Software reliability growth model with change-point and environmental function

Recent research applies soft computing techniques to fit software reliability growth models. However, runtime performance and the distribution of the distance from an optimal solution over multiple runs must be explicitly considered to justify the practical utility of these approaches, promote comparison, and support reproducible research. This paper presents a meta-optimization framework to design stable and efficient multi-phase algorithms for fitting software reliability growth models. The approach combines initial parameter estimation techniques from statistical algorithms, the global search properties of soft computing, and the rapid convergence of numerical methods. Designs that exhibit the best balance between runtime performance and accuracy are identified. The approach is illustrated through nonhomogeneous Poisson process and covariate software reliability growth models, including a cross-validation step on data sets not used to identify designs. The results indicate the nonhomogeneous Poisson process model considered is too simple to benefit from soft computing because it incurs additional runtime with no increase in accuracy attained. However, a multi-phase design for the covariate software reliability growth model consisting of the bat algorithm followed by a numerical method achieves better performance and converges consistently, compared to a numerical method only. The proposed approach supports higher-dimensional covariate software reliability growth model fitting suitable for implementation in a tool.

This paper proposes a new scheme for constructing software reliability growth models (SRGM) based on a nonhomogeneous Poisson process (NHPP). The main focus is to provide an efficient parametric decomposition method for software reliability modeling, which considers both testing efforts and fault detection rates (FDR). In general, the software fault detection/removal mechanisms depend on previously detected/removed faults and on how testing efforts are used. From practical field studies, it is likely that we can estimate the testing efforts consumption pattern and predict the trends of FDR. A set of time-variable, testing-effort-based FDR models were developed that have the inherent flexibility of capturing a wide range of possible fault detection trends: increasing, decreasing, and constant. This scheme has a flexible structure and can model a wide spectrum of software development environments, considering various testing efforts. The paper describes the FDR, which can be obtained from historical records of previous releases or other similar software projects, and incorporates the related testing activities into this new modeling approach. The applicability of our model and the related parametric decomposition methods are demonstrated through several real data sets from various software projects. The evaluation results show that the proposed framework to incorporate testing efforts and FDR for SRGM has a fairly accurate prediction capability and it depicts the real-life situation more faithfully. This technique can be applied to wide range of software systems.

In this chapter we discuss the software reliability growth models (SRGMs) that describe the relationship between the number of faults removed and the number of test cases used. Firstly we describe the discrete exponential and S-shaped models in a perfect debugging environment. We also discuss flexible discrete SRGM, which can depict either exponential or S-shaped growth curves, depending upon the parameter values estimated from the past failure data. Further, we describe an SRGM for the fault removal phenomenon in a perfect debugging environment. Most testing processes are imperfect in practice, therefore we also discuss a discrete model that incorporates the impact of imperfect debugging and fault generation into software reliability growth modeling. Faults in the software are generally not of the same type, rather the faults contained in a large software may differ from each other in terms of the amount of time and skill of the removal team required to remove them. Three discrete models: the generalized Erlang model, modeling severity of faults with respect to testing time, and a model with faults of different severity incorporating logistic learning function have been discussed. A discrete model in a distributed environment is also discussed. The above discrete SRGMs assume a constant fault detection rate while testing the software under consideration. In practice, however, the fault detection rate varies because of changes in the testing skill, the system environment, and the testing strategy used to test the software. SRGMs for the fault removal phenomenon, the generalized Erlang model, and the generalized Erlang model with logistic function are discussed, incorporating the concept of change point. It is also shown how equivalent continuous models can be derived. This chapter describes the state-of-the-art in discrete modeling.

Multiple Software Reliability Growth Models (SRGM) has been illustrated to inspire designers and software developers to develop quality software. These models implicitly assume that expenditure is constant throughout testing effort. Recently importance was given to the testing phase by the development team and it requires controlled screening closely to raise its overall operational efficiency. Software Reliability Growth Models exhibits a precise relation between the failure patterns with time. Considering this as a basic building block a SRGM which is a Non-Homogeneous Poisson Process in nature is i in this work. The various aspects of our proposed model are testing effort function and fault detection rate (FDR). Mainly in Software Reliability Growth Model it was assumed that fault removal process are perfect which is not true in reality as new faults may get introduced during removal or some faults may not get removed due to its complexity. Thus in this model the concept of imperfect debugging was considered and assists us to justify the software reliability more convincingly through the help of testing effort function.

Performance analysis of software reliability growth models with testing-effort and change-point

Non-homogeneous Poisson process (NHPP) model with typical reliability growth patterns is an important technology about evaluating software reliability. Two parameters which affect software reliability are original failures number and failure-detected rate. The paper firstly defines the software failure distributed and discusses a few kinds' software reliability models. Non-homogeneous Poisson process model is presented. The models with different parameters are discussed and analyzed. The model's restrict condition and some of parameters, original failures number and failure-detected ratio, are extrapolated. Assessment methodology about key parameters is given.

In reality, the fault detection (or correction) phenomenon and software reliability estimation in the operational phase are different from that in the testing phase. The fault removal continues at a slower rate during the operational phase. In this paper, we will investigate some techniques for software reliability prediction and measurement in the operational phase. We first review how some software reliability growth models (SRGMs) based on non-homogeneous Poisson processes (NHPPs) can be readily derived based on a unified theory for NHPP models. Under this general framework, we can not only verify some conventional SRGMs but also derive some new SRGMs that can be used for software reliability measurement in the operational phase. That is, based on the unified theory, we can incorporate the concept of multiple changepoints into software reliability modeling. We can formularize and simulate the fault detection process in the operational phase. Some numerical illustrations based on real software failure data are also presented. The experimental results show that the proposed models can easily reflect the possible changes of fault detection process and offer quantitative analysis on software failure behavior in field operation.

This investigation deals with a N-modules software reliability growth model (SRGM) wherein each module attains multiple types of faults of different severity levels. During the debugging phase, there may arise some new faults due to assumption of imperfect debugging. The reliability growth during the software testing phase governed by a non-homogeneous Poisson Process (NHPP). The proposed study is devoted to analyze the fault debugging phenomenon in all modules of software and to obtain expected number of faults observed, isolated and removed. The software reliability and optimum total cost of the software development during the testing phase are evaluated. The causes of fault occurrences in each module are different. The faults may occur with different failure rates and follow the nonlinear behavior with respect to the testing time. The NHPP model incorporates the testing-effort expenditure required for the faults debugging activities and governed by Weibull and logistic distributions which influence considerably not only the fault observation rate but also the time to isolate the faults and the time to remove the faults from all N-modules. In addition to predict the reliability of N-modular software, this study proposes optimal release policies for the SRGM by minimizing the expected cost subject to budget and testing-effort constraints, while ensuring a prescribed level of reliability and incorporating the effects of testing effort and efficiency. Some specific models are also deduced by setting the appropriate parameters so as to match with the existing models in the literature. Sensitivity results are presented through a numerical experiment to demonstrate the validity of the analytical formulations and the computational tractability of the model. An evolutionary algorithm, namely Particle Swarm Optimization (PSO) based on a dynamic penalty method, is employed to determine the optimal release time.

It is one of the important issues in modern software development to make a highly reliable software system by efficient and economical testing. As one of these solutions, many companies have taken in testing-progress management and quality/reliability assessment based on software reliability growth models. Consequently, many software reliability growth models reflecting various development factors and operational environment of the software system have been proposed. Most of these models have assumed the software system as one domain. That is, the models have assumed that the set of the testing-paths influenced by execution of test-cases is extended with testing-progress and it expands to whole software system finally. However, a software system has the structure that the main-component calls plural sub-components ordinarily. Therefore, unless the main-component is tested, the sub-component called from it is not tested. In this chapter, we propose software reliability growth models based on such components' characteristics. Especially, these models reflecting the different testing-environment for composed components are formulated by nonhomogeneous Poisson processes. Furthermore, using fault-detection data observed in actual development projects, we show numerical examples of software reliability assessment and results of goodness-of-fit comparisons with existing software reliability growth models.

Many software reliability growth models have been proposed in the past decade. Those models tacitly assume that testing-effort expenditures are constant throughout software testing. This paper develops realistic software reliability growth models incorporating the effect of testing-effort. The software error detection phenomenon in software testing is modeled by a nonhomogeneous Poisson process. The software reliability assessment measures and the estimation methods of parameters are investigated. Testing-effort expenditures are described by exponential and Rayleigh curves. Least-squares estimators and maximum likelihood estimators are used for the reliability growth parameters. The software reliability data analyses use actual data. The software reliability growth models with testing-effort can consider the relationship between the software reliability growth and the effect of testing-effort. Thus, the proposed models will enable us to evaluate software reliability more realistically.

In the software testing process, many factors can affected the failure distribution, such as the testing strategy, running environment and resource allocation, etc. Once these factors are transformed during testing phase, they could result in the failure intensity function increasing or decreasing non-monotonically and abrupt fluctuations at a certain time interval. Especially, in large software systems, detected complex faults and failures are more difficult to isolate, reproduce and remove in comparison of detected simple faults and failures. Therefore, the fault detection rate shows the irregular fluctuation over time in the software testing process. In this paper, we propose an imperfect software debugging model derived from an Ito -type stochastic differential equation (SDE). In the actual testing process, the cumulative number of fault detection can be considered a stochastic event. Thus, we can model fault detection process using SDE. We estimate the parameters of the proposed model using maximum likelihood estimation. We also use five historical fault data sets to test the performance of the proposed model. To show that the proposed model is the best model among all models, we use a new optimal method to select the best model from various software reliability models. Experimental results show that the proposed model has better fitting and predictive performance than non-homogeneous Poisson process models and other perfect software reliability models based on SDE.

In order to incorporate the effect of test coverage, two novel software reliability growth models (SRGMs) are proposed in this paper using failure data and test coverage simultaneously. One is continuous using testing time, and the other is discrete with respect to the number of executed test cases instead of testing time. Since one of the most important factors of the coverage-based SRGMs is the test coverage function (TCF), we first discuss a discrete TCF based on Beta function. Then we develop mean value functions (MVF) of the two models integrating test coverage and imperfect debugging. Finally the proposed TCF and MVFs are evaluated and validated on actual software reliability data collected from real software development projects. The results demonstrate clearly that both the proposed TCF and SRGMs provide better estimation and fitting for the data sets under comparisons.

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.

Software reliability assessment for an exponential-S-shaped reliability growth phenomenon

Owing to release of software in multiple releases, code changes take place in software. Because of this added complexity in software, the testing team may be unable to correct the fault upon detection, leaving the actual fault to reside in the software, termed as imperfect debugging or there may be replacement of original fault by other fault, leading to error generation. Many other factors exist that affect the testing phase of software like strategies of testing, test cases, skill, efficiency, and learning of testing team. All these factors cannot be kept stable during the whole process of testing. They may change at any time moment causing the background processes to experience change, which is known as change‐point. Keeping all these critical testing environment factors under consideration, a new software reliability growth model has been proposed, which is derived from an non homogenous Poisson process (NHPP)based unified scheme for multi‐release two‐stage fault detection/observation and correction/removal software reliability models. The developed model is numerically illustrated on tandem data set for four releases.