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Monotonicity of likelihood support bounds for system failure rates

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  • Lloyd, Chris J.

Abstract

Simple expressions are derived for lower and upper support limits for the system failure probability of a series or parallel system based on binomial failure data. These limits are shown to be non-decreasing functions of the number of failures of any component for a fixed number of tests and non-increasing functions of the number of tests of any component for a fixed number of failures. This logically essential property, not shared by many other approximate upper limits, is critical to the efficient computation of Buehler bounds, using support limits as an ordering function.

Suggested Citation

  • Lloyd, Chris J., 2005. "Monotonicity of likelihood support bounds for system failure rates," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 91-97, June.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:2:p:91-97
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    References listed on IDEAS

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    1. Reiser, Benjamin & Jaegar, Mordechai, 1991. "A comment on Buehler optimal confidence bounds for series systems reliability," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 65-67, January.
    2. Chris J. Lloyd & Paul Kabaila, 2003. "On the Optimality and Limitations of Buehler Bounds," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(2), pages 167-174, June.
    3. Alan Winterbottom, 1984. "The Interval Estimation of System Reliability from Component Test Data," Operations Research, INFORMS, vol. 32(3), pages 628-640, June.
    4. Harris, Bernard & Soms, Andrew P., 1991. "Theory and counterexamples for confidence limits on system reliability," Statistics & Probability Letters, Elsevier, vol. 11(5), pages 411-417, May.
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