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Modelling and Analysis of Degradation and Maintenance

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Extended Warranties, Maintenance Service and Lease Contracts

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

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Abstract

Models play an important role in solving decision problems. They are used to (i) analyse the effect of changes to decision variables on system performance (for example, the effect of different PM actions on system failures) and (ii) decide on the optimal values of decision variables to achieve some specified objectives (for example, optimum PM to minimise total maintenance costs).

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Notes

  1. 1.

    Service time refers to the duration in the working state for a non-failed item.

  2. 2.

    There are many books that discuss the modelling process in detail; see for example, Murthy et al. (1990) and the references cited therein.

  3. 3.

    Appendix A [B] reviews material from probability theory [stochastic processes] that is relevant for reliability modelling.

  4. 4.

    We will use both notations throughout the book.

  5. 5.

    Expressions for the various distributions mentioned in this subsection can be found in Appendix A.

  6. 6.

    We will be using calendar clock unless specifically some other clock (such as local, age) is indicated.

  7. 7.

    The concept of minimal repair was first proposed by Barlow and Hunter (1961).

  8. 8.

    For more on imperfect repair, see Pham and Wang (1996).

  9. 9.

    See Kijima (1989), Doyen and Gaudoin (2004) for more details.

  10. 10.

    Nakagawa (2005) discusses several models based on this formulation.

  11. 11.

    For more on CBM, see Williams et al. (1994).

  12. 12.

    Kline (1984) suggests that the log-normal distribution is appropriate for modelling the repair times for many different products.

  13. 13.

    For details of formulation and analysis of the two processes (NHPP and renewal) can be found in Appendix B.

  14. 14.

    This is justified as, in general, the time for a repair/replacement ≪ time between events (CM or PM actions). However, if downtime is needed for determining penalty costs, then it needs to be modelled. However, it can be ignored for modelling subsequent failures as its impact is, in general, negligible.

  15. 15.

    This is also known as the exponential law or the Cox-Lewis intensity function.

  16. 16.

    For more on MCF and ROCOF, see, Ascher and Feingold (1984), Rigdon and Basu (2000).

  17. 17.

    For a proof of this, see Nakagawa and Kowada (1983)

  18. 18.

    See Blischke and Murthy (1994) for more details.

  19. 19.

    This expression is used as the objective function to determine the optimal decision variable \( \nu \) if the goal is to minimise the asymptotic cost per unit time.

  20. 20.

    For notational ease, we omit the parameters of the functions.

  21. 21.

    See Johnson and Kotz (1972), Hutchinson and Lai (1990) for more on 2-D distributions. Murthy et al. (2003) discuss a variety of 2-D Weibull distributions useful in modelling failures.

  22. 22.

    For more on 2-D renewal processes, see Hunter (1974a, b, 1996).

  23. 23.

    For further discussion, see Baik et al. (2004, 2006).

References

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Authors and Affiliations

  1. School of Mechanical and Mining Engineering, University of Queensland, Brisbane, Australia

    D. N. P. Murthy

  2. Dundee Business School, University of Abertay Dundee, Dundee, UK

    Nat Jack

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  1. D. N. P. Murthy
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Correspondence to D. N. P. Murthy .

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Murthy, D.N.P., Jack, N. (2014). Modelling and Analysis of Degradation and Maintenance. In: Extended Warranties, Maintenance Service and Lease Contracts. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-6440-1_3

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  • DOI: https://doi.org/10.1007/978-1-4471-6440-1_3

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  • Print ISBN: 978-1-4471-6439-5

  • Online ISBN: 978-1-4471-6440-1

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