IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i7p3426-3440.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(07)00428-8
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. M. J. R. Healy, 1982. "A Linear Estimator of Standard Deviation in Symmetrically Trimmed Normal Samples," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 174-175, June.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fernandez, Arturo J., 2006. "Bayesian estimation based on trimmed samples from Pareto populations," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1119-1130, November.
    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.
    3. Gaver, Donald P. & Jacobs, Patricia A., 2014. "Reliability growth by failure mode removal," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 27-32.
    4. Peng, Yizhen & Wang, Yu & Zi, YanYang & Tsui, Kwok-Leung & Zhang, Chuhua, 2017. "Dynamic reliability assessment and prediction for repairable systems with interval-censored data," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 301-309.
    5. J. McGree & J. Eccleston, 2010. "Investigating design for survival models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 295-311, November.
    6. Jin Zhang, 2013. "Simplification of joint confidence regions for the parameters of the Pareto distribution," Computational Statistics, Springer, vol. 28(4), pages 1453-1462, August.
    7. Liu, Junfeng & Wang, Yi, 2013. "On Crevecoeur’s bathtub-shaped failure rate model," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 645-660.
    8. Arturo Fernández, 2010. "Bayesian estimation and prediction based on Rayleigh sample quantiles," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(6), pages 1239-1248, October.
    9. A. Asgharzadeh & S. F. Bagheri & N. A. Ibrahim & M. R. Abubakar, 2020. "Optimal confidence regions for the two-parameter exponential distribution based on records," Computational Statistics, Springer, vol. 35(1), pages 309-326, March.
    10. 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.
    11. Rameshwar Gupta & Ramesh Gupta, 2008. "Analyzing skewed data by power normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 197-210, May.
    12. Carlos Pérez-González & Arturo Fernández, 2009. "Accuracy of approximate progressively censored reliability sampling plans for exponential models," Statistical Papers, Springer, vol. 50(1), pages 161-170, January.
    13. Chumnaul, Jularat & Sepehrifar, Mohammad, 2018. "Generalized confidence interval for the scale parameter of the power-law process with incomplete failure data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 17-33.
    14. Dijoux, Yann & Fouladirad, Mitra & Nguyen, Dinh Tuan, 2016. "Statistical inference for imperfect maintenance models with missing data," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 84-96.
    15. J. M. Lennartz & S. Bedbur & U. Kamps, 2021. "Minimum area confidence regions and their coverage probabilities for type-II censored exponential data," Statistical Papers, Springer, vol. 62(1), pages 171-191, February.
    16. Gilardoni, Gustavo L. & Oliveira, Maristela D. de & Colosimo, Enrico A., 2013. "Nonparametric estimation and bootstrap confidence intervals for the optimal maintenance time of a repairable system," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 113-124.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3426-3440. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.