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Better Buehler confidence limits

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  • Kabaila, Paul

Abstract

Consider the reliability problem of finding a 1-[alpha] upper (lower) confidence limit for [theta] the probability of system failure (non-failure), based on binomial data on the probability of failure of each component of the system. The Buehler 1-[alpha] confidence limit is usually based on an estimator of [theta]. This confidence limit has the desired coverage properties. We prove that in large samples the Buehler 1-[alpha] upper confidence limit based on an approximate 1-[alpha] upper limit for [theta] is less conservative, whilst also possessing the desired coverage properties.

Suggested Citation

  • Kabaila, Paul, 2001. "Better Buehler confidence limits," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 145-154, April.
    • Handle: RePEc:eee:stapro:v:52:y:2001:i:2:p:145-154
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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. Kabaila, Paul, 1995. "The Effect of Model Selection on Confidence Regions and Prediction Regions," Econometric Theory, Cambridge University Press, vol. 11(3), pages 537-549, 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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    Cited by:

    1. Kabaila, Paul, 2008. "Statistical properties of exact confidence intervals from discrete data using studentized test statistics," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 720-727, April.
    2. Kabaila, Paul & Lloyd, Chris J., 2003. "The efficiency of Buehler confidence limits," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 21-28, October.

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