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Optimal Allocations in the Construction of k-Out-of-n Reliability Systems

Author

Listed:
  • C. Derman

    (Columbia University)

  • G. J. Lieberman

    (Stanford University)

  • S. M. Ross

    (University of California, Berkeley)

Abstract

We want to build n components so as to form an n component system which will function if at least k of the components function. If x dollars are invested in building a component, then this component will function with probability P(x). Given a total income of A dollars, the problem of interest is to determine how much money we should invest in each component so as to maximize the probability of attaining a functioning system. This problem is considered both in the sequential and in the nonsequential cases. Conditions under which it is optimal to allocate A/n units at each stage, when A is your initial fortune, are presented. The special case P(x) = min(x, 1) is also considered in detail.

Suggested Citation

  • C. Derman & G. J. Lieberman & S. M. Ross, 1974. "Optimal Allocations in the Construction of k-Out-of-n Reliability Systems," Management Science, INFORMS, vol. 21(3), pages 241-250, November.
    • Handle: RePEc:inm:ormnsc:v:21:y:1974:i:3:p:241-250
    DOI: 10.1287/mnsc.21.3.241
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    Cited by:

    1. Michael Katehakis & Ingram Olkin & Sheldon Ross & Jian Yang, 2013. "On the life and work of Cyrus Derman," Annals of Operations Research, Springer, vol. 208(1), pages 5-26, September.
    2. Li, Haibao & Cai, Zhiqiang & Zhang, Shuai & Zhao, Jiangbin & Si, Shubin, 2024. "Time series importance measure-based reliability optimization for cellular manufacturing systems," Reliability Engineering and System Safety, Elsevier, vol. 244(C).

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