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Imperfect inspection and replacement of a system with a defective state: A cost and reliability analysis

Author

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  • Berrade, M.D.
  • Scarf, P.A.
  • Cavalcante, C.A.V.
  • Dwight, R.A.

Abstract

We consider a system with three possible states, good, defective and failed. Failures are detected as soon as they occur; the defective state, which is only revealed by inspection, does not prevent the system from fulfilling the function for which it was designed. We present a maintenance model consisting of periodic inspections to check the state of the system, in which inspections are subject to error. At a false positive inspection the system is unnecessarily replaced; at a false negative inspection a defect remains unrevealed with reliability implications for future operation. The model is illustrated with an example from the railways. In this context, we suppose that system lifetime is heterogeneous so that the time the system spends in the defective state is a random variable from a mixed distribution. We determine under what circumstances the cost of maintenance cannot be justified by its efficacy, and suggest that when there is the possibility that replacement is poorly executed (lifetime heterogeneity) the natural response to imperfect inspection of increasing the inspection frequency can be counter-productive.

Suggested Citation

  • Berrade, M.D. & Scarf, P.A. & Cavalcante, C.A.V. & Dwight, R.A., 2013. "Imperfect inspection and replacement of a system with a defective state: A cost and reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 120(C), pages 80-87.
    • Handle: RePEc:eee:reensy:v:120:y:2013:i:c:p:80-87
    DOI: 10.1016/j.ress.2013.02.024
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    References listed on IDEAS

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    1. Wang, Wenbin, 2012. "An overview of the recent advances in delay-time-based maintenance modelling," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 165-178.
    2. Scarf, Philip A. & Cavalcante, Cristiano A.V., 2010. "Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives," European Journal of Operational Research, Elsevier, vol. 206(2), pages 384-394, October.
    3. Cavalcante, Cristiano A.V. & Scarf, Philip A. & de Almeida, Adiel T., 2011. "A study of a two-phase inspection policy for a preparedness system with a defective state and heterogeneous lifetime," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 627-635.
    4. Berrade, M.D. & Cavalcante, Cristiano A.V. & Scarf, Philip A., 2012. "Maintenance scheduling of a protection system subject to imperfect inspection and replacement," European Journal of Operational Research, Elsevier, vol. 218(3), pages 716-725.
    5. Scarf, Philip A. & Cavalcante, Cristiano A.V., 2012. "Modelling quality in replacement and inspection maintenance," International Journal of Production Economics, Elsevier, vol. 135(1), pages 372-381.
    Full references (including those not matched with items on IDEAS)

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