S-shaped Software Reliability Growth Model Research Articles

Efficiency Evaluation of Software Faults Correction Based on Queuing Simulation

Fault-counting data are collected in the testing process of software development. However, the data are not used for evaluating the efficiency of fault correction activities because the information on the fault detection and correction times of each fault are not recorded in the fault-counting data. Furthermore, it is difficult to collect new data on the detection time of each fault to realize efficiency evaluation for fault correction activities from the collected fault-counting data due to the cost of personnel and data collection. In this paper, we apply the thinning method, using intensity functions of the delayed S-shaped and inflection S-shaped software reliability growth models (SRGMs) to generate sample data of the fault detection time from the fault-counting data. Additionally, we perform simulations based on the infinite server queuing model, using the generated sample data of the fault detection time to visualize the efficiency of fault correction activities.

Integration of Testing Effort Function into Delayed S-Shaped Software Reliability Growth Model with Imperfect Debugging — a Proposed Bokhari Model

Integration of Testing Effort Function into Delayed S-Shaped Software Reliability Growth Model with Imperfect Debugging — a Proposed Bokhari Model

An Assessment of Incorporating Log-Logistic Testing Effort Into Imperfect Debugging Delayed S-Shaped Software Reliability Growth Model

Software reliability growth models (SRGM) are employed to aid us in predicting and estimating reliability in the software development process. Many SRGM proposed in the past claim to be effective over previous models. While some earlier research had raised concern regarding use of delayed S-shaped SRGM, researchers later indicated that the model performs well when appropriate testing-effort function (TEF) is used. This paper proposes and evaluates an approach to incorporate the log-logistic (LL) testing-effort function into delayed S-shaped SRGMs with imperfect debugging based on non-homogeneous Poisson process (NHPP). The model parameters are estimated by weighted least square estimation (WLSE) and maximum likelihood estimation (MLE) methods. The experimental results obtained after applying the model on real data sets and statistical methods for analysis are presented. The results obtained suggest that performance of the proposed model is better than the other existing models. The authors can conclude that the log-logistic TEF is appropriate for incorporating into delayed S-shaped software reliability growth models.

Analysis of Delayed S Shaped Software Reliability Growth Model with Time Dependent Fault Content Rate Function

Many software reliability growth models based upon a non-homogeneous Poisson process (NHPP) have been proposed to measure and asses the reliability of a software system quantitatively. Generally, the error detection rate and the fault content function during software testing is considered to be dependent on the elapsed time testing. In this paper we have proposed three software reliability growth models (SRGM’s) incorporating the notion of error generation over the time as an extension of the delayed S-shaped software reliability growth model based on a non-homogeneous Poisson process (NHPP). The model parameters are estimated using the maximum likelihood method for interval domain data and three data sets are provided to illustrate the estimation technique. The proposed model is compared with the existing delayed S-shaped model based on error sum of squares, mean sum of squares, predictive ratio risk and Akaike’s information criteria using three different data sets. We show that the proposed models perform satisfactory better than the existing models.

The Generalized Inflection S-Shaped Software Reliability Growth Model

In this paper, the new generalized inflection S-shaped software reliability growth model is proposed. It is a very flexible finite failure Poisson process that possesses two distinguishing features: 1) includes as special cases the popular inflection S-shaped model, Goel generalized nonhomogenous Poisson process, and Goel–Okumoto model and 2) differently than these latter models, allows for modeling nonmonotonic failure rate per fault functions. The properties of the generalized inflection S-shaped model are discussed and intuitive arguments are provided to justify its structure. Maximum-likelihood estimators of model parameters are formulated and their properties are summarized. A special attention is devoted to the nonexistence issue of maximum-likelihood estimates. The problem of estimating the optimal release time of a software product is also addressed. Affordability and flexibility of the proposed model are demonstrated via four applicative examples, based on real sets of software reliability data. Attained results show that the generalized inflection S-shaped model provides outputs that may significantly differ from those provided by the models nested within it. As a side result, the developed examples also show that the nonexistence issue of maximum-likelihood estimates, in the case of finite failure Poisson processes, cannot be considered an oddity and that its occurrence is not necessarily related to model complexity.

Determination of the Optimal Allocation of Testing Resource for Modular Software Reliability Growth Using LINGO

It is quite natural to produce reliable software systems since the breakdown of the computer systems, which is caused by software faults, results in a tremendous loss and damage for social life. Hence, software reliability is a key factor in software development process. Testing phase of software begins with module testing whereby, modules are tested independently to remove substantial amount of faults within a specified testing resource. Therefore, in this paper four optimization problems are discussed for optimal allocation of testing resources for a modular software system. These optimization problems are formulated as nonlinear programming problems (NLPP), which incorporates log-logistic testing-effort function into inflection S-shaped software reliability growth model based on a non-homogeneous Poisson process. The NLPPs are solved using LINGO, a user-friendly software package for optimization. Finally, numerical example is given to demonstrate and to validate the performance of proposed strategies. In addition, the results of the strategies proposed in this paper are compared with [1]. It is revealed that the proposed strategies yield a gain in efficiency.

Optimal Release Policies of Delayed Discrete Reliability Growth Model With Imperfect Debugging

Abstract The present investigation was concerned with the delayed discrete S-shaped software reliability growth model with imperfect debugging. In this paper, we developed a discrete model based on non-homogeneous Poisson process by considering two types of fault removal processes. Optimal release policy was suggested to predict the optimal test run after which the software should be released. The sensitivity analysis was performed on the cost and reliability functions. We used the adaptive neuro fuzzy inference system approach to facilitate the computational results and compared it with the analytical results.

Determining the optimal allocation of testing resource for modular software system using dynamic programming

Reliability is a major concern in the process of software development because unreliable software can cause failure in the computer system that can be hazardous. A way to enhance the reliability of software is to detect and remove the faults during the testing phase, which begins with module testing wherein modules are tested independently to remove a substantial number of faults within a limited resource. Therefore, the available resource must be allocated among the modules in such a way that the number of faults is removed as much as possible from each of the modules to achieve higher software reliability. In this article, we discuss the problem of optimal resource allocation of the testing resource for a modular software system, which maximizes the number of faults removed subject to the conditions that the amount of testing-effort is fixed, a certain percentage of faults is to be removed and a desired level of reliability is to be achieved. The problem is formulated as a non linear programming problem (NLPP), which is modeled by the inflection S-shaped software reliability growth models (SRGM) based on a non homogeneous Poisson process (NHPP) which incorporates the exponentiated Weibull (EW) testing-effort functions. A solution procedure is then developed using a dynamic programming technique to solve the NLPP. Furthermore, three special cases of optimum resource allocations are also discussed. Finally, numerical examples using three sets of software failure data are presented to illustrate the procedure developed and to validate the performance of the strategies proposed in this article. Experimental results indicate that the proposed strategies may be helpful to software project managers for making the best decisions in allocating the testing resource. In addition, the results are compared with those of Kapur et al. (2004), Huang and Lyu (2005), and Jha et al. (2010) that are available in the literature to deal the similar problems addressed in this article. It reveals that the proposed dynamic programming method for the testing-resource allocation problem yields a gain in efficiency over other methods.

Exponentiated Weibull distribution approach based inflection S-shaped software reliability growth model

Abstract The aim of this paper was to estimate the number of defects in software and remove them successfully. This paper incorporates Weibull distribution approach along with inflection S-shaped Software Reliability Growth Models (SRGM). In this combination two parameter Weibull distribution methodology is used. Relative Prediction Error (RPE) is calculated to predict the validity criterion of the developed model. Experimental results on actual data from five data sets are compared with two other existing models, which expose that the proposed software reliability growth model predicts better estimation to remove the defects. This paper presents best software reliability growth model with including feature of both Weibull distribution and inflection S-shaped SRGM to estimate the defects of software system, and provide help to researchers and software industries to develop highly reliable software products.

An S-shaped software reliability model with imperfect debugging and improved testing learning process

In this paper, we propose a non-homogeneous Poisson process (NHPP) based S-shaped software reliability growth model (SRGM) in presence of imperfect debugging with a new exponentially increasing fault content function and S-shaped fault detection rate. We develop the fault content function considering learning capability of testing team during software development process. Fault content increases rapidly at the beginning of testing process while it grows gradually at the end of testing process due to increasing efficiency of testing team with testing time. We use maximum likelihood estimation (MLE) method to estimate model parameters. Applicability of the proposed model has been presented by comparing with established models in terms of goodness of fit and predictive validity using two software failure data sets. Experimental results show that the proposed model gives better fit to real failure data sets and predicts future failure behaviour of software development accurately than established models.

SPC for Software Reliability using Inflection S-Shaped Model

Traditional statistical analysis methods account for natural variation but require aggregation of measurements over time,which can delay decision making.Statistical process control (SPC) is a branch of statistics that combines rigorous time series analysis methods with graphical presentation of data,often yielding insights into the data more quickly and in a way more understandble to lay decision makers .SPC and its primary tool-the control chart-provide researchers and practitioners with a method of better understanding and communicating data from software reliability improvement process efforts .This paper provides an s-shaped software reliability growth model based on the Non-Homogenous Poisson Process (NHPP).The maximum likelihood approach is used to estimate the unknown parameters of the model.

A study of testing‐effort dependent inflection S‐shaped software reliability growth models with imperfect debugging

PurposeThe purpose of this paper is to investigate how to incorporate the exponentiated Weibull (EW) testing‐effort function (TEF) into inflection S‐shaped software reliability growth models (SRGMs) based on non‐homogeneous Poisson process (NHPP). The aim is also to present a more flexible SRGM with imperfect debugging.Design/methodology/approachThis paper reviews the EW TEFs and discusses inflection S‐shaped SRGM with EW testing‐effort to get a better description of the software fault detection phenomenon. The SRGM parameters are estimated by weighted least square estimation (WLSE) and maximum‐likelihood estimation (MLE) methods. Furthermore, the proposed models are also discussed under imperfect debugging environment.FindingsExperimental results from three actual data applications are analyzed and compared with the other existing models. The findings reveal that the proposed SRGM has better performance and prediction capability. Results also confirm that the EW TEF is suitable for incorporating into inflection S‐shaped NHPP growth models.Research limitations/implicationsThis paper presents the WLSE results with equal weight. Future research may be carried out for unequal weights.Practical implicationsSoftware reliability modeling and estimation are a major concern in the software development process, particularly during the software testing phase, as unreliable software can cause a failure in the computer system that can be hazardous. The results obtained in this paper may facilitate the software engineers, scientists, and managers in improving the software testing process.Originality/valueThe proposed SRGM has a flexible structure and may capture features of both exponential and S‐shaped NHPP growth models for failure phenomenon.

Bayesian Optimal Release Time Based on Inflection S-Shaped Software Reliability Growth Model

The inflection S-shaped software reliability growth model (SRGM) proposed by Ohba (1984) is one of the well- known SRGMs. This paper deals with the optimal software release problem with regard to the expected software cost under this model based on the Bayesian approach. To reflect the effect of the learning experience for the updated software system, we consider several improvement factors to adjust the values of parameters characterizing the inflection S-shaped SRGM. Appropriate prior distributions are assumed for such factors and the expected total software cost is formulated. The optimal release time is shown to be finite and uniquely determined. Because of the flexibility of prior distributions, the proposed Bayesian methods may be applied in many different situations. Numerical results are presented on the basis of the real data.

Comparison of Software Reliability Assessment Methods for Open Source Software and Reliability Assessment Tool

We propose software reliability assessment methods for concurrent distributed system development by using the Analytic Hierarchy Process. Also, we make a comparison between the inflection S-shaped software reliability growth model and the other models based on a nonhomogeneous Poisson process applied to reliability assessment of the entire system composed of several software components. Moreover, we analyze software fault count data to show numerical examples of software reliability assessment for the open source project. Furthermore, we investigate an efficient software reliability assessment method for the open source system development. Also, we develop the software testing-management tool for open source software system by using Java programming language. We show several performance examples of the software testing-management tool for the open source software.

S-shaped software reliability growth models derived from stochastic differential equations

This paper presents a software reliability growth model based on Itô type Stochastic Differential Equations (SDE). As the size of a software system becomes larger, the number of faults remaining in the system during the testing phase can be considered to be a continuous stochastic process. In practice, if the per-fault detection rate is subject to certain random effects, we may consider the use of a SDE to describe the average behavior of the software fault detection process during the testing phase. As a result, we derive several software reliability measures by utilizing the mean value function which is the expected value of the SDE. We also derive the maximum likelihood estimators of the unknown parameters for the model. Futhermore, we compare our model with other software reliability growth models in terms of several reliability measures and goodness-of-fit for the same data set.

Optimum release policy for an inflection s-shaped software reliability growth model

Optimum software release policy is discussed for a software system based on a cost-reliability criterion, whose software reliability growth is described by an inflection s-shaped growth model. Numerical results are also presented.

An S-shaped software reliability growth model with two types of errors

An S-shaped software reliability growth model (SRGM) based on a non-homogeneous Poisson process (NHPP) with two types of errors has been proposed. The errors have been classified depending upon their severity. We have estimated the model parameters and obtained the optimum release policies which minimize the cost subject to achieving a given level of reliability. Numerical results illustrating the applicability of the proposed model are also presented.

S-Shaped Software Reliability Growth Models and Their Applications

The s-shaped growth curves of detected software errors can be observed in software testing. The delayed s-shaped and inflection s-shaped software reliability growth models based on a nonhomogeneous Poisson process are discussed. The software reliability growth types of the models are investigated in terms of the error detection rate per error. In addition, a viable method for the software quality assessment, which integrates the capture-recapture method and the models above, is discussed, and its application to actual test data is illustrated.

S-shaped software reliability growth models with four types of software error data

In general, we should apply the most suitably statistical inferences to observed data. In this paper, our interests are statistical inferences on the observed data of software reliability growth models described by a non-homogeneous Poisson process having an S-shaped mean value function. We should consider such observed data in terms of censoring and removing. Censoring occurs when the test is stopped at detection of a specified number of errors or a specified time. Removing occurs when a specified number of detected errors or a total number of detected errors up to a specified time are removed. Classifying the types of software error data by censoring and removing, we can consider four types of the observed data. We give the maximum likelihood estimates of parameters in the models for four types of the observed data. The asymptotic distributions of the parameters are also discussed.