On the Development of Discrete Software Reliability Growth Models

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.

To meet highly competitive market challenges along with technological upgrades and changing user requirements, software firms offer newer versions of their products by adding new features and new functionalities. But this also results in increase in the fault content of software. In this paper we propose a discrete software reliability growth model (SRGM) for fault removal process incorporating the effect of up-gradations on the subsequent releases of the software. It is further assumed that faults present in the software are not of the same type and may be classified as simple and hard faults depending upon the effort and time consumed for their removal. The proposed model has been validated on a real life dataset for software with four releases. The results obtained are encouraging and fairly accurate.

In the software industry, Software Reliability Growth Models (SRGMs) with confidence intervals (C.I.) are frequently employed as valuable tools to assist manager to determine the optimal timing for software releases and enhancing the effectiveness of testing processes. However, many SRGMs lack clear explanations regarding the estimation of variance for cumulative software errors. This limitation can impede their ability to accurately derive C.I. for the mean value function (MVF), making it challenging for developers to evaluate potential risks and uncertainties within the software system. Consequently, the practical application of these models may be compromised. To address this issue, this paper proposes the utilization of Ohba’s Inflection S-shaped model and Yamada’s delayed S-shaped model to construct SRGMs with C.I., thereby providing developers with improved guidance for making optimal release time decisions.

Software reliability growth model with change-point and environmental function

We familiarized the readers that non-homogeneous Poisson process (NHPP) based software reliability growth models (SRGM) are generally classified into two groups. The first group of models uses the execution time (i.e. CPU time) or calendar time to describe the software failure and fault removal phenomena. Such models are called continuous time models. KeywordsChange PointSoftware ReliabilityProbability Generate FunctionSimple FaultDiscrete Time SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

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

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.

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.

Due to demand of highly reliable software system and intense competition of the market the software developers are forced to come up with new features and enhancements in the software at a very frequent rate. Though it adds a new leash of life to the product, but it also leads to complexity and bugs in the software system. The phenomenon of adding features and functionalities to the existing products is called up-gradation. Most of the work done in software reliability engineering pertains to single release software system. These models do not take into consideration the effect of up-gradations on the subsequent releases. In this paper, we propose a discrete software reliability growth model for fault removal process of multi release software products. The proposed model is validated on real failure dataset for software with four releases. The results obtained are encouraging and fairly accurate.

Software reliability assessment models based on cumulative bernoulli trial processes

The hyper-geometric distribution is used to estimate the number of initial faults residual in software at the beginning of the test-and-debug phase. The hyper-geometric distribution growth model (HGD model) is well suited to making estimates for the observed growth curves of the accumulated number of detected faults. The advantage of the proposed model is the applicability to all kinds of observed data. By application of a single model, exponential growth curves as well as S-shaped growth curves can be estimated. The precise formulation of the HGD model is presented. The exact relationship of this model to the NHPP Goel-Okumoto growth model and the delayed S-shaped growth model is shown. With the introduction of a variable fault detection rate, the goodness of fit of the estimated growth curve to the growth curve of real observed faults is increased significantly. Different examples of the applicability of the model to real observed data are presented. >

The safety-critical software of Reactor Protection System (RPS) plays a significant role for the safe operation of the nuclear power plant (NPP). However, it also brings challenges both to the reliability analysis of the RPS and to the Probabilistic Risk Assessment of the NPPs. The reliability analysis of safety-critical software is also expected by the nuclear regulation agencies and the software development groups for test evaluation and optimization. The detected faults during the software test process are regarded to have close connection with the software reliability and there have been hundreds of test-based software reliability models. Due to the particularity of its function, the safety-critical software of an NPP is especially sensitive to the faults with higher severity levels which should be paid special attention to. Severity levels of faults are commonly taken into account during software reliability modelling. In this paper, a novel software reliability growth model considering actual severity data was built based on a non-homogeneous Poisson process. Ratio of fatal faults with highest severity level to all accumulated faults was modelled with logistic curve. Then the mean value functions of both fatal and general faults were derived. A belief factor was employed to describe the trend of severity classification. In the end, the test data of a practical project was used to verify this model. The analysis results showed that this model had better prediction effect than Goel-Okumoto model and Inflection S-shaped model even when limited test data were collected. This novel model can be used as a helpful tool to evaluate both the reliability and the release time of the safety-critical software of an NPP.

This paper presents a generalized logistic software reliability growth model that integrates time-dependent fault detection rate and imperfect removing rate per fault. We also derive a time-dependent logistic growth model and compare descriptive and predictive ability of a set of “classical” NHPP reliability models with the one we developed based on a software failure data set. The results show that inclusion of both time-dependent imperfect removing and fault-detection rates into a logistic growth function may be worth the extra model complexity and the increased number of parameters required for a better relative fit based on several selection criteria.

In the prevailing scenario, development of distributed systems is gaining popularity to get the benefits of early and enhanced developments. Software Reliability Growth Models (SRGMs) play a significant role in quantitative assessment of software reliability. Software's developed in Distributed Development Environment (DDE) are characterized by enhanced availability and increased reliability. Software with their components developed in distributed environment show an astounded trend as they have high speed and elevated reliability performance. In this study we present multi-up gradations modeling for removal of fault for newly developed and reused components in distributed environment using probability distribution functions. Explicit expressions for the mean number of individual types of faults are obtained by considering ‘n’ reused components and ‘p’ newly developed components. And for such systems, we have used some probability distribution functions for finding best method to capture the faults lying dormant in the system and likewise have selected accurate SRGM for distributed environment. Due to uncertain market forces and stout contention, the developers cannot satisfy the customers with software having static and limited functionalities. Customers generally expect periodic modifications and add-ons in the software to maintain their inclination towards the same product. To keep a pace with these fast changing preferences of the customers, distributed development environment with multiple periodic up-gradations is the need of hour, hence turning the customer's urge to developer's obligation. We are introducing a modeling framework of a software which is developed under distributed environment and upgraded time to time. To validate the analytical results of the proposed framework, numerical illustration is provided.