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Application of EM Algorithm to NHPP-Based Software Reliability Assessment with Generalized Failure Count Data

Author

Listed:
  • Hiroyuki Okamura

    (Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 7398527, Japan)

  • Tadashi Dohi

    (Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 7398527, Japan)

Abstract

Software reliability models (SRMs) are widely used for quantitative evaluation of software reliability by estimating model parameters from failure data observed in the testing phase. In particular, non-homogeneous Poisson process (NHPP)-based SRMs are the most popular because of their mathematical tractability. In this paper, we focus on the parameter estimation algorithm for NHPP-based SRMs and discuss the EM algorithm for generalized fault count data. The presented algorithm can be applied for failure time data, failure count data, and their mixture. The paper derives the EM-step formulas for basic 12 NHPP-based SRMs and demonstrate a numerical experiment to present the convergence property of our algorithms. The developed algorithms are suitable for an automatic tool for software reliability evaluation.

Suggested Citation

  • Hiroyuki Okamura & Tadashi Dohi, 2021. "Application of EM Algorithm to NHPP-Based Software Reliability Assessment with Generalized Failure Count Data," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:985-:d:544811
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    References listed on IDEAS

    as
    1. Okamura, Hiroyuki & Dohi, Tadashi & Osaki, Shunji, 2013. "Software reliability growth models with normal failure time distributions," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 135-141.
    2. Hiroyuki Okamura & Tadashi Dohi, 2016. "Phase-type software reliability model: parameter estimation algorithms with grouped data," Annals of Operations Research, Springer, vol. 244(1), pages 177-208, September.
    3. B. Littlewood, 1975. "A Reliability Model for Systems with Markov Structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(2), pages 172-177, June.
    4. Hiroyuki Okamura & Tadashi Dohi, 2013. "Application of EM Algorithm to NHPP-Based Software Reliability Assessment with Ungrouped Failure Time Data," Springer Series in Reliability Engineering, in: Tadashi Dohi & Toshio Nakagawa (ed.), Stochastic Reliability and Maintenance Modeling, edition 127, pages 285-313, Springer.
    5. Jeske D. R. & Pham H., 2001. "On the Maximum Likelihood Estimates for the Goel-Okumoto Software Reliability Model," The American Statistician, American Statistical Association, vol. 55, pages 219-222, August.
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