Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T20:18:47.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Group replacement of a multicomponent system which is subject to deterioration only

Published online by Cambridge University Press:  01 July 2016

B. D. Sivazlian  and
J. F. Mahoney
B. D. Sivazlian
Affiliation:
University of Florida, Gainesville
J. F. Mahoney
Affiliation:
University of Florida, Gainesville
Get access Rights & Permissions [Opens in a new window]

Abstract

The stationary characteristics of an n-component periodic review system which is subject to stochastic deterioration (but not to failure) are investigated. When the n-component vector which expresses the state of deterioration of the system pierces a certain surface the entire multicomponent system is replaced by items of identical cost structure at the time of the next review. In the absence of this situation nothing is replaced. It is assumed that there is a fixed cost associated with each replacement and that the operating cost of each item is a strictly increasing function of its state of deterioration. The conditions for minimizing the long-term cost of maintaining a system which operates under the stated policy were found through solution of a problem in variational calculus. Two examples are worked. A useful graph which aids in the solution of such problems is provided.

Keywords

GROUP REPLACEMENTMULTIDIMENSIONAL RENEWAL PROCESSMULTIPLE INTEGRALSCALCULUS OF VARIATION
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 4 , December 1978 , pp. 867 - 885
Copyright
Copyright © Applied Probability Trust 1978 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Barlow, R. E. and Proschan, F. (1967) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
[2] Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Wiley, New York.Google Scholar
[3] Derman, C. (1963) On optimal replacement rules when changes of state are Markovian. In Mathematical Optimization Techniques, ed. Bellman, R., University of California Press, Berkeley, Chapter 9.Google Scholar
[4] Derman, C. and Sacks, J. (1960) Replacement of periodically inspected equipment. Naval Res. Logist. Quart. 7, 597–607.CrossRefGoogle Scholar
[5] Edwards, G. (1922) A Treatise on the Integral Calculus, Vol. 2. Macmillan, New York.Google Scholar
[6] Hunter, J. J. (1974) Renewal theory in two dimensions: basic results. Adv. Appl. Prob. 6, 376–391.CrossRefGoogle Scholar
[7] Hunter, J. J. (1974) Renewal theory in two dimensions: asymptotic results. Adv. Appl. Prob. 6, 546–562.Google Scholar
[8] Jorgensen, D. W., McCall, J. J. and Radner, J. (1967) Optimal Replacement Policy. North-Holland, Amsterdam.Google Scholar
[9] Mikusinski, J. (1959) Operational Calculus. Pergamon, New York.Google Scholar
[10] Mode, C. J. (1967) A renewal density theorem in the multi-dimensional case. J. Appl. Prob. 4, 62–76.Google Scholar
[11] Prabhu, N. U. (1965) Stochastic Processes. Macmillan, New York.Google Scholar
[12] Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, New York.Google Scholar
[13] Sivazlian, B. D. (1971) A class of multiple integrals. SIAM J. Math. Anal. 2, 72–75.Google Scholar
[14] White, D. J. (1969) Dynamic Programming. Holden-Day, San Francisco.Google Scholar