Gompertz software reliability model: Estimation algorithm and empirical validation

Abstract

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.

Modelling and study the effect of selected design features for the operating parameters

“…However, for a general description of each peak number of parameters, such as halfwidth, amplitude ratio H/L need to be introduced and jet linking them to the spatial distribution of the electrodes is essential. The number of parameters can be limited by using sigmoid function [19] for the description of the outlined curve. Therefore, to approximate the current density distribution at the surface of the collecting electrode composition of asymmetric sigmoid function was applied, resulting in an ability to model asymmetric waveform.…”

Why Some Families of Probability Distributions Are Practically Efficient: A Symmetry-Based Explanation

“…This distribution describes aging and life expectancy [2,36]; it is also used to in software engineering, to describe the "life expectancy" of software [33].…”

The Beta-Gompertz Distribution

“…This distribution is a generalization of the exponential (E) distribution and is commonly used in many applied problems, particularly in lifetime data analysis (Johnson, Kotz & Balakrishnan 1995, p. 25). The G distribution is considered for the analysis of survival, in some sciences such as gerontology (Brown & Forbes 1974), computer (Ohishi, Okamura & Dohi 2009), biology (Economos 1982), and marketing science (Bemmaor & Glady 2012). The hazard rate function (hrf) of G distribution is an increasing function and often applied to describe the distribution of adult life spans by actuaries and demographers (Willemse & Koppelaar 2000).…”