Gompertz software reliability model: Estimation algorithm and empirical validation

• Published in: The Journal of systems and software Vol. 82; no. 3; pp. 535 - 543
• Main Authors: Ohishi, Koji, Okamura, Hiroyuki, Dohi, Tadashi
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.03.2009; Elsevier Sequoia S.A
• Subjects: Algorithms; Computer programs; EM algorithm; Extremal distributions; Failure; Gompertz curve; Gompertz curves; Mathematical models; NHPP; Poisson distribution; Reliability assessment; Software; Software development; Software reliability; Software reliability model; Stochastic models; Studies; Systems development; Japan; Gompertz curve; Reliability assessment; Software reliability model; EM algorithm; Extremal distributions; NHPP
• ISSN: 0164-1212; 1873-1228
• DOI: 10.1016/j.jss.2008.11.840

Gompertz curve has been used to estimate the number of residual faults in testing phases of software development, especially by Japanese software development companies. Since the Gompertz curve is a deterministic function, the curve cannot be applied to estimating software reliability which is the probability that software system does not fail in a prefixed time period. In this article, we propose a stochastic model called the Gompertz software reliability model based on non-homogeneous Poisson processes. The proposed model can be derived from the statistical theory of extreme-value, and has a similar asymptotic property to the deterministic Gompertz curve. Also, we develop an EM algorithm to determine the model parameters effectively. In numerical examples with software failure data observed in real software development projects, we evaluate performance of the Gompertz software reliability model in terms of reliability assessment and failure prediction.