab. Eng. Syst. Saf..

[35]  Ren Asmussen,et al.  Fitting Phase-type Distributions via the EM Algorithm , 1996 .