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Phase-type software reliability model: parameter estimation algorithms with grouped data

Author

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  • Hiroyuki Okamura

    (Hiroshima University)

  • Tadashi Dohi

    (Hiroshima University)

Abstract

This paper introduces a phase-type software reliability model (PH-SRM) and develops parameter estimation algorithms with grouped data. The PH-SRM is one of the most flexible models, which contains the existing non-homogeneous Poisson process (NHPP) models, and can approximate any type of NHPP-based models with high accuracy. Hence PH-SRM is promising to reduce the effort to select the best models in software reliability assessment. However, PH-SRM may involve many parameters compared to typical NHPP models. Thus the efficient parameter estimation algorithm is required. This paper enhances the parameter estimation algorithms for PH-SRM, so that they can handle grouped data. The grouped data is commonly applied to collect the data such as the number of bugs per day in practice. Thus the presented algorithms are helpful for the reliability assessment in practical software development project. Concretely, we consider the EM (expectation–maximization) algorithm for PH-SRM with both fault-detection time and grouped data. Finally, we examine performance of PH-SRM from the viewpoints of fitting ability.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:244:y:2016:i:1:d:10.1007_s10479-015-1870-0
    DOI: 10.1007/s10479-015-1870-0
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    References listed on IDEAS

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    1. Peng, R. & Li, Y.F. & Zhang, W.J. & Hu, Q.P., 2014. "Testing effort dependent software reliability model for imperfect debugging process considering both detection and correction," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 37-43.
    2. 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.
    3. 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.
    4. P. K. Kapur & H. Pham & A. Gupta & P. C. Jha, 2011. "Software Reliability Growth Models," Springer Series in Reliability Engineering, in: Software Reliability Assessment with OR Applications, chapter 0, pages 49-95, Springer.
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    Cited by:

    1. Surya, Budhi Arta, 2022. "Conditional multivariate distributions of phase-type for a finite mixture of Markov jump processes given observations of sample path," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. Triet Pham & Hoang Pham, 2019. "A generalized software reliability model with stochastic fault-detection rate," Annals of Operations Research, Springer, vol. 277(1), pages 83-93, June.
    3. 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.

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