IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v53y2006i4p354-362.html
   My bibliography  Save this article

A sequential Bayesian generalization of the Jelinski–Moranda software reliability model

Author

Listed:
  • Alan Washburn

Abstract

The Jelinski–Moranda model of software reliability is generalized by introducing a negative‐binomial prior distribution for the number of faults remaining, together with a Gamma distribution for the rate at which each fault is exposed. This model is well suited to sequential use, where a sequence of reliability forecasts is made in the process of testing or using the software. We also investigate replacing the Gamma distribution with a worst‐case assumption about failure rates (the worst‐case failure rate in models such as this is not infinite, since faults with large failure rates are immediately discovered and removed). © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • Alan Washburn, 2006. "A sequential Bayesian generalization of the Jelinski–Moranda software reliability model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 354-362, June.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:4:p:354-362
    DOI: 10.1002/nav.20148
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20148
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20148?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. B. Littlewood & J. L. Verrall, 1973. "A Bayesian Reliability Growth Model for Computer Software," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 332-346, November.
    2. Carl M. Harris, 1968. "The Pareto Distribution as a Queue Service Discipline," Operations Research, INFORMS, vol. 16(2), pages 307-313, April.
    Full references (including those not matched with items on IDEAS)

    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. Malinovskii, Vsevolod K. & Kosova, Ksenia O., 2014. "Simulation analysis of ruin capital in Sparre Andersen’s model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 184-193.
    2. Bercher, J.-F. & Vignat, C., 2008. "A new look at q-exponential distributions via excess statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5422-5432.
    3. Elfessi, Abdulaziz & Chun Jin, 1996. "On robust estimation of the common scale parameter of several Pareto distributions," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 345-352, September.
    4. D. Kern, 1983. "Minimum variance unbiased estimation in the Pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 30(1), pages 15-19, December.
    5. Lian, Yongqiang & Tang, Yincai & Wang, Yijun, 2017. "Objective Bayesian analysis of JM model in software reliability," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 199-214.
    6. Thomas G. Koch, 2014. "Bankruptcy, Medical Insurance, And A Law With Unintended Consequences," Health Economics, John Wiley & Sons, Ltd., vol. 23(11), pages 1326-1339, November.
    7. Majdah Badr & Muhammad Ijaz, 2021. "The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-20, March.
    8. Littlewood, Bev & Salako, Kizito & Strigini, Lorenzo & Zhao, Xingyu, 2020. "On reliability assessment when a software-based system is replaced by a thought-to-be-better one," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    9. Gorbunova, A.V. & Lebedev, A.V., 2023. "Nonlinear approximation of characteristics of a fork–join queueing system with Pareto service as a model of parallel structure of data processing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 409-428.
    10. Thomas G. Koch, 2017. "The Shifting Shape of Risk: Endogenous Market Failure for Insurance," Risks, MDPI, vol. 5(1), pages 1-13, January.
    11. Constantinos Petropoulos, 2017. "Estimation of the order restricted scale parameters for two populations from the Lomax distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 483-502, May.
    12. Zeinab Amin, 2008. "Bayesian inference for the Pareto lifetime model under progressive censoring with binomial removals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(11), pages 1203-1217.
    13. Amal S. Hassan & Marwa Abd-Allah, 2019. "On the Inverse Power Lomax Distribution," Annals of Data Science, Springer, vol. 6(2), pages 259-278, June.
    14. Yen-Chang Chang & Lii-Yuh Leu, 1998. "A State Space Model for Software Reliability," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 789-799, December.
    15. Brill, P.H. & Huang, M.L. & Hlynka, M., 2020. "On the service time in a workload-barrier M/G/1 queue with accepted and blocked customers," European Journal of Operational Research, Elsevier, vol. 283(1), pages 235-243.
    16. Sanaa Al-Marzouki & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2019. "Type II Topp Leone Power Lomax Distribution with Applications," Mathematics, MDPI, vol. 8(1), pages 1-26, December.
    17. Pithia, K.D. & Edwards, S.F., 1994. "Rheology of liquid foams," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(4), pages 565-576.
    18. Muhammad Ahsan Ul Haq & G. G. Hamedani & M. Elgarhy & Pedro Luiz Ramos, 2020. "Marshall-Olkin Power Lomax Distribution: Properties and Estimation Based on Complete and Censored Samples," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-48, January.
    19. Kasteridis, Panagiotis & Rice, Nigel & Santos, Rita, 2022. "Heterogeneity in end of life health care expenditure trajectory profiles," Journal of Economic Behavior & Organization, Elsevier, vol. 204(C), pages 221-251.
    20. Saralees Nadarajah & Samuel Kotz, 2003. "Reliability for Pareto models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 191-204.

    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:wly:navres:v:53:y:2006:i:4:p:354-362. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.