A software reliability model incorporating martingale process with gamma-distributed environmental factors

Mengmeng Zhu, Hoang Pham

Research output: Contribution to journalArticle

4 Scopus citations


As the increasing application of software system in various industry, software reliability gains more attention from the researchers and practitioners in the past few decades. The goal of such an expanding application of software system is to continuously bring convenience and functionality in everyday life. Lots of environmental factors defined by many studies may have positive/negative impact on software reliability during the development process (Zhu et al. in J Syst Softw 109:150–160, 2015; Clarke and O’Connor in Inf Softw Technol 54(5):433–447, 2012; Zhu and Pham in J Syst Softw 1–18, 2017b). However, most existing software reliability models have not incorporated these environmental factors in the model consideration. In this paper, we propose a theoretic software reliability model incorporating the fault detection process is a stochastic process due to the randomness caused by the environmental factors. The environmental factor, Percentage of Reused Modules, is described as a gamma distribution in this study based on the collected data from industry. Open Source Software project data are included to demonstrate the effectiveness and predictive power of the proposed model.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalAnnals of Operations Research
StateAccepted/In press - Jun 27 2018

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research


  • Brownian motion
  • Environmental factors
  • Gamma distribution
  • Martingale process
  • Non-homogeneous Poisson process
  • Percentage of Reused Modules
  • Software reliability growth model
  • Standard Gaussian white noise

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