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Software reliability growth models (SRGMs) based on the non-homogeneous Poisson process have played a significant role in predicting the number of remaining errors in software, enhancing software reliability. Software errors are commonly attributed to the mental errors of software developers, which necessitate timely detection and resolution. However, it has been observed that the human error-making mechanism is influenced by factors such as learning and fatigue. In this paper, we address the issue of integrating the fatigue factor of software testers into the learning process during debugging, leading to the development of more realistic SRGMs. The first model represents the software tester’s learning phenomenon using the tangent hyperbolic function, while the second model utilizes an exponential function. An exponential decay function models fatigue. We investigate the behavior of our proposed models by comparing them with similar SRGMs, including two corresponding models in which the fatigue factor is removed. Through analysis, we assess our models’ quality of fit, predictive power, and accuracy. The experimental results demonstrate that the model of tangent hyperbolic learning with fatigue outperforms the existing ones regarding fit, predictive power, or accuracy. By incorporating the fatigue factor, the models provide a more comprehensive and realistic depiction of software reliability.

In this research, a novel approach is developed where a testing team delivers the software product first and extends the testing process for additional time in the user environment. During the operational phase, users also participate in the fault detection process and notify the defects to the software. In this study, a reliability growth model is proposed using a unified approach based on the expenditure of efforts during the testing process. Besides, debugging process is considered imperfect as new faults may enter the software during each fault removal. The developed model further considers that the developer’s rate of defect identification changes with a software release. Thus, the software time-to-market acts as a change-point for the failure observation phenomenon. It is asserted that the accuracy of a software reliability estimation improves by implementing the concept of change-point. The main aim of the paper is to evaluate the optimal release time and testing termination time based on two attributes, particularly, reliability, and cost. A multi-attribute utility theory (MAUT) is applied to find a trade-off between the two conflicting attributes. Finally, a numerical example is presented by using the historical fault count data. The behavior of two decision variables is measured and compared with the existing release time strategy.

In software engineering literature, numerous software reliability growth models have been designed to evaluate and predict the reliability of the software products and to measure the optimal time-to-market of the software systems. Most existing studies on software release time assessment assumes that when software is released, its testing process is terminated. In practice, however, the testing team releases the software product first and continues the testing process for an added period in the operational phase. Therefore, in this study, a coherent reliability growth model is developed to predict the expected reliability of the software product. The debugging process is considered imperfect as new faults can be introduced into the software during each fault removal. The proposed model assumes that the fault observation rate of the testing team modifies after the software release. The release time of the software is therefore regarded as the change-point. It has been established that the veracity of the performance of the growth models escalates by incorporating the change-point theory. A unified approach is utilized to model the debugging process wherein both testers and users simultaneously identify the faults in the post-release testing phase. A joint optimization problem is formulated based on the two decision criteria: cost and reliability. In order to assimilate the manager’s preferences over these two criteria, a multi-criteria decision-making technique known as multi-attribute utility theory is employed. A numerical illustration is further presented by using actual data sets from the software project to determine the optimal software time-to-market and testing termination time.

This paper proposes a generalized model to cover imperfect debugging and the uncertainty of the operating environment and its effect on fault detection rate into software reliability evaluation based on a non-homogeneous Poisson process (NHPP). Many NHPP software reliability growth models (SRGMs) have been developed to estimate the software reliability measures over the past 40 years, but most of these models assume that the operating environment is the same as the testing environment. However, in fact, due to the unpredictability of the uncertain factors in the operating environments for the software, they may considerably influence the software's reliability in an unpredictable way. So when a software system works in a field environment, its reliability is usually different from the original reliability prediction in the testing phase of the software development process, also from all its similar applications in other fields. In this paper, a general model is used to derive models that incorporate the uncertainty of operating environments, which provides the flexibility in considering a different fault detection rate and random environmental factor and so on. Several published models are shown to be covered by this general model and a new model is also developed and examined. The numerical illustrative examples of the proposed model have been validated on two sets of real software failure data in terms of six criteria. The comparison results demonstrate that the new model can fit and predict significantly better than other existing models.

In this study, an imperfect debugging software reliability growth model (SRGM) with Bayesian analysis was proposed to determine an optimal software release in order to minimize software testing costs and also enhance the practicability. Generally, it is not easy to estimate the model parameters by applying MLE (maximum likelihood estimation) or LSE (least squares estimation) with insufficient historical data. Therefore, in the situation of insufficient data, the proposed Bayesian method can adopt domain experts’ prior judgments and utilize few software testing data to forecast the reliability and the cost to proceed with the prior analysis and the posterior analysis. Moreover, the debugging efficiency involves testing staff’s learning and negligent factors, and therefore, the human factors and the nature of debugging process are taken into consideration in developing the fundamental model. Based on this, the estimation of the model’s parameters would be more intuitive and can be easily evaluated by domain experts, which is the major advantage for extending the related applications in practice. Finally, numerical examples and sensitivity analyses are performed to provide managerial insights and useful directions for software release strategies.

In the software development life cycle, the quality and reliability of software are critical to software developers. Poor quality and reliability not only cause the loss of customers and sales but also increase the operational risk due to unreliable codes. Therefore, software developers should try their best to reduce such potential software defects by undertaking a software testing project. However, to pursue perfect and faultless software is unrealistic since the budget, time, and testing resources are limited, and the software developers need to reach a compromise that balances software reliability and the testing cost. Using the model presented in this study, software developers can devise multiple alternatives for a software testing project, and each alternative has its distinct allocation of human resources. The best alternative can therefore be selected. Furthermore, the allocation incorporates debuggers’ learning and negligent factors, both of which influence the efficiency of software testing in practice. Accordingly, the study considers both human factors and the nature of errors during the debugging process to develop a software reliability growth model to estimate the related costs and the reliability indicator. Additionally, the issue of error classification is also extended by considering the impacts of errors on the system, and the expected time required to remove simple or complex errors can be estimated based on different truncated exponential distributions. Finally, numerical examples are presented and sensitivity analyses are performed to provide managerial insights and useful directions to inform software release strategies.

Many NHPP software reliability growth models (SRGMs) have been proposed to assess software reliability during the past 40 years, but most of them have focused on modeling the fault detection process (FDP) in two ways: one is to ignore the fault correction process (FCP), i.e., faults are assumed to be instantaneously removed after the failure caused by the faults is detected. However, in real software development, it is not always reliable as fault removal usually needs time, i.e., the faults causing failures cannot always be removed at once and the detected failures will become more and more difficult to correct as testing progresses. Another way to model the fault correction process is to consider the time delay between the fault detection and fault correction. The time delay has been assumed to be constant and function dependent on time or random variables following some kind of distribution. In this paper, some useful approaches to the modeling of dual fault detection and correction processes are discussed. The dependencies between fault amounts of dual processes are considered instead of fault correction time-delay. A model aiming to integrate fault-detection processes and fault-correction processes, along with the incorporation of a fault introduction rate and testing coverage rate into the software reliability evaluation is proposed. The model parameters are estimated using the Least Squares Estimation (LSE) method. The descriptive and predictive performance of this proposed model and other existing NHPP SRGMs are investigated by using three real data-sets based on four criteria, respectively. The results show that the new model can be significantly effective in yielding better reliability estimation and prediction.

The software testing process basically aims at building confidence in the software for its use in real world applications. The reliability of a software system is always important to us. As we carry out the error detection and correction phenomenon on our software, the reliability of the software grows. With an aim to model this growth in the software reliability, many formulations in the form of Software Reliability Growth Models have been proposed. Many of these are based on Non-Homogeneous Poisson Process framework. In this paper, a parallel comparison of the performance of the proposed software reliability growth models is carried out, considering linear and exponential fault content functions for study of imperfect debugging situations. The performance of the proposed models has been compared with some famous existing software reliability models and the proposed models have been validated on some real-world datasets. Three goodness-of-fit criteria that include mean square error, predictive-ratio risk and predictive power are used to carry out the performance comparison of the models. Using these comparison criteria on six actual failure datasets, it is concluded that the proposed Model-2 which always outperforms Model-1, fits the actual failure data better and has better predictive power than other considered SRGMs for at least two data sets.

In allusion to the flaws in software cost model and optimal release policy, inadequate consideration for real debugging, a cost model and optimal release policy for SRGM (Software Reliability Growth Model) incorporating imperfect debugging is proposed. A SRGM is presented, based on incomplete debugging, introduction of new faults and TE (Testing Effort). It is verified to describe real testing process well by actual failure data set and has better performance as compared to other models. Based on the proposed SRGM, a formulation of cost function is also established especially considering the impact of imperfect debugging on cost. Furthermore, the optimal release policies given limited reliability objective and the uncertainty in actual total cost exceeding expected one are developed and elaborated. Finally, a numerical example and related data analyses are illustrated and parameter sensitivity analysis is performed.