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Optimum Replacement of a System Subject to Shocks: A Mathematical Lemma

Author

Listed:
  • Prem S. Puri

    (Purdue University, West Lafayette, Indiana)

  • Harshinder Singh

    (Panjab University, Chandigarh, India)

Abstract

We consider a system that is subject to shocks that occur randomly over time. We assume that the system must be replaced after it has functioned for a random length of time τ, a moment of a major failure that is a stopping time with respect to the process { N ( t ), t ≥ 0} that models the number of shocks occurring in [0, t ]. It may, however, be economical to replace the system at time min( t , τ) prior to its failure, for some fixed but optimally chosen t . Costs are due to shocks, maintenance and replacement. We introduce an optimality criterion, based on cost considerations, which we use to find an optimal replacement time t 0 . In the process, we prove a general mathematical lemma that helps in arriving at the optimal replacement time for general classes of processes { N ( t )}, stopping times τ and the cost structures involved. We also give a discrete time version of the lemma.

Suggested Citation

  • Prem S. Puri & Harshinder Singh, 1986. "Optimum Replacement of a System Subject to Shocks: A Mathematical Lemma," Operations Research, INFORMS, vol. 34(5), pages 782-789, October.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:5:p:782-789
    DOI: 10.1287/opre.34.5.782
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    Citations

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    Cited by:

    1. Henry W. Block & Thomas H. Savits & Harshinder Singh, 2002. "A Criterion for Burn-in that Balances Mean Residual Life and Residual Variance," Operations Research, INFORMS, vol. 50(2), pages 290-296, April.
    2. Berg, Menachem P., 1995. "The marginal cost analysis and its application to repair and replacement policies," European Journal of Operational Research, Elsevier, vol. 82(2), pages 214-224, April.
    3. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George & Love, Ernie, 2006. "An extended optimal replacement model of systems subject to shocks," European Journal of Operational Research, Elsevier, vol. 175(1), pages 399-412, November.
    4. Sheu, Shey-Huei & Griffith, William S., 2002. "Extended block replacement policy with shock models and used items," European Journal of Operational Research, Elsevier, vol. 140(1), pages 50-60, July.
    5. Sheu, Shey-Huei, 1998. "A generalized age and block replacement of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 108(2), pages 345-362, July.
    6. Sheu, Shey-Huei & Chang, Chin-Chih & Zhang, Zhe George & Chien, Yu-Hung, 2012. "A note on replacement policy for a system subject to non-homogeneous pure birth shocks," European Journal of Operational Research, Elsevier, vol. 216(2), pages 503-508.
    7. Shey‐Huei Sheu & William S. Griffith, 1996. "Optimal number of minimal repairs before replacement of a system subject to shocks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 319-333, April.

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