Optimal replacement with a single unloaded standby

  • C. G. Henin
  • P. J. Ryan


The problem of optimal replacement for two andn components with a single unloaded standby is solved. The solution is determined by the relative costs of failure for each component and is independent of the actual failure time, other than immediate replacement being specified. Conditions for the existence of a single critical number policy are derived and the general policy is described.


Economic Theory Public Finance Relative Cost Failure Time Critical Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Si risolve il problema della sostituzione ottimale perdue en componenti con un singolo pezzo di «unloaded standby». La soluzione è determinata dai costi relativi del guasto per ogni componente ed è indipendente dal tempo specifico in cui il guasto è avvenuto, salvo che sia assunta l'immediata sostituzione. Si derivano condizioni per l'esistenza di una politica basata su un solo numero critico e si studia la politica generale.


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  1. [1]
    R. E. Barlow andF. Proschan,Mathematical Theory of Reliability. John Wiley and Sons, New York, 1965.Google Scholar
  2. [2]
    R. E. Barlow andF. Proschan,Statistical Theory of Reliability and Life Testing Probability models. International Series in Decision Processes, Holt, Rinehart & Winston, 1975.Google Scholar
  3. [3]
    M. Berg andB. Epstein,A Modified Block Replacement Policy. Naval Research Logistics Quarterly, 23-1, March 1976.Google Scholar
  4. [4]
    B. R. Bhat,Used Item Replacement Policy. Journal of Applied Probability, 6, (1969).Google Scholar
  5. [5]
    D. P. Gaver,On the Loss Resulting from Spare Part Deficiency (unpublished paper 1969).Google Scholar
  6. [6]
    B. V. Gnedenko, Y. K. Belyayev andA. D. Solovyev,Mathematical Methods of Reliability Theory. Academic Press, 1969.Google Scholar
  7. [7]
    C. G. Henin,Optimal Replacement Policies for a Single Loaded Sliding Standby. Management Science, Vol. 18, No. 11, July 1972.Google Scholar
  8. [8]
    C. G. Henin andS. Perrakis,Optimal Replacement Policies with Two or More Loaded Sliding Standbys. Naval Research Logistics Quarterly, 29-4, December 1982.Google Scholar
  9. [9]
    D. W. Jorgenson, J. J. MacCall andR. Radner,Optimal Replacement Policy, North-Holland Publishing Co., 1967.Google Scholar
  10. [10]
    Z. Kander,Inspection Policies for Deteriorating Equipment Characterized by N Quality Levels. Naval Research Logistics Quarterly, 25-2, June 1978.Google Scholar
  11. [11]
    H. Luss,Maintenance Policies when Deterioration Can Be Observed by Inspections. Operations Research, 24-2, March–April 1976.Google Scholar
  12. [12]
    B. L. Mitler andM. M. Yazdi,The Distribution of Recoverable Inventory Items from a Repair Center when the Number of Consumption Centers is large. Naval Research Logistics Quarterly, 25-4, December 1978.Google Scholar
  13. [13]
    W. S. Pierskalla andJ. A. Voelker,Survey of Maintenance Models. The Control and Surveillance of Deteriorating Systems. Naval Research Logistics Quarterly, 23-3, September 1976.Google Scholar
  14. [14]
    A. M. Polovko,Fundamentals of Reliability Theory. Academic Press, 1968.Google Scholar
  15. [15]
    D. M. Topkis,Optimal Ordering and Rationing Policies, in a Nonstationary Dynamic Inventory Model with n Demand Classes. Management Science, Vol. 15, No. 3, Nov. 1968.Google Scholar
  16. [16]
    R. C. Woodman,Replacement Policies for Components that Deteriorate. Operational Research Quarterly, 18, 267–280, 1967.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • C. G. Henin
    • 1
  • P. J. Ryan
    • 1
  1. 1.Faculty of AdministrationUniversity of OttawaOttawaCanada

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