A Comprehensive Evaluation of Software Reliability Modeling Based on Marshall-Olkin Type Fault-Detection Time Distribution

Marshall-Olkin type distribution is defined as a maximum or minimum value distribution of N i.i.d. (secondary) random variables, where N is a geometric distributed random variable. Gopal, and Damondaran (2011) and Xiao (2015) considered the special cases where the underlying random variables are exponentially and Weibull distributed, respectively, and investigated an applicability of these specific Marshall-Olkin type distributions to software reliability modeling with non-homogeneous Poisson process. In this paper, we further generalize the existing software reliability growth model (SRGM) to more general ones by assuming that the secondary probability distribution is given by one of eleven representative distributions with positive support. For these new SRGMs, we develop efficient parameter estimation algorithms based on the EM (Expectation-Maximization) principle, and provide two stable statistical inference schemes in the respective cases where the software fault-detection time and its grouped data are available, respectively. In numerical examples with sixteen data sets (eight for each of detection time data or grouped data), the resulting Marshall-Olkin type SRGMs are compared with the existing eleven SRGMs in terms of goodness-of-fit performance, and reliability prediction.

I. Introduction

Software reliability is an attribute of software qualities to ensure that software can continuously provide its service without any failure. In particular, quantitative software reliability evaluation is helpful to control software testing, and there have been a variety of approaches of quantitative software reliability evaluation in the past literature. One of the most attractive approaches is a model-based approach that describes software reliability growth phenomena in testing phase. So, if the number of faults in software is finite, then the number of detected faults gradually decreases as testing time elapses. Software reliability model or equivalently software reliability growth model (SRGM) is defined as a stochastic model to represent such software reliability growth phenomena. From the mathematical point of view, non-homogeneous Poisson processes (NHPPs) are commonly used to describe software fault detection processes due to their mathematical tractability. During the last four decades, a number of NHPP-based SRGMs have been proposed [15]. [18]. [19]. [32].