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Markov counting and reward processes for analysing the performance of a complex system subject to random inspections

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  • Ruiz-Castro, Juan Eloy

Abstract

In this paper, a discrete complex reliability system subject to internal failures and external shocks, is modelled algorithmically. Two types of internal failure are considered: repairable and non-repairable. When a repairable failure occurs, the unit goes to corrective repair. In addition, the unit is subject to external shocks that may produce an aggravation of the internal degradation level, cumulative damage or extreme failure. When a damage threshold is reached, the unit must be removed. When a non-repairable failure occurs, the device is replaced by a new, identical one. The internal performance and the external damage are partitioned in performance levels. Random inspections are carried out. When an inspection takes place, the internal performance of the system and the damage caused by external shocks are observed and if necessary the unit is sent to preventive maintenance. If the inspection observes minor state for the internal performance and/or external damage, then these states remain in memory when the unit goes to corrective or preventive maintenance. Transient and stationary analyses are performed. Markov counting and reward processes are developed in computational form to analyse the performance and profitability of the system with and without preventive maintenance. These aspects are implemented computationally with Matlab.

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  • Ruiz-Castro, Juan Eloy, 2016. "Markov counting and reward processes for analysing the performance of a complex system subject to random inspections," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 155-168.
  • Handle: RePEc:eee:reensy:v:145:y:2016:i:c:p:155-168
    DOI: 10.1016/j.ress.2015.09.004
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    References listed on IDEAS

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    1. Huang, Chun-Chen & Yuan, John, 2010. "A two-stage preventive maintenance policy for a multi-state deterioration system," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1255-1260.
    2. Pourkarim Guilani, Pedram & Sharifi, Mani & Niaki, S.T.A. & Zaretalab, Arash, 2014. "Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods," Reliability Engineering and System Safety, Elsevier, vol. 129(C), pages 29-35.
    3. Soro, Isaac W. & Nourelfath, Mustapha & Aït-Kadi, Daoud, 2010. "Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 95(2), pages 65-69.
    4. Li, Y.F. & Peng, R., 2014. "Availability modeling and optimization of dynamic multi-state series–parallel systems with random reconfiguration," Reliability Engineering and System Safety, Elsevier, vol. 127(C), pages 47-57.
    5. Chakravarthy, Srinivas R., 2012. "Maintenance of a deteriorating single server system with Markovian arrivals and random shocks," European Journal of Operational Research, Elsevier, vol. 222(3), pages 508-522.
    6. Shumin Li & Shubin Si & Liudong Xing & Shudong Sun, 2014. "Integrated importance of multi-state fault tree based on multi-state multi-valued decision diagram," Journal of Risk and Reliability, , vol. 228(2), pages 200-208, April.
    7. Nakagawa, T. & Mizutani, S., 2009. "A summary of maintenance policies for a finite interval," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 89-96.
    8. Faghih-Roohi, Shahrzad & Xie, Min & Ng, Kien Ming & Yam, Richard C.M., 2014. "Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 57-62.
    9. Wu, Jun & Xie, Min & Adam Ng, Tsan Sheng, 2011. "On a general periodic preventive maintenance policy incorporating warranty contracts and system ageing losses," International Journal of Production Economics, Elsevier, vol. 129(1), pages 102-110, January.
    10. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George, 2012. "Optimal maintenance policy for a system subject to damage in a discrete time process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 1-10.
    11. Taghipour, Sharareh & Banjevic, Dragan, 2012. "Optimal inspection of a complex system subject to periodic and opportunistic inspections and preventive replacements," European Journal of Operational Research, Elsevier, vol. 220(3), pages 649-660.
    12. Ruiz-Castro, Juan Eloy & Fernández-Villodre, Gemma, 2012. "A complex discrete warm standby system with loss of units," European Journal of Operational Research, Elsevier, vol. 218(2), pages 456-469.
    13. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, March.
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    Cited by:

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    2. Juan Eloy Ruiz-Castro, 2021. "Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units," Mathematics, MDPI, vol. 9(8), pages 1-29, April.
    3. Che, Haiyang & Zeng, Shengkui & Guo, Jianbin & Wang, Yao, 2018. "Reliability modeling for dependent competing failure processes with mutually dependent degradation process and shock process," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 168-178.
    4. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.
    5. Ruiz-Castro, Juan Eloy, 2020. "A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    6. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.
    7. Li, Xiang-Yu & Li, Yan-Feng & Huang, Hong-Zhong & Zio, Enrico, 2018. "Reliability assessment of phased-mission systems under random shocks," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 352-361.
    8. Sakurahara, Tatsuya & O'Shea, Nicholas & Cheng, Wen-Chi & Zhang, Sai & Reihani, Seyed & Kee, Ernie & Mohaghegh, Zahra, 2019. "Integrating renewal process modeling with Probabilistic Physics-of-Failure: Application to Loss of Coolant Accident (LOCA) frequency estimations in nuclear power plants," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.

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