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Reliability inference and sample-size determination under double censoring for some two-parameter models

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  • Fernández, Arturo J.

Abstract

Assuming that some extreme sample values have been censored or discarded, a reliability analysis of several two-parameter models, as the exponential, Pareto and power-function laws, is presented. Explicit expressions for the distribution, density and moments of the natural generalized pivot of the true reliability are deduced. Its asymptotic normality is also shown. Reliability point estimates are derived by selecting summary features of the pivotal quantity. Reliability confidence limits, which are shown to provide exact coverage probabilities, are readily found by solving simple nonlinear equations. Quite accurate approximate limits are given in closed forms. In addition, a procedure for determining confidence intervals of shortest length is proposed. Reliability tests, which are carried out using generalized p-values, satisfy the conventional repeated-sampling property. Minimum sample sizes and decision rules of optimal reliability demonstration plans, which accept good (bad) products with a certain high (low) probability, are obtained via iterative methods. A numerical example is included for illustrative purposes.

Suggested Citation

  • Fernández, Arturo J., 2008. "Reliability inference and sample-size determination under double censoring for some two-parameter models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3426-3440, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3426-3440
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    References listed on IDEAS

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    1. Luis A. Escobar & William Q. Meeker, 1994. "Fisher Information Matrix for the Extreme Value, Normal and Logistic Distributions and Censored Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(3), pages 533-540, September.
    2. Yu, Jun-Wu & Tian, Guo-Liang & Tang, Man-Lai, 2008. "Statistical inference and prediction for the Weibull process with incomplete observations," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1587-1603, January.
    3. Fernandez, Arturo J., 2006. "Bounding maximum likelihood estimates based on incomplete ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2014-2027, April.
    4. Shu-Fei Wu, 2007. "Interval Estimation for the Two-Parameter Exponential Distribution Based on the Doubly Type II Censored Sample," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(3), pages 489-496, June.
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    6. Arturo Fernández, 2004. "One- and two-sample prediction based on doubly censored exponential data and prior information," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 403-416, December.
    7. Arturo J. fernández & José I. Bravo & Íñigo Fuentes, 2002. "Computing maximum likelihood estimates from type II doubly censored exponential data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(2), pages 187-200, June.
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    Cited by:

    1. Fernández, Arturo J., 2010. "Two-sided tolerance intervals in the exponential case: Corrigenda and generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 151-162, January.
    2. Fernández, Arturo J., 2012. "Minimizing the area of a Pareto confidence region," European Journal of Operational Research, Elsevier, vol. 221(1), pages 205-212.

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