Int J Performability Eng ›› 2019, Vol. 15 ›› Issue (5): 1265-1272.doi: 10.23940/ijpe.19.05.p1.12651272

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Improved Algorithm for Non-Homogeneous Poisson Process Software Reliability Growth Models Incorporating Testing-Effort

Vidhyashree Nagarajua, Thierry Wandjib, and Lance Fiondellaa,*   

  1. a University of Massachusetts Dartmouth, North Dartmouth, 02747, USA
    b Naval Air Systems Command, Patuxent River, 20670, USA
  • Submitted on ;
  • Contact: * E-mail address: lfiondella@umassd.edu
  • Supported by:
    This work was partially supported by the Naval Air Warfare Center (NAVAIR) under contract N00421-16-T-0373 and the National Science Foundation under Grant Number #1526128.

Abstract: Critical systems are becoming increasingly software intensive, necessitating reliable software to ensure proper operation. Non-homogeneous Poisson process software reliability growth models are commonly used to characterize fault detection as a function of testing time, which enables quantitative assessment of software reliability. Many early models assumed that the testing-effort was constant throughout software testing. To remove this assumption, researchers have proposed models incorporating testing-effort, yet this significantly increases model complexity to the degree that most previous studies utilized a two-step procedure involving least squares estimation (LSE) and algorithms, including Newton's method to estimate the parameters of a testing-effort model. This approach may limit the quality of the model fit achieved. Moreover, the research trend over the past 30 years has been to propose progressively more complex models, sacrificing practical considerations such as predictive accuracy. This paper proposes a two-step procedure that utilizes the expectation conditional maximization (ECM) algorithm, referred to as the ECM/ECM approach, to obtain the parameter estimates of a software reliability growth model incorporating testing-effort. The results of the proposed approach are compared to past methods as well as a simpler model that does not consider testing-effort to assess whether the additional complexity introduced by testing-effort functions compromises predictive accuracy. Our results indicate that the ECM/ECM approach achieves a better goodness of fit with respect to four measures, including three predictive measures. In some cases, the simpler model omitting testing-effort outperforms methods considering testing-effort. These results suggest that the proposed ECM/ECM approach can achieve better parameter estimates than the previously proposed LSE/MLE approach and that algorithms to improve fit and predictive accuracy may better serve users of software reliability models.

Key words: software reliability, non-homogeneous Poisson process, software reliability growth models, maximum likelihood estimation, expectation conditional maximization algorithm, Newton-Raphson method, testing-effort, least squares estimation