Non-homogeneous Poisson Process Software Reliability Research Articles

Optimal test activity allocation for covariate software reliability and security models

Traditional software reliability growth models enable quantitative assessment of the software testing process by characterizing the fault detection in terms of testing time or effort. However, the majority of these models do not identify specific testing activities underlying fault discovery and thus can only provide limited guidance on how to incrementally allocate effort. Although there are several novel studies focused on covariate software reliability growth models, they are limited to model development, application, and assessment.This paper presents a non-homogeneous Poisson process software reliability growth model incorporating covariates based on the discrete Cox proportional hazards model. An efficient and stable expectation conditional maximization algorithm is applied to identify the model parameters. An optimal test activity allocation problem is formulated to maximize fault discovery. The proposed method is illustrated through numerical examples on two data sets.

Performance Optimized Expectation Conditional Maximization Algorithms for Nonhomogeneous Poisson Process Software Reliability Models

Nonhomogeneous Poisson process (NHPP) and software reliability growth models (SRGM) are a popular approach to estimate useful metrics such as the number of faults remaining, failure rate, and reliability, which is defined as the probability of failure free operation in a specified environment for a specified period of time. We propose performance-optimized expectation conditional maximization (ECM) algorithms for NHPP SRGM. In contrast to the expectation maximization (EM) algorithm, the ECM algorithm reduces the maximum-likelihood estimation process to multiple simpler conditional maximization (CM)-steps. The advantage of these CM-steps is that they only need to consider one variable at a time, enabling implicit solutions to update rules when a closed form equation is not available for a model parameter. We compare the performance of our ECM algorithms to previous EM and ECM algorithms on many datasets from the research literature. Our results indicate that our ECM algorithms achieve two orders of magnitude speed up over the EM and ECM algorithms of [1] when their experimental methodology is considered and three orders of magnitude when knowledge of the maximum-likelihood estimation is removed, whereas our approach is as much as 60 times faster than the EM algorithms of [2] . We subsequently propose a two-stage algorithm to further accelerate performance.

Comparison of Non-Homogeneous Poisson Process Software Reliability Models in Web Applications

Software reliability is an important quality factor that effects project success. By modelling software reliability, it can be estimated when and with how much effort a project can be deployed. Consequently, this can contribute to the resource and schedule planning of a project. Therefore, software reliability models SRM are frequently used for measuring the maturity of a software. A number of studies exist in the literature that compare SRMs in terms of their modelling performance. However, there is a need of evaluating these SRMs by taking into account the software project domain. This study aims to compare the performance of SRMs in the context of Web applications. In accordance to this purpose, six different software reliability models, namely Goel-Okumoto, Musa Exponential, Inflected S-shaped, Delayed S-shaped, Yamada and Pham Nordmann Zhang Imperfect Fault Detection PNZ , are evaluated by using the defect records of four Web application projects developed by a Turkish software organization. 100%, 70% and 50% of the recorded data is used as input to the maximum likelihood parameter estimation MLPE method and the results of these three cases are investigated and commented separately in the research. The goodness of fit and the predictive validity of the models to the project data are tested by calculating Mean Square Error MSE , Mean Magnitude Relative Error MMRE , Percentage Relative Error Deviation PRED and Average Balanced Predicted Relative Error A.BPRE measures. For each NHPP model 48 separate cases which are combinations of the three defect inflow data cases 100%, 70% and 50% , four projects and four measures, are investigated and ranked. It is shown that the NHPP models can be applied to Web applications and Delayed S-shaped model displays the best results among the alternatives. However, it is understood that the Goel-Okumoto and Yamada models give identical results and that these two models converge to each other with respect to the project defect data that has been used. Combined, these two models obtain the highest ranking scores and it is concluded that these two models perform better than the other models with respect to Web based software.

Discrete Nonhomogeneous Poisson Process Software Reliability Growth Models Based on Test Coverage

To incorporate the effect of test coverage, we proposed two novel discrete nonhomogeneous Poisson process software reliability growth models in this article using failure data and test coverage, which are both regarding the number of executed test cases instead of execution time. Because one of the most important factors of the coverage‐based software reliability growth models is the test coverage function (TCF), we first discussed a discrete TCF based on beta function. Then we developed two discrete mean value functions (MVF) integrating test coverage and imperfect debugging. Finally, the proposed discrete TCF and MVFs are evaluated and validated on two actual software reliability data sets. The results of numerical illustration demonstrate that the proposed TCF and the MVFs provide better estimation and fitting under comparisons. Copyright © 2012 John Wiley & Sons, Ltd.

Cramer–von Mises Tests for the Compatibility of Two Software Operating Environments

Higher-precision inferences about impending software failures can be achieved when the same software reliability model that fits failure data from the test interval also fits data from the field interval. If the test and field environments differ significantly in terms of how the software is used, then a single model for the pooled data may not be adequate. In this article we formulate the hypothesis of compatible test and field environments in terms of a statistical hypothesis and develop a Cramer–von Mises (CvM) test procedure within the context of a well-known nonhomogeneous Poisson process software reliability model. The CvM test has a compelling advantage over a previously proposed likelihood ratio test (LRT0), because it does not require specification of the class of alternatives, which are frequently unknown for real-life problems. Moreover, although there are existence issues with LRT0, the CvM test always exists. An asymptotic approximation for the p value of the CvM test is derived, and an algorithm for a small-sample bootstrap approximation is presented. A simulation study shows that the CvM test works well for the class of alternatives for which LRT0 also would work well and continues to work well for other alternatives for which LRT0 has no statistical motivation or otherwise has existence problems. Data from a real software project are used to illustrate the hypothesis testing procedures.

NHPP software reliability and cost models with testing coverage

This paper proposes a software reliability model that incorporates testing coverage information. Testing coverage is very important for both software developers and customers of software products. For developers, testing coverage information helps them to evaluate how much effort has been spent and how much more is needed. For customers, this information estimates the confidence of using the software product. Although research has been conducted and software reliability models have been developed, some practical issues have not been addressed. Testing coverage is one of these issues. The model is developed based on a nonhomogeneous Poisson process (NHPP) and can be used to estimate and predict the reliability of software products quantitatively. We examine the goodness-of-fit of this proposed model and present the results using several sets of software testing data. Comparisons of this model and other existing NHPP models are made. We find that the new model can provide a significant improved goodness-of-fit and estimation power. A software cost model incorporating testing coverage is also developed. Besides some traditional cost items such as testing cost and error removal cost, risk cost due to potential faults in the uncovered code is also included associated with the number of demands from customers. Optimal release policies that minimize the expected total cost subject to the reliability requirement are developed.

Comparisons of nonhomogeneous Poisson process software reliability models and its applications

In this paper, existing software reliability models based on an nonhomogeneous Poisson process (NHPP) are summarized. A recently developed NHPP model with imperfect debugging and time-dependent fault detection rate is examined. The results show that this proposed model provides improved descriptive and predictive power when compared with other existing NHPP models. The model can also be incorporated into a software cost model for reliability assessment. The optimal release policies which minimize the expected total software cost is also presented.