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An algorithm for the estimation of minimal cut and path sets from field failure data

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  • Dharmadhikari, Avinash
  • Kulathinal, S. B.
  • Mandrekar, Vidyadhar

Abstract

The problem of analyzing the field failure data generated through non-repairable systems is age old and faced by all industries. Current practice, in most of the industries, is to disassemble the failed system, and observe the failed components. Based on such a list generally percentages are computed to summarize the data and technical actions are taken on a component which has higher percentage of failures, without paying any attention to the technical configuration of the system. Such an approach may be misleading. It is known that a system as a coherent structure of the components, fails as soon as all the components in a specific cut set fail. In this paper, we propose an algorithmic approach to identify minimal cut sets of the system which in turn identifies the critical cut set where technical action is necessary. We establish the consistency of the estimators of minimal cut sets and path sets. Lastly, the algorithm is illustrated by a suitable example.

Suggested Citation

  • Dharmadhikari, Avinash & Kulathinal, S. B. & Mandrekar, Vidyadhar, 2002. "An algorithm for the estimation of minimal cut and path sets from field failure data," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 1-11, May.
  • Handle: RePEc:eee:stapro:v:58:y:2002:i:1:p:1-11
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    References listed on IDEAS

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    1. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
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    3. Roussas, George G., 1995. "Asymptotic normality of a smooth estimate of a random field distribution function under association," Statistics & Probability Letters, Elsevier, vol. 24(1), pages 77-90, July.
    4. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 1-12, October.
    5. Cai, Zongwu & Roussas, George G., 1997. "Smooth estimate of quantiles under association," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 275-287, December.
    6. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    7. Roussas, George G., 1991. "Kernel estimates under association: strong uniform consistency," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 393-403, November.
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    1. repec:pal:jorsoc:v:54:y:2003:i:9:d:10.1057_palgrave.jors.2601598 is not listed on IDEAS

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