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Top1. Introduction
Software reliability is the probability of failure-free software operation over a specified time within a specified environment for a specified purpose (Musa & Okumoto, 1984). Software reliability engineering focuses on effective assessment and improvement of reliability of the software. Reliability must be assessed effectively to determine required testing efforts, testing progress, possible product release date and product trust worthiness (Farooq et al., 2012). Software reliability growth models aid us in predicting and estimating reliability of the product. Many SRGM proposed in the past have significantly improved the software reliability assessment process as they model probabilistic failure process more effectively (Musa et al., 1987) (Xie, 1991) (Lyu, 1996). However, many models do not consider testing effort or its effectiveness or at best assume that utilization of testing resources is constant (Musa et al., 1987) (Xie, 1991) (Tamura & Yamada, 2005) (Ohba, 1984) (Kan, 2002). Testing-effort functions (TEF) describe the test effort distribution over exposure period and its effectiveness. Many SRGM’s proposed by (Musa et al., 1987) (Yamada et al., 1993) (Huang et al., 2000) (Kuo et al., 2001) (Huang & Kuo, 2002) (Kapur et al., 2004) (Bokhari & Ahmad, 2006) (Ahmad et al., 2010b) (Bokhari & Ahmad, 2014) explicitly consider the TEF by describing the relationship among the time spent on testing quantified in calendar time, consumed testing effort and the number of faults detected by testing (Huang et al., 2007). Of all the models, exponential growth model, inflection S-shaped and delayed S-shaped growth models prove effective in fitting failure data (Ahmad et al., 2010b) (Ahmad et al., 2011) (Bokhari et al., 2017). However, some earlier research suggested that observed data may not be fit properly in delayed S-shaped SRGM if testing-effort is not constant (Ohba, 1984). However, later research indicated that delayed S-shaped SRGM perform effectively if TEF is described well (Yamada et al., 1993) (Huang & Kuo, 2002). Many approaches have been suggested to effectively describe TEF. In this paper, we first review the Log-logistic (LL) testing-effort function. Moreover, we propose and evaluate an approach how to incorporate the Log-logistic (LL) testing-effort function into delayed S-shaped SRGM’s based on non-homogeneous Poisson process (NHPP). Weighted least square estimation (WLSE) and maximum likelihood estimation (MLE) methods are used to estimate the model parameters. The experimental results obtained after applying model on real data sets and statistical methods used for analysis are presented. The results show that the performance of the proposed model is better than the other existing models. We can conclude that incorporating Log-Logistic testing-effort function into delayed S-shaped NHPP growth models is an appropriate and proves to be effective.
The paper is structured as: Section 2 explains how SRGM can be described with Log-logistic testing-effort Function, section 3 describes how Log-logistic TEF can be incorporated in delayed S-Shaped SRGM, section 4 explains the techniques used for estimating the model parameters, section 5 list and defines various comparison criteria used in data analysis, section 6 shows the results obtained after applying the proposed SRGM to three real world application. This section also shows the results of performance comparison between proposed model and already existing other SRGMs. Section 7 presents results of model being applied in imperfect debugging conditions and its comparison with other models, and section 8 presents the conclusion of the paper.