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A Review of Delay Time Analysis for Modelling Plant Maintenance

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Stochastic Models in Reliability and Maintenance

Summary

Delay time analysis is a pragmatic mathematical concept readily embraced by engineers, which has been developed as a means to model maintenance decision problems. Attention is focused upon the maintenance engineering decisions of what to do, as opposed to the logistical decisions of how to do it. This paper reviews the cumulative knowledge and experience of delay time modelling. The decision environment within which Delay time models are intended as decision aids is briefly reviewed, and the initial development of simple DT models for a repairable component and a complex plant presented. Variations on the basic model are outlined and discussed, including perfect and nonperfect inspection, steady state and non-steady state conditions, and homogeneous and non-homogeneous Poisson arrival rate of defects. Attention is given to the parameter estimation process, and both subjective and objective estimation techniques are outlined. Case sketches present practical experience in using the DT concept to model actual plant, to assess the benefits obtained, and to validate modelling and parameter assessment. References are given throughout to related work as well as to future developments.

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References

  1. Geraerds, W. M. J. (1978), “Estimation of cost of maintenance expenditure within the Netherlands,” Internal Report, Faculty of Technology Management, Eindhoven University of Technology, Netherlands

    Google Scholar 

  2. Turban, E. (1967), “The use of mathematical models in plant maintenance decision-making,” Management Science, 13, B342–358

    Article  Google Scholar 

  3. Pierskalla, W. P. and Voelker, J. A. A. (1976), “A survey of maintenance models: the control and surveillance of deteriorating systems,” Naval Research Logistics Quarterly, 223, 53–88

    Google Scholar 

  4. Christer, A. H. (1984), “Operational Research applied to industrial maintenance and replacement,” Development in OR (Eglese. and Rand.). 31–58, Pergamon, ???

    Google Scholar 

  5. Thomas, L. C. (1986), “A survey of maintenance and replacement models for maintainability and reliability of multi-item systems,” Reliability Engineering, 16, 297–309

    Article  Google Scholar 

  6. Valdez-Flores, C. and Feldman, R. M. (1989), “A survey of preventive maintenance models for stochastically deteriorating single unit system,” Naval Research Logistics Quarterly, 36, 419–446

    Article  Google Scholar 

  7. Cho, D. L. and Parlar, M. (1991), “A survey of maintenance models for multi-unit systems,” European Journal of Operational Research, 51, 1–31

    Article  Google Scholar 

  8. Pintelon, L. M. and Gelders, L. (1992), “Maintenance management decision-making,” European Journal of Operational Research, 58, 30 1317.

    Google Scholar 

  9. Scarf, P. S. (1997), “On the application of mathematical models to maintenance,” European Journal of Operational Research, 99, 493–506

    Article  Google Scholar 

  10. Dekker, R. and Scarf, P. A. (1998), “On the impact of optimisation models in maintenance decision-making: the state of the art,” Reliability Engineering and System Safety, 66, 111–119

    Google Scholar 

  11. Hsu, J. S. (1988), “Equipment replacement policy–a survey,” Production and Inventory Management Journal, 29, 23–27

    Google Scholar 

  12. Christer, A. H. and Waller, W. M. (1987), “A descriptive model of capital plant replacement,” Journal of the Operational Research Society, 38, 473–477

    Google Scholar 

  13. Gits, C. W. (1992), “Design of maintenance concepts,” International Journal of Production Economics, 24, 217–226

    Article  Google Scholar 

  14. Dekker, R., Smit, A. C. and Losekoot, J. M. (1992), “Combining maintenance activities in an operational planning phase: a set partitioning problem,” IMA Journal of Mathematics Applied in Business and Industry, 3, 315–331

    Google Scholar 

  15. Dekker, R. (1995), “Integrating optimisation, priority setting, planning and combining of maintenance activities,” European Journal of Operational Research, 82, 225–240

    Article  Google Scholar 

  16. Wildeman, R. E., Dekker, R. and Smit, A. C. J. M. (1997), “A dynamic policy for grouping maintenance activities, ” European Journal of Operational Research, 99, 530–551

    Article  Google Scholar 

  17. Christer, A. H., MacCallum, K. J., Kobbacy, K. A. H., Rolland, D. and Hesset, C. (1989), “A system model of underwater inspection operation,” Journal of the Operational Research Society, 40, 551–565

    Google Scholar 

  18. Armitage, W. (1968), “Maintenance Effectiveness,” OR in Maintenance, ( Jardine, A K S MUP, ed. ). 196–223

    Google Scholar 

  19. Corder, A. S. (1976), Maintenance Management Techniques. McGraw Hill, New York

    Google Scholar 

  20. Nikojima, S. (1989), Total Productive Maintenance Development Programme: Implementing Total Productive Maintenance. Production Press, Cambridge, Massachusetts

    Google Scholar 

  21. Mowbray, J. (1997), Reliability Centred Maintenance. Butterworth-Heineman

    Google Scholar 

  22. Christer, A. H., Wang, W. and Sharp, J. (1997), “A state space condition monitoring model for erosion furnace prediction and replacement,” European Journal of Operational Research, 101, 1–14

    Article  Google Scholar 

  23. Aghjagan, H. N. (1989), “Lubeoil analysis expert system,” Proceedings of the Canadian Maint. Eng. Conference, Toronto

    Google Scholar 

  24. Ormerod, R. J. (1993), “The OR/MS contribution to maintenance management: comments on maintenance management decision making,” European Journal of Operational Research, 65, 140–142

    Article  Google Scholar 

  25. Barlow, R. E. and Proschan, F. (1996), Mathematical Theory of Reliability. SIAM, Philadelphia

    Google Scholar 

  26. Ascher, H. E. and Feingold, H. (1984), Repairable Systems Reliability: Modelling Inference, Misconceptions and Their Causes. Lecture Notes in Stasts, Marcel Dekker, New York

    Google Scholar 

  27. Christer, A. H. (1976), “Innovatory decision making,” Proceedings of the NATO Conference on Role and Effectiveness of Theories of Decision Theory in Practice (Bowen, K. C. and White, D. J.), Hodder and Sroughton, 368–377

    Google Scholar 

  28. Christer, A. H. and Wang, W. (1995), “A delay-time based maintenance model of a multi-component system,” IMA Journal of Mathematics Applied in Business and Industry, 6, 205–222

    Google Scholar 

  29. 29. Chilcott, J. and Christer, A. H. (1991), “Modelling of condition based maintenance at the coal face,” International Journal of Production Economics,221–11

    Google Scholar 

  30. 30. Christer, A. H. and Lee, C. S. (2000), “Refining the delay-time PM inspection model with non-negligible system downtime estimates of the expected number of failures,” Department Report, CORAS, Salford University, to appear in International Journal of Production Economics, 2000

    Google Scholar 

  31. Cox, D. R. (1957), Renewal Theory. Chapman and Hall, London

    Google Scholar 

  32. Baker, R. D. and Wang, W. (1993), “Developing and testing the delay-time model,” Journal of the Operational Research Society, 44, 361–374

    Google Scholar 

  33. Christer, A. H. and Doherty, T. (1977), “Scheduling overhauls for soaking pits,” Operational Research Quarterly,28, 915–926

    Article  Google Scholar 

  34. Christer, A. H. (1987), “Delay-time models of reliability of equipment subject to inspection monitoring,” Journal of the Operational Research Society, 38, 329–334

    Google Scholar 

  35. Cerone, P. (1991), “On a simplified delay-time model of reliability of equipment subject to inspection monitoring,” Journal of the Operational Research Society, 42, 505–511

    Google Scholar 

  36. Christer, A. H. and Lee, S. K. (1997), “Modelling ship operational reliability over a mission under regular inspections,” Journal of the Operational Research Society, 48, 688–699

    Google Scholar 

  37. Wang, W. and Christer, A. H. (1997), “A modelling procedure to optimise component safety over a finite time horizon,” Quality and Reliability Engineering, An International Journal, 13, 217–224

    Google Scholar 

  38. Christer, A. H., Wang, W., Sharp, J. and Baker, R. D. (1997), “A stochastic modelling problem of high-tech steel production,” in Stochastic Modelling in Innovative Manufacturing ( Christer, A. H., Osaki, S. and Thomas, L. C. eds.). 196–214, Springer-Verlag, Berlin

    Chapter  Google Scholar 

  39. Christer, A. H. (1992), “Prototype modelling of irregular condition monitoring of production plant,” IMA Journal of Mathematics Applied in Business and Industry, 3, 219–232

    Google Scholar 

  40. Scarf, P. S. and Christer, A. H. (1997), “Applications of capital replacement models with finite planning horizons,” Internatinal Journal of Technology Management, 13, 25–36

    Article  Google Scholar 

  41. Christer, A. H. and Waller, W. M. (1987), “Tax adjusted replacement models,” Journal of the Operational Research Society, 38, 993–1006

    Google Scholar 

  42. Sun Wei, Yang Hong Wei, Qu Fazeng, (1999), “The determination of unequal inspection intervals for repairable mechanical product,” Proceedings of the 4th International Conference Reliability Maintainability and Safety, (ICRNS ‘89) Shanghai, China Machine Press, Beijing, 531535

    Google Scholar 

  43. Christer, A. H. (1982), “Modelling inspection policies for building maintenance,” Journal of the Operational Research Society, 33, 723752

    Google Scholar 

  44. Christer, A. H. (1988), “Condition based inspection models of major civil engineering structures,” Journal of the Operational Research Society, 39, 71–82

    Google Scholar 

  45. Redmond, D. and Christer, A. H. (1997), “An application of delay time analysis to concrete structures,” European Journal of Operational Research, 99, 619–631

    Article  Google Scholar 

  46. Christer, A. H. and Waller, W. M. (1984), “Reducing production downtime using delay-time analysis,” Journal of the Operational Research Society, 35, 499–512

    Google Scholar 

  47. Christer, A. H. and Whitelaw, J. (1983), “An OR approach to breakdown maintenance: problem recognition,” Journal of the Operational Research Society, 34, 1041–1052

    Google Scholar 

  48. Pellegrin, C. C. (1991), “A graphical procedure for on-condition maintenance policy: imperfect inspection model and interpretation,” IMA Journal of Mathematics Applied in Business and Industry, 3, 177–191

    Google Scholar 

  49. Desa, M. I. and Christer, A. H. (1992), “Maintenance and availability modelling of bus transport in Malaysia: Issue and problems,” Proceedings of the International Conference on OR in Developing Countries, Ahmadabad, India

    Google Scholar 

  50. References

    Google Scholar 

  51. Christer, A. H. and Redmond, D. F. (1992), “Revising models of maintenance and inspection,” International Journal of Production Economics, 24, 227–234

    Article  Google Scholar 

  52. Singpurwalla, N. P. and Percy, D. F. (1998), “Bayesian calculations in maintenance modelling,” Technical report, 03, Department of Computer Mathematical Sciences, University of Salford, United Kingdom

    Google Scholar 

  53. Christer, A. H. and Redmond, D. F. (1990), “A recent mathematical development in maintenance theory,” IMA Journal of Mathematics Applied in Business and Industry, 2, 97–108

    Google Scholar 

  54. Feller, W. (1971), An Introduction to Probability Theory and Its Applications, II. John Wiley Sons

    Google Scholar 

  55. Wang, W. (1997), “Subjective estimation of the delay-time distribution in maintenance modelling,” European Journal of Operational Research, 99, 515–529

    Article  Google Scholar 

  56. Cooke, R. M. (1991), “Experts in uncertainty: expert opinion and subjective probability in science,” OUP

    Google Scholar 

  57. Baker, R. D. and Wang, W. (1992), “Estimating the delay-time distribution of faults in repairable machinery for failure data,” IMA Journal of Mathematics Applied in Business and Industry, 3, 259–282

    Google Scholar 

  58. Baker, R. D. and Christer, A. H. (1994), “Operational research modelling of engineering aspects of maintenance,” European Journal of Operational Research, 73, 407–422

    Article  Google Scholar 

  59. Ross, S. M. (1996), Stochastic Process. John Wiley Sons

    Google Scholar 

  60. Christer, A. H., Wang, W., Baker, R. and Sharp, J. (1995), “Modelling maintenance practice of production plant using the delay time concept,” IMA Journal of Mathematics Applied in Business and Industry, 6, 6783

    Google Scholar 

  61. Christer, A. H., Wang, W. and Choi, K. M. (1998), “The delay-time modelling of preventive maintenance of plant given limited PM data and selective repair at PM,” IMA Journal of Mathematics Applied in Business and Industry, 9, 4

    Google Scholar 

  62. Christer, A. H., Wang, W., Sharp, J. and Baker, R. (1998), “A case study of modelling preventive maintenance of production plant using subjective data,” Journal of the Operational Research Society, 49, 210219

    Google Scholar 

  63. Christer, A. H., Lee, C. S. and Wang, W. (2000), “A delay-time parameter estimation problem and case study in PM modelling,” to appear in International Journal of Production Economics

    Google Scholar 

  64. Baker, R. D. and Scarf, P. A. (1995), “Can models fitted to small data samples lead to maintenance policies with near optimum cost?,” IMA Journal of Mathematics Applied in Business and Industry, 6, 3–12

    Google Scholar 

  65. Christer, A. H. (1992), “Prototype modelling of irregular condition monitoring of production plant,” IMA Journal of Mathematics Applied in Business and Industry, 3, 219–232

    Google Scholar 

  66. Baker, R. D. (1998), “What can industrial inspection models learn from medical analogues? Determining the optimal screening policy for breast cancer,” IMA Journal of Mathematics Applied in Business and Industry, 9, 4

    Google Scholar 

  67. Kobbacy, K. A. H., Proudlove, N. C. and Harper, M. (1995), “An intelligent maintenance optimisation system,” Journal of the Operational Research Society, 46, 831–853

    Google Scholar 

  68. Ascher, H. E. and Kobbacy, K. A. H. (1995), “Modelling preventive maintenance for deteriorating repairable systems,” IMA Journal of Mathematics Applied in Business and Industry, 6, 85–99

    Google Scholar 

  69. Winder, C. van and Dekker, R. (1998), “Rationalisation of building maintenance by Markov decision models: a pilot case study,” Journal of the Operational Research Society, 49, 928–935

    Google Scholar 

  70. Christer, A. H. and Waller, W. M. (1984), “Delay time models of industrial inspection maintenance,” Journal of the Operational Research Society, 35, 401–406

    Google Scholar 

  71. 70. Christer, A. H. and Wang, W., Choi, K. M. and Van der Duyn Schouten. (1998), “The robustness of the semi-Markov and delay time maintenance models to the Markov assumption,” to appear in European Journal of Operational Research

    Google Scholar 

  72. Christer, A. H. and Waller, W. M. (1984), “An OR approach to Planned Maintenance Modelling (PM) for a vehicle fleet,” Journal of the Operational Research Society, 35, 967–984

    Google Scholar 

  73. Redmond, D.F., Christer, A. H., Rigden, S. R. and Burley, E. (1997), “OR modelling of the deterioration and maintenance of concrete structures,” European Journal of Operational Research, 99, 619–631

    Article  Google Scholar 

  74. Burley, E., Christer, A. H. and Rigden, S. D. (1989), “Inspection practice for concrete structure in the U.K.,” Proceedings of the Conference British Cement Association, Life of Concrete Structures

    Google Scholar 

  75. Wang, W. (1999), “A model of multiple nested inspections of production plant,” to appear in Computer and Operations Research

    Google Scholar 

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Christer, A.H. (2002). A Review of Delay Time Analysis for Modelling Plant Maintenance. In: Osaki, S. (eds) Stochastic Models in Reliability and Maintenance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24808-8_4

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  • DOI: https://doi.org/10.1007/978-3-540-24808-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07725-8

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