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Some probability functions in reliability and their applications

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  • Ji Hwan Cha
  • Jie Mi

Abstract

There has been much research on the general failure model recently. In the general failure model, when the unit fails at its age t, Type I failure (minor failure) occurs with probability 1 − p(t) and Type II failure (catastrophic failure) occurs with probability p(t). In the previous research, some specific shapes (constant, non‐decreasing, or bathtub‐shape) on the probability function p(t) are assumed. In this article, general results on some probability functions are obtained and applied to study the shapes of p(t). The results are also applied to determining the optimal inspection and allocation policies in maintenance problems. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • Ji Hwan Cha & Jie Mi, 2007. "Some probability functions in reliability and their applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(2), pages 128-135, March.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:2:p:128-135
    DOI: 10.1002/nav.20192
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    References listed on IDEAS

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    1. Ciriaco Valdez‐Flores & Richard M. Feldman, 1989. "A survey of preventive maintenance models for stochastically deteriorating single‐unit systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 419-446, August.
    2. Frank Beichelt, 1993. "A unifying treatment of replacement policies with minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 51-67, February.
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    Cited by:

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    2. Qiu, Qingan & Cui, Lirong & Wu, Bei, 2020. "Dynamic mission abort policy for systems operating in a controllable environment with self-healing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 203(C).

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