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Optimizing Availability and Performance of a Two-Unit Redundant Multi-state Deteriorating System

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Book cover Recent Advances in Multi-state Systems Reliability

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

Abstract

The most of the contemporary large scale technological systems are functioning under multiple stages of degradation, from their perfect state to their total failure. The study of the performance and the availability of multi-stage systems is of great importance since their deterioration and/or failure may lead to important losses. Under a proper inspection and maintenance policy, it is feasible the operation of the system to be improved significantly. Our main goal is to model multi-state systems with redundancy and to identify the optimal maintenance policies. The system is inspected periodically. Depending on the condition of the system, either no action takes place or maintenance is carried out, either minimal or major. The proposed model takes also into account the scenario of imperfect and failed maintenance. The asymptotic behaviour of the system is studied and optimization problems for the asymptotic availability, the downtime cost and the expected cost due to maintenance and unavailability, with respect to inspection intervals, are formulated and solved.

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References

  1. Lisnianski A, Frenkel I, Ding Y (2010) Multi-state system reliability analysis and optimization for engineers and industrial managers. Springer, London

    Book  MATH  Google Scholar 

  2. Chawla R, Kumar G (2013) Condition based maintenance modeling for availability analysis of a repairable mechanical system. Int J Innov Eng Technol 2(2):371–379

    Google Scholar 

  3. Li W, Pham H (2005) Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks. IEEE Trans Reliab 54(2):297–303

    Article  Google Scholar 

  4. Shafiee M, Finkelstein M (2015) An optimal age-based group maintenance policy for multi-unit degrading systems. Reliab Eng Syst Saf 134:230–238

    Article  Google Scholar 

  5. Murchland J (1975) Fundamental concepts and relations for reliability analysis of multistate systems. In: Barlow RE, Fussell JB, Singpurwalla N (eds) Reliability and fault tree analysis: theoretical and applied aspects of system reliability. SIAM, Philadelphia, pp 581–618

    Google Scholar 

  6. El-Neweihi E, Proschan F (1984) Degradable systems: a survey of multistate system theory. Commun Stat Theory Methods 13:405–432

    Article  MathSciNet  MATH  Google Scholar 

  7. Barlow RE, Wu AS (1978) Coherent systems with multi-state components. Math Operat Res 3:275–281

    Article  MATH  Google Scholar 

  8. Chen D, Cao Y, Trivedi KS, Hong Y (2003) Preventive maintenance of multi-state system with phase-type failure time distribution and non-zero inspection time. Int J Reliab Qual Saf Eng 10(3):323–344

    Article  Google Scholar 

  9. Malefaki S, Koutras VP, Platis AN (2014) Optimizing the availability and the operational cost of a periodically inspected multi-state deteriorating system with condition based maintenance policies. In: 2014 Ninth international conference on availability, reliability and security (ARES), 403–411:8–12

    Google Scholar 

  10. Platis AN, Koutras VP, Malefaki S (2014) Achieving high availability levels of a deteriorating system by optimizing condition based maintenance policies. In: Steenbergen SMDJM, van Gelder PHAJM, Vrouwenvelder A (eds) Safety, reliability and risk analysis: beyond the Horizon. Taylor & Francis Group, pp 829–837

    Google Scholar 

  11. Ross SM (1979) Multivalued state component systems. Ann Prob 7:379–383

    Article  MathSciNet  MATH  Google Scholar 

  12. Aghezzaf E-H, Khatab A (2016) Phuoc Le Tam: optimizing production and imperfect preventive maintenance plannings integration in failure-prone manufacturing systems. Reliab Eng Syst Saf 145:190–198

    Article  Google Scholar 

  13. Blischkem WR, Murthy DNPL (2003) Case studies in reliability and maintenance. Wiley, USA

    Google Scholar 

  14. Coita DW (2003) Maximization of system reliability with a choice of redundancy strategies. IIE Trans 35(6):535–543

    Article  Google Scholar 

  15. Lisnianski A, Ding Y, Frenkel I, Khvatskin L (2007) Maintenance optimization for multi-state aging systems. Proceedings of 5-th international conference on mathematical methods in reliability, methodology and practice, Glasgow, United Kingdom

    Google Scholar 

  16. Natvig B (2011) Probabilistic modeling of monitoring and maintenance. In: Multi-state systems reliability theory with applications. Wiley, UK

    Google Scholar 

  17. Amari SV, McLaughlin Lm Pham H (2006) Cost-effective condition-based maintenance using markov decision processes, In: Reliability and maintainability symposium 2006 RAMS ’06. Annual 464–469:23–26

    Google Scholar 

  18. Lapa CMF, Pereira CMNA, de Barros MP (2006) A model for preventive maintenance planning by genetic algorithms based in cost and reliability. Reliab Eng Syst Saf 91(2):233–240

    Article  Google Scholar 

  19. Kapur PK, Kapoor KR (1980) Joint optimum preventive maintenance and repair limit replacement policies. IEEE Trans Reliab R-29(3):279–281

    Google Scholar 

  20. Naga Srinivasa Rao P, Achutha Naikan VN (2006) A condition-based preventive maintenance policy for Markov deteriorating systems. Int J Perform Model 2(2):175–189

    Google Scholar 

  21. Shey SH, Chang CC, Chen YL, Zhe GZ (2015) Optimal preventive maintenance and repair policies for multi-state systems. Reliab Eng Syst Saf 47:78–87

    Article  Google Scholar 

  22. Thein S, Chang YS, Makatsoris C (2012) A study of condition based preventive maintenance model for repairable multi stage deteriorating system. Int J Adv Logist 1(1):83–102

    Article  Google Scholar 

  23. Ding SH, Kamaruddin S (2015) Maintenance policy optimization-literature review and directions. Int J Adv Manuf Technol 76(5):1263–1283

    Article  Google Scholar 

  24. Wie X, Yiguang H, Trivedi KS (2005) Analysis of a two level software rejuvenation policy. Reliab Eng Syst Saf 87(1):13–22

    Article  Google Scholar 

  25. Malefaki S, Koutras VP, Platis AN (2016) Multi-State deteriorating system dependability with maintenance using monte carlo simulation. In: Proceedings of SMRLO’16 2016: second international symposium on stochastic models in reliability engineering, Life science and operations management, February 2016, SCE—Shamoon College of Engineering, Beer Sheva, Israel, pp 61–70, IEEE CPS, 978-1-4673-9941-8/16. doi:10.1109/SMRLO.2016.54

  26. Sarkar J, Sarkar S (2010) Availability of a periodically inspected system under perfect repair. J Stat Plan Inference 91(1):77–90

    Article  MathSciNet  MATH  Google Scholar 

  27. Chen D, Trivedi KS (2002) Closed-form analytical results for condition-based maintenance. Reliab Eng Syst Saf 76(1):43–51

    Article  Google Scholar 

  28. Sim SH (1988) Optimal preventive maintenance with repair. IEEE Trans Reliab 37(1):92–96

    Article  MATH  Google Scholar 

  29. Chen D, Trivedi KS (2001) Analysis of periodic preventive maintenance with general system failure distribution. In: Proceedings 2001 pacific rim international symposium on dependable computing, 2001. pp 103–107

    Google Scholar 

  30. Cheng C-Y, Chen MC (2003) The periodic preventive maintenance policy for deteriorating systems by using improvement factor model. Int J Appl Sci Eng 114–122

    Google Scholar 

  31. Sim SH, Endrenyi J (1993) A failure-repair model with minimal and major maintenance. IEEE Trans Reliab 42(1):134–140

    Article  MATH  Google Scholar 

  32. Pellegrin C (1992) Choice of a periodic on-condition maintenance policy. Int J Prod Res 30(5):1153–1173

    Article  Google Scholar 

  33. Kline MB (1984) Suitability of the lognormal distribution for corrective maintenance repair times. Reliab Eng 9(2):65–80

    Article  Google Scholar 

  34. Kulkarni VG (1995) Modeling and analysis of stochastic systems. Chapman & Hall, London

    Google Scholar 

  35. Limnios N (1997) Dependability analysis of Semi-Markov systems. Reliab Eng Syst Saf 55(3):203–207

    Article  Google Scholar 

  36. Limnios N, Oprian G (2001) Semi-Markov processes and reliability. Birkhuser, Boston

    Book  Google Scholar 

  37. Taga Y (1963) On the limiting distributions in Markov renewal processes with finitely many states. Ann Inst Statist Math 15(1):1–10

    Article  MathSciNet  MATH  Google Scholar 

  38. Koutras VP, Malefaki S, Platis AN (2017) Optimization of the dependability and performance measures of a generic model for multi-state deteriorating systems under maintenance. Reliab Eng Syst Saf (accepted)

    Google Scholar 

  39. Platis AN, Drosakis EG (2009) Coverage modeling and optimal maintenance frequency of an automated restoration mechanism. IEEE Trans Reliab 58(3):470–475

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering & Aeronautics, University of Patras, 26504, Rio, Patras, Greece

    Sonia Malefaki

  2. Department of Financial and Management Engineering, University of the Aegean, 82100, Chios, Greece

    Vasilis P. Koutras & Agapios N. Platis

Authors
  1. Sonia Malefaki
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  2. Vasilis P. Koutras
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  3. Agapios N. Platis
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Corresponding author

Correspondence to Sonia Malefaki .

Editor information

Editors and Affiliations

  1. Planning, Development and Technology Division, The System Reliability Department, Israel Electric Corporation Ltd., Haifa, Israel

    Anatoly Lisnianski

  2. Center for Reliability and Risk Management, Industrial Engineering and Management Department, SCE—Shamoon College of Engineering, Beer Sheva, Israel

    Ilia Frenkel

  3. Department of Mathematics, University of the Aegean, Karlovasi, Samos, Greece

    Alex Karagrigoriou

Appendix

Appendix

In the next tables the systems states and all the transitions for the proposed two-unit systems are presented analytically. (See Tables 3, 4 and 5).

Table 3 System state and transitions for the two-unit system with minimal and major maintenance actions
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Table 4 System state and transitions for the two-unit system with minimal maintenance actions
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Table 5 System state and transitions for the two-unit system with major maintenance actions
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Malefaki, S., Koutras, V.P., Platis, A.N. (2018). Optimizing Availability and Performance of a Two-Unit Redundant Multi-state Deteriorating System. In: Lisnianski, A., Frenkel, I., Karagrigoriou, A. (eds) Recent Advances in Multi-state Systems Reliability. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-63423-4_5

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  • DOI: https://doi.org/10.1007/978-3-319-63423-4_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63422-7

  • Online ISBN: 978-3-319-63423-4

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