Software reliability growth model with normal distribution and its parameter estimation

Estimating remaining defects (or failures) in software can help test managers make release decisions during testing. Several methods exist to estimate defect content, among them a variety of software reliability growth models (SRGMs). SRGMs have underlying assumptions that are often violated in practice, but empirical evidence has shown that many are quite robust despite these assumption violations. The problem is that, because of assumption violations, it is often difficult to know which models to apply in practice. We present an empirical method for selecting SRGMs to make release decisions. The method provides guidelines on how to select among the SRGMs to decide on the best model to use as failures are reported during the test phase. The method applies various SRGMs iteratively during system test. They are fitted to weekly cumulative failure data and used to estimate the expected remaining number of failures in software after release. If the SRGMs pass proposed criteria, they may then be used to make release decisions. The method is applied in a case study using defect reports from system testing of three releases of a large medical record system to determine how well it predicts the expected total number of failures.

Researchers have proposed and implemented a plethora of bug prediction approaches in terms of different mathematical models for measuring the reliability growth of the software and to predict the latent bugs lying dormant in the software. During the last four decades, software reliability growth models (SRGM) have been successfully used to measure the reliability growth of closed source software. The SRGM developed were based on either calendar time or on testing effort. In late 90s, due to the advancement in communication and internet technologies, the development of open source software gets an edge and is proven to be very successful in different fields. Recently, researchers have measured the latent bugs in the open source software using an SRGM which has been developed for closed source software and concluded that the existing SRGM can well predict the latent bugs, but, still, it needs more investigation. In open source software, the source codes are frequently changes (the complexity of code changes) to meet the new feature introduction, feature enhancement and bug repair. In this paper, we have developed two complexity of code changes/entropy based bug prediction models namely (i) time vs entropy and (ii) entropy vs bugs. We have compared the proposed models with the existing time vs bugs SRGM. The empirical work has been carried out using three subsystems of Mozilla project. The statistical significance of different approaches has been tested using a non-parametric Kolmogorov–Smirnov (K–S) test. The bug prediction approaches have been compared on the basis of various performance measures namely R-Square (R2), Adjusted R-Square (adj. R2), Bias, variation and root mean square prediction errors. We found that the potential complexity of code changes based bug prediction approach i.e. time vs entropy is better over the time vs bugs and entropy vs bugs on the basis of different comparison criteria and statistical test.

One of the established trends of research areas and practices in software engineering that dealt with the measurement and enhancement of reliability is software reliability engineering. Stochastic software reliability models find typical usage for analysis. These are the models that perform modeling on failure process of the software and exploit other software metrics or failure data as cornerstone for parameter estimation. The ability of the models for estimating and predicting the current reliability and future failure behavior, respectively, is high. Due to any failures and faults in the system, a product becomes unreliable. The lack of understanding of nature of the software makes the measurement of software reliability as a challenging task. It is not possible to determine a best way to measure the reliability and other aspects of software. This paper proposes an efficient software reliability growth model (SRGM) in which logistic exponential TEF is exploited. This model offers increased failure rate recognition and suitable ways to resolve faults and so on. Our work estimates the SRGM parameters using optimization algorithm. Such estimation can aid in developing precise software reliability model. In order to accomplish the optimization, we use artificial bee colony (ABC) algorithm. As the parameters optimization considerably improves the quality of parameters to be used for reliability growth model, reliability growth can also be improved considerably.

Reliability is the one of the important quality measure of software product. Testing is one important phase in software development life cycle whose intention is to find the bugs present in the software product. A mathematical model which describes the software testing in software development cycle termed as software reliability growth models. Past few decades many software reliability growth models were proposed. Estimating the accurate release time of software is an important challenging issue of software Development Company. If the software product is released early contain more errors makes software to be less reliable, where as late release will increase the development cost. It is observed that more than half of the total development cost is concentrated during the maintenance phase. Estimating the reliability and accurate development cost of software product by software reliability growth model at maintenance phase is an important issue. Warranty is defined to be an agreement between the customer and vendor of the software to provide the extra protection to the product. Several papers have concentrated on optimal release time by considering the warranty cost. All early proposed NHPP warranty cost models considered a perfect-debugging software reliability growth model while estimating the software maintenance cost. But it was observed that, the software product is influenced by several factors like environment, resources and nature of the faults during the operational phase. In such circumstances it is quite not right to consider a perfect NHPP software reliability growth model in operational phase. In this paper we proposed an imperfect debugging software reliability growth model by combining the cost and reliability at a given warranty period to estimate the optimal release time of software product.

Number of software Reliability growth models has been proposed in the literature. A mathematical technique which describes the software testing phenomenon known as the software reliability growth model. Software reliability growth models are used to predict the number of faults and reliability of the software. In the view of this software reliability growth models are basically differentiated as the continuous and discrete models. There is a plenty of development in the continuous models but little towards the discrete models. In this paper we have presented a discrete reliability growth model with different discrete testing effort functions and the same time software release policy is discussed. A new imperfect debugging discrete software reliability growth model with testing effort is proposed. All calculations are done on real data. The results shows the proposed testing effort models are perfectly fit to the data.

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.

Software reliability growth model with change-point and environmental function

Software reliability assessment models based on cumulative bernoulli trial processes

A large number of software reliability growth models (SRGMs) have been proposed during the past 30 years to estimate software reliability measures such as the number of remaining faults, software failure rate, and software reliability. Selection of an optimal SRGM for use in a particular case has been an area of interest for researchers in the field of software reliability. Tools and techniques for software reliability model selection found in the literature cannot be used with high confidence as they use a limited number of model selection criteria. For the first time, we developed a deterministic quantitative model based on a distance based approach (DBA) method, then applied it for evaluation, optimal selection, and ranking of SRGMs. DBA recognizes the need for relative importance of criteria for a given application, without which inter-criterion comparison could not be accomplished. It requires a set of model selection criteria, along with a set of SRGMs, and their level of criteria for optimal selection; and it successfully presents the results in terms of a merit value which is used to rank the SRGMs. We use two distinct, real data sets for demonstration of the DBA method. The result of this study will be a ranking of SRGMs based on the Euclidean composite distance of each alternative to the designated optimal SRGM.

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.

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 order to overcome the limitations of debugging process, insufficient consideration of imperfect debugging and testing-effort (TE) in software reliability modeling and analysis, a software reliability growth model (SRGM) explicitly incorporating imperfect debugging and TE is developed. From the point of view of incomplete debugging and introduction of new fault, software testing process is described and a relatively unified SRGM framework is presented considering TE. The proposed framework models are fairly general models that cover a variety of the previous works on SRGM with ID and TE. Furthermore, a special SRGM incorporating an improved Logistic testing-effort function (TEF) into imperfect debugging modeling is proposed. The effectiveness and reasonableness of the proposed model are verified by published failure data set. The proposed model closer to real software testing has better descriptive and predictive power than other models

Software developers need information for deciding the optimal time for software release with improved software reliability. However, it is not easy for them to decide when and how to release newly developed software to the market. For a decision, the reliability and test costs of the software need to be balanced carefully for avoiding unnecessary confusion and users’ complaints. To address this need, related research has been carried out to propose an appropriate tool for such decisions. In many studies, software reliability growth models (SRGMs) were applied using the concept of confidence intervals to estimate the reliability of software. Confidence intervals were calculated on the basis of the assumption of a normal distribution showing the symmetrical occurrence of data with the mean as a center. However, the reliability data of software do not always have such symmetry for assuming the normal distribution. Therefore, it is necessary to propose a method for overcoming the mean value randomness that causes asymmetry in the related data. In previous studies, estimating variance and mean of errors of software was not considered, which led to the unreliable estimation of the confidence intervals of the mean value for decision making. Previous studies also lacked practicability in applications due to statistics from the asymmetrical data distribution. As a result, software developers could not effectively evaluate the possible risk related to the software release time. To improve the estimation, we employ the inflection S-shape model to propose the SRGM on the basis of confidence intervals assumed to come from the normal distribution. The proposed model allows determining the optimal time for software release with the consideration of its potential risk. For efficient determination, the architecture and user interface of the computation system are also proposed.

A significant number of software reliability growth models (SRGMs) have been proposed in the literature over the past three decades or so. Most of these models ignored the possibility of imperfect debugging with subsequent introduction of new errors into the software system. In this paper, we present an SRGM which consists of a dual process of debugging followed by introduction of errors in the event of an imperfect debugging. The model also allows for the process to be repeated over several stages. The reliability growth of this model is investigated and is shown to exhibit either an exponential or S-shaped curve. Finally, some reliability measures associated with the SRGM are presented together with illustrative numerical examples.

With the growth of complexity in the software system, to deliver reliable software products on time becomes a critical issue. Many software reliability growth models (SRGMs) have been proposed in the past three decades. However, most software reliability assessment processes and parameter estimations of models depend on the computations of the general-purposed numerical software. In this paper, we will present a powerful computer-aided reliability assessment tool for software based on object-oriented analysis and design-CARATS. CARATS can use both traditional SRGMs and neural-network methods to assess software reliability. This would greatly help project managers to make decisions during software development life cycle. Due to the characteristics of the special-purposed and object-oriented design, CARATS can analyze the software reliability easily, and is also more flexible to adopt different SRGMs than other existing software reliability analysis tools.