Software Reliability Growth Models Based on Non-Homogeneous Poisson Process

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.

The non-homogeneous Poisson process (NHPP) model is a very important class of software reliability models and is widely used in software reliability engineering. NHPPs are characterized by their intensity functions. In the literature it is usually assumed that the functional forms of the intensity functions are known and only some parameters in intensity functions are unknown. The parametric statistical methods can then be applied to estimate or to test the unknown reliability models. However, in realistic situations it is often the case that the functional form of the failure intensity is not very well known or is completely unknown. In this case we have to use functional (non-parametric) estimation methods. The non-parametric techniques do not require any preliminary assumption on the software models and then can reduce the parameter modeling bias. The existing non-parametric methods in the statistical methods are usually not applicable to software reliability data. In this paper we construct some non-parametric methods to estimate the failure intensity function of the NHPP model, taking the particularities of the software failure data into consideration.

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.

This article is mainly focused on finding the best possible way to rectify bug fixing rate (BFR) and bug fixing time (BFT). Further, versatile software projects have been verified when materialising the bug fixing rate. To increase the bug fixing rate, bug traceability is reduced by virtue of version tag in each and every component of a software deliverable. Software build release time is optimised by using mathematical optimisation techniques such as software reliability growth and non-homogeneous Poisson process models. This is very much essential in the present market scenario. The build inconsistency and automation are also rectified in this erudite research work. The developed software is free from defects and improves the software quality by increasing bug fixing rate.

The mean time between failures (MTBF) estimation has been intensively investigated in recent years. MTBF can be used to decide on a maintenance strategy or inspection timeline intervals for the RSG-GAS reactor (or GAS multipurpose reactor). The RSG-GAS reactor is a pool-type reactor where light water is used as a moderator, coolant, and shielding. The purpose of this paper is to propose the nonhomogeneous Poisson process (NHPP) model to obtain the MTBF estimation value. Thus, the RSG-GAS reactor installation would have higher safety, a longer lifetime, and substantial reliability with a minor failure rate, including the subcomponents of the JE01-AP03 primary centrifugal pump. In this research work, the methodology processes data accumulation and estimates the parameters of the NHPP model to determine the maintenance schedule or inspection timeline intervals based on the MTBF value when the confidence level reaches the targeted percentage. The results indicate that a MTBF estimation has been acquired for the RSG-GAS reactor installation. In the implemented case, an inspection timeline is defined for the JE01-AP03 primary centrifugal pump with a reliability growth value of 0.41 and a MTBF estimation circa 42 days.

Software has become a vital factor in the fourth industrial revolution. Owing to the increase in demand for software products in various fields (big data, artificial intelligence, the Internet of Things, etc.), the software industry has expanded more than ever before. Therefore, software reliability has become very important, and efforts are being made to increase it. One of these efforts is the development of software reliability models (SRMs). SRMs have been studied for a long time as a model that predicts software reliability by using the number of software faults. Software failures can occur for several reasons, including independent software faults such as code errors and software hangs, as well as dependent cases where code errors lead to other software faults. Recently, due to the diversity of software operating environments, software faults are more likely to occur in a dependent manner, and, for this reason, they are likely to increase rapidly from the beginning and progress slowly to the maximum number thereafter. In addition, many large companies have focused on open-source software (OSS) development, and OSS is being developed by many users. In this study, we propose a new SRM that considers the number of finite faults and dependent faults, and examine the goodness-of-fit of a new SRM and other existing non-homogeneous Poisson process models based on the OSS datasets. Through numerical examples, the proposed model demonstrated a significantly better goodness-of-fit when compared to other existing models, and it also exhibited better results on the newly proposed integrated criteria.

We propose an approach of component-based software reliability analysis which includes the benefits of both time domain, and structure based approaches. This approach overcomes the deficiency of existing black box and white box techniques that fall short of addressing repair, and internal system structures simultaneously. Our solution adopts a method of testing data transformation to cover both methods, and is expected to improve reliability prediction. This paradigm starts with consideration of component-based software testing process in view of the assumption of NHPP models. It accounts for software structures by the way of modeling the testing process. According to the testing model it builds the mapping relation from the testing profile to the operational profile of component-based software which enables the testing data transformation to build the reliability dataset required by non-homogeneous Poisson process (NHPP) models. At last an example is evaluated to validate and show the effectiveness of this approach.

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.

NHPP models with Markov switching for software reliability

In this paper we consider non-parametric estimation methods for software reliability assessment without specifying the fault distribution, where the underlying stochastic process to describe software fault-counts in the system testing is given by a non-homogeneous Poisson process. A comprehensive approach based on the kernel estimation is provided with several kernel functions and bandwidth estimations. Next, we develop interval estimation methods via the non-parametric bootstrap, and derive the confidence regions of several reliability measures such as the expected cumulative number of software faults, software intensity function, quantitative software reliability as well. The resulting data-driven methodology can give the useful probabilistic information on the software reliability prediction under the incomplete knowledge on fault distribution. In illustrative examples with a real software fault data, it is shown that the proposed methods provide useful software reliability measures under uncertainty from the view point of frequentist analysis.

Software reliability growth models based on a nonhomogeneous Poisson process (NHPP) have been considered as one of the most effective among various models since they integrate the information regarding testing and debugging activities observed in the testing phase into the software reliability model. Although most of the existing NHPP models have progressed successfully in their estimation/prediction accuracies by modifying the assumptions with regard to the testing process, these models were developed based on the instantaneous fault-removal assumption. In this paper, we develop a generalized NHPP software reliability model considering quasi-renewal time-delay fault removal. The quasi-renewal process is employed to estimate the time delay due to identifying and prioritizing the detected faults before actual code change in the software reliability assessment. Model formulation based on the quasi-renewal time-delay assumption is provided, and the generalized mean value function (MVF) for the proposed model is derived by using the method of steps. The general solution of the MVFs for the proposed model is also obtained for some specific existing models. The numerical examples, based on a software failure data set, show that the consideration of quasi-renewal time-delay fault-removal assumption improves the descriptive properties of the model, which means that the length of time delay is getting decreased since testers and programmers adapt themselves to the working environment as testing and debugging activities are in progress.

This paper focuses on the process capability index considering the irregular fluctuation of the operation of OSS. Recently, many open source software (OSS) are developed under various open source projects. Considering the characteristics of OSS, many OSS are used via the internet network, such as the software update service, software version upgrade, cloud service, HTTP server, mobile devices, etc. From the above mentioned characteristics of OSS, the debugging process and operating phase of OSS development will take an irregular fluctuation in the long term of operation. In particular, we apply Wiener process model to the noisy cases in the operation of OSS. Moreover, we compare the method of process capability assessment based on Wiener process model considering the irregular fluctuation for OSS projects with several nonhomogeneous Poisson process (NHPP) models. Also, we analyze actual data to show numerical examples of the proposed method considering the characteristics of recent OSS projects and the existing NHPP models.

Over time, software has become increasingly important in various fields. If the current software is more dependent than in the past and is broken owing to large and small issues, such as coding and system errors, it is expected to cause significant damage to the entire industry. To address this problem, the field of software reliability is crucial. In the past, efforts in software reliability were made to develop models by assuming a nonhomogeneous Poisson-process model (NHPP); however, as models became more complex, there were many special cases in which models fit well. Hence, this study proposes a software reliability model using deep learning that relies on data rather than mathematical and statistical assumptions. A software reliability model based on recurrent neural networks (RNN), long short-term memory (LSTM), and gated recurrent units (GRU), which are the most basic deep and recurrent neural networks, was constructed. The dataset was divided into two, Datasets 1 and 2, which both used 80% and 90% of the entire data, respectively. Using 11 criteria, the estimated and learned results based on these datasets proved that the software reliability model using deep learning has excellent capabilities. The software reliability model using GRU showed the most satisfactory results.

Software reliability models are used to estimate and predict the reliability, number of remaining faults, failure intensity, total software development cost, etc., of a software. Testing coverage is very important for both software developers and customers of software products. Testing converge is a measure that enables software developers to evaluate the quality of tested software and determine how much additional effort is needed to improve the reliability of the software. This paper proposes a software reliability growth model based on a non-homogeneous Poisson process (NHPP) that incorporates a logistic–exponential testing coverage function with imperfect debugging. The proposed model relates the test coverage to fault detection phenomena in debugging. Goodness-of-fit test of the proposed model is conducted using different criteria for two sets of software failure data. The proposed model is compared with other existing NHPP models. A software cost model incorporating testing coverage and an optimal release policy based on the number of remaining faults are developed.

Open-source software is gaining popularity in industrial projects due to its accessibility and cost-effectiveness. However, concerns persist about its quality and reliability. To assess software reliability quantitatively, software reliability models are utilized, with the unknown parameters of these models typically determined using statistical techniques. In many cases, these methods fail to converge to the global optimal solution of parameter estimation of nonlinear mathematical models and are quite sensitive to the initial guesses of unknown parameters. This necessitates employing a high-quality parameter estimation technique. The study demonstrates the potential application of nine nature-inspired swarm intelligence-based algorithms to address nonlinear parameter estimation problems and effectively identify the global optimal solution with high likelihood, irrespective of the initial guess. These typical algorithms are classified into several categories, including animal-inspired algorithms such as grey wolf optimizer, insect-inspired algorithms such as artificial bee colony, social spider optimization, firefly algorithm, and moth flame optimization, bird-inspired algorithms such as particle swarm optimization, sea creature-inspired algorithms such as whale optimization algorithm, and plant-inspired algorithms such as flower pollination algorithm and dandelion optimizer. Three real-world, open-source reliability datasets are utilized to assess the efficacy of these algorithms in estimating the parameters of two prominent non-homogeneous Poisson process models in software reliability.