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Advancements in science and technology have led to the widespread use of computer systems in various applications, emphasizing the importance of software reliability. Software failures can have severe consequences, making thorough testing crucial. Software reliability growth models (SRGMs) play a significant role in enhancing reliability by predicting improvement over time. This article introduces a comprehensive approach to software reliability that incorporates a dynamic fault detection rate, along with fault removal efficiency. The fault detection rate measures the rate at which faults are identified during testing, reflecting the effectiveness of the testing process. By incorporating this dynamic component, the model provides a more accurate estimation of software reliability and enables adaptive testing strategies and resource allocation. Achieving a high fault detection rate is desirable, but organizations must consider the cost implications and strike a balance between reliability and time-to-market constraints. This article extends the analysis to calculate the optimal release time and optimal warranty period that minimize development costs, subject to the desired reliability. By considering these factors, development teams can make informed decisions regarding the timing of software release and the duration of the warranty period, optimizing both reliability and cost. [ABSTRACT FROM AUTHOR]

In our fast-paced modern world, software systems have become indispensable in both personal and professional spheres. With increasing reliance on software products, the demand for reliable and high-quality software has intensified, placing significant pressure on developers to stay competitive. Software reliability growth models (SRGMs) play a vital role in assessing the dependability of software systems during their development. These models mathematically analyze the relationship between detected faults, testing time, and failures, enabling the prediction of software failures. This paper introduces an approach to software reliability evaluation, considering the dynamic nature of fault removal efficiency (FRE) during development. Additionally, the model accounts for the change rate of residual errors, considering both error introduction and correction processes. Moreover, the adoption of S-shaped curves captures the learning process of software developers, enhancing the model's accuracy. This approach guides software developers to make informed decisions, leading to improved software reliability and performance, meeting escalating demands. [ABSTRACT FROM AUTHOR]

Software reliability is a critical aspect of ensuring the quality and dependability of software systems. However, existing software reliability models often make assumptions that do not align with real-world scenarios, such as perfect fault removal and independent faults. In this paper, we address this gap by developing a software reliability model that considers fault-dependent detection, imperfect fault removal, and the maximum number of faults that may present in the system. By accounting for these factors, our proposed model aims to provide a more accurate representation of software reliability. We evaluate the effectiveness of our model by comparing it to existing models using three commonly used goodness-of-fit criteria. The results demonstrate the importance of incorporating these considerations in software reliability modeling and highlight the superiority of our approach in capturing the complexities associated with software faults. Additionally, this paper conducts an analysis of optimal release planning, which yields highly encouraging results for software managers and engineers. This analysis adds significant value to the existing literature, further emphasizing the practical relevance of our proposed model. [ABSTRACT FROM AUTHOR]

Software developers' goal is to develop reliable and superior software. Due to the fact that software errors frequently generate large societal or financial losses, software reliability is essential. Software reliability growth models are a widely used technique for software reliability assessment. This study examines various nonhomogeneous Poisson process models with the newly developed software reliability distribution and evaluates the unknown model parameters based on frequentist and Bayesian methods of estimation. Finally, we conduct evaluations on real datasets using a variety of evaluation criteria to compare the results of previous software reliability growth models and show how the proposed model may be applied under both approaches in a practical setting. According to this study, the innovative model's mean square error, R2, Adj−R2$Adj - {R}^2$, bias, predicted relative variation, Theil statistic, and mean error of prediction values show the lowest values under the Bayesian approach for data sets II to IV, and both approaches perform well for data set I. These implementation findings demonstrate the effectiveness of our specific approach based on our examination of failure data. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid forecasting model combining auto-regressive integrated moving average (ARIMA) and artificial neural network (ANN) techniques to improve the software fault forecasting and hence improvising the reliability of software. Software reliability forecasting plays a critical role in software development and maintenance, as it helps to identify potential errors and improve the overall performance of software systems. The proposed model leverages the strengths of both ARIMA and ANN, allowing for more accurate predictions and better handling of complex and dynamic software systems. The effectiveness of the hybrid model is evaluated using real-world software data, demonstrating its superiority over traditional forecasting methods. This research contributes to the development of more robust and reliable software systems, which are essential in today's rapidly evolving technological landscape. [ABSTRACT FROM AUTHOR]

Numerous software reliability growth models (SRGMs) are proposed in the last four decades to track the reliability growth of software during the testing phase. In many existing models, it is assumed that the faults in the software are of the same type. However, this assumption may not be realistic. Software contains different faults and the detection/correction of different faults can require different efforts. In this paper, we propose a more general software reliability model considering heterogeneous faults, where the parameters for the detection time and correction delay of different faults are assumed to be faults specific and allowed to follow arbitrary distributions. Considering different parameters makes the model more flexible and adaptable to different practical software development situations. Some specific models are derived under different assumptions on the distributions of fault detection time, fault correction delay, and the corresponding parameters. Both MLE and LSE are proposed for parameter estimation. Illustrative examples with real data set are studied to compare the proposed models with homogeneous faults model, and the results have shown advantages of our models. The optimal software release policy based on the proposed model is also studied. [ABSTRACT FROM AUTHOR]

Non-Homogeneous Poisson Process (NHPP) is a standard framework in the field of software reliability analysis. The core of NHPP consists in determining the Mean Value Function (MVF) of cumulative error number at a specific time slot. However, practice shows the difficulty in finding a general model to fit all sorts of fault data. A certain model is only sensitive to the specific object(s). Modeling failure MVF for NHPP still faces a number of challenges such as making reasonable explanation of assumption, determining fault detection rate per error, fault modification efficiency, error introduction rate, etc. In this research, we propose a novel Software Reliability Growth Model (SRGM) by leveraging generalized imperfect debugging NHPP framework. We first provide physical explanations for assumptions on error modification, error introduction and fault detection rate per error. Meanwhile, we generate a typical constraint relationship between the total error introduction rate and change rate of generalized residual errors. We also describe the fault detection rate per error with the form of exponential decay function, and use error reduction factor to form the new model. Furthermore, we make extensive discussions based on our proposed model. The experimental results confirm that our proposed model is effective on fault fitting and prediction, especially excellent on short-term prediction.

The reliability of software has a tremendous influence on the reliability of systems. Software dependability models are frequently utilized to statistically analyze the reliability of software. Numerous reliability models are based on the nonhomogeneous Poisson method (NHPP). In this respect, in the current study, a novel NHPP model established on the basis of the new power function distribution is suggested. The mathematical formulas for its reliability measurements were found and are visually illustrated. The parameters of the suggested model are assessed utilizing the weighted nonlinear least-squares, maximum-likelihood, and nonlinear least-squares estimation techniques. The model is subsequently verified using a variety of reliability datasets. Four separate criteria were used to assess and compare the estimating techniques. Additionally, the effectiveness of the novel model is assessed and evaluated with two foundation models both objectively and subjectively. The implementation results reveal that our novel model performed well in the failure data that we examined. [ABSTRACT FROM AUTHOR]

Within exponential families, which may consist of multi-parameter and multivariate distributions, a variety of divergence measures, such as the Kullback–Leibler divergence, the Cressie–Read divergence, the Rényi divergence, and the Hellinger metric, can be explicitly expressed in terms of the respective cumulant function and mean value function. Moreover, the same applies to related entropy and affinity measures. We compile representations scattered in the literature and present a unified approach to the derivation in exponential families. As a statistical application, we highlight their use in the construction of confidence regions in a multi-sample setup.

In this study, the mean value and variance functions of type II counter process constituted as a delayed renewal process are obtained analytically. In the applications of the delayed renewal process, generally, the functional forms of the distributions are known but some parameters of the distributions are unknown. In those cases, the mean value and the variance functions must be estimated from the data. In this study, after obtaining the mean value and variance functions of type II counter process analytically, depending on the analytical expressions, we deal with the problem of estimating these functions and some estimators are proposed. Performance of the estimators is evaluated for small sample sizes by a simulation study according to bias and mean square error criteria. [ABSTRACT FROM AUTHOR]

In order to assess software reliability, many Software Reliability Growth Models (SRGMs) have been proposed in the past 40 years. In principle, two widely used methods for the parameter estimation of SRGMs are the Maximum Likelihood Estimation (MLE) and the Least Squares Estimation (LSE). However, the approach of these two estimations may impose some restrictions on SRGMs, such as the existence of derivatives from formulated models or the needs for complex calculation. In this paper, a Modified Genetic Algorithm (MGA) is proposed to assess the reliability of software considering the time domain software failure data and SPC using inflection S-shaped model which is Non-Homogenous Poisson Process (NHPP)-based. Experiments based on real software failure data are performed and the results show that the proposed Genetic Algorithm (GA) is more effective and faster than traditional algorithms. [ABSTRACT FROM AUTHOR]

As most software reliability models do not clearly explain the variance in the mean value function of cumulative software errors, they might not be effective in deducing the confidence interval regarding the mean value function. In such cases, software developers cannot estimate the possible risk variation in software reliability by using the randomness of the mean value function, thus reducing the decision-making reliability when determining an optimal software release time. In this paper, the method of stochastic differential equations is used to build a software reliability model, which is validated based on practical data previously used in six published papers. Moreover, the estimation of the parameters of the proposed model, which can be defined as the autonomous error-detected factor and the learning factor, is also illustrated, and the results of model validation empirically confirm that the proposed model is able to account for a fairly large portion of the variance of the mean value function. Additionally, the confidence intervals of the mean value function regarding software faults are employed to assist software developers in determining the optimal release times at different confidence levels. Finally, a numerical example is given to verify the effectiveness of the proposed model. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Goel proposed generalization of the Goel-Okumoto (G-O) software reliability growth model (SRGM), in order to model the failure intensity function, i.e. the rate of occurrence of failures (ROCOF) that initially increases and then decreases (I/D), which occurs in many projects due to the learning phenomenon of the testing team and a few other causes. The ROCOF of the generalized non-homogenous poisson process (NHPP) model can be expressed in the same mathematical form as that of a two-parameter Weibull function. However, this SRGM is susceptible to wide fluctuations in time between failures and sometimes it seems unable to recognize the I/D pattern of ROCOF present in the datasets and hence does not adequately describe such data. The authors therefore propose a shifted Weibull function ROCOF instead for the generalized NHPP model. This modification to the Goel-generalized NHPP model results in an SRGM that seems to perform better consistently, as confirmed by the goodness of fit statistic and predictive validity metrics, when applied to failure datasets of 11 software projects with widely varying characteristics. A case study on software release time determination using the proposed SRGM is also given. [ABSTRACT FROM AUTHOR]

Due to the large scale application of software systems, software reliability plays an important role in software developments. In this paper, a software reliability growth model (SRGM) is proposed. The testing time on the right is truncated in this model. The instantaneous failure rate, mean-value function, error detection rate, reliability of the software, estimation of parameters and the simple applications of this model are discussed. [ABSTRACT FROM AUTHOR]

Within exponential families, which may consist of multi-parameter and multivariate distributions, a variety of divergence measures, such as the Kullback–Leibler divergence, the Cressie–Read divergence, the Rényi divergence, and the Hellinger metric, can be explicitly expressed in terms of the respective cumulant function and mean value function. Moreover, the same applies to related entropy and affinity measures. We compile representations scattered in the literature and present a unified approach to the derivation in exponential families. As a statistical application, we highlight their use in the construction of confidence regions in a multi-sample setup. [ABSTRACT FROM AUTHOR]