a b s t r a c tGompertz 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.
This paper focuses on an estimation problem of model parameters in software reliability modeling. We introduce the EM (expectation-maximization) algorithms for software reliability models and compare them with the classical parameter estimation methods. Especially, we extensively develop the EM algorithms for two cases; (i) the time interval data of software fault detection are available, (ii) additive software reliability models based on non-homogeneous Poisson processes are used. In numerical examples, we compare the iterative schemes based on the EM algorithms with classical methods such as the Newton's method and the Fisher's scoring method and show that the EM algorithms are attractive in terms of convergence property.
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