Optimal Software Release Policy Research Articles

On a cost and availability analysis for software systems via phase type non-homogeneous Poisson process

To build highly reliable software products, software testing is required. The software engineer has a problem determining whether to complete the testing process and when to release the software system to the market. As the focus on high software increases, project managers must consider the cost of testing, testing availability time, and release time strategy. This research article utilizes a phase type non-homogeneous Poisson process to investigate the cost analysis and operational availability of a software reliability model. The software failure inter-arrival time is considered to follow a phase type distribution. The phase type software reliability model is valuable in reducing the time and effort required to select the appropriate models for software reliability evaluation. An explicit expression for the expected, bi-criterion cost analysis and operational availability is derived using standard results of the renewal reward theorem. The optimal software release policy T* is obtained analytically. Numerical illustrations and sensitivity analysis have been presented to illustrate the cost and availability analysis’s efficiency and demonstrate conformity with the study’s observations.

Using Modified Diffusion Models for Reliability Estimation of Open Source Software

Software development is a highly unpredictable process, and ensuring software quality and reliability before releasing it to the market is crucial. One of the common practices during software development is the reuse of code. It can be achieved by utilizing libraries, frameworks, and other reusable components. Practically, when a fault is detected in replicated code, developers must check for similar faults in other copies, as there is a dependency between faults. To prevent recurrence of observed failures, developers must remove the corresponding leading fault and any related dependent faults. Many software reliability growth models (SRGMs) have been proposed and studied in the past, but most SRGMs assume that developers usually detect only one fault causing a failure. In actuality, it is necessary to consider the possibility of detecting multiple faults that may share similarities or dependencies. Additionally, some SRGMs rely on specific assumptions that may not always be valid, such as perfect debugging and/or immediate debugging. In this study, the modified diffusion models are proposed to handle these unrealistic situations, and are expected to better capture the dynamics of open source software (OSS) development. Experiments using real OSS data show that the proposed models can accurately describe the fault correction process of OSS. Finally, an optimal software release policy is proposed and studied. This policy takes into account some factors, including the remaining number of faults in the software, the expenses associated with identifying and rectifying those faults, and the level of market demand for the software. By considering these factors, developers can determine the optimal time to release the software to the market.

A model of software fault detection and correction processes considering heterogeneous faults

AbstractNumerous software reliability growth models (SRGMs) are proposed in the last four decades to track the reliability growth of software during the testing phase. In many existing models, it is assumed that the faults in the software are of the same type. However, this assumption may not be realistic. Software contains different faults and the detection/correction of different faults can require different efforts. In this paper, we propose a more general software reliability model considering heterogeneous faults, where the parameters for the detection time and correction delay of different faults are assumed to be faults specific and allowed to follow arbitrary distributions. Considering different parameters makes the model more flexible and adaptable to different practical software development situations. Some specific models are derived under different assumptions on the distributions of fault detection time, fault correction delay, and the corresponding parameters. Both MLE and LSE are proposed for parameter estimation. Illustrative examples with real data set are studied to compare the proposed models with homogeneous faults model, and the results have shown advantages of our models. The optimal software release policy based on the proposed model is also studied.

Software Belief Reliability Growth Model Based on Uncertain Differential Equation

Software reliability plays an important role in modern society. To evaluate software reliability, software reliability growth models (SRGMs) investigate the number of software faults in the testing phase. Obviously, testing progresses are inevitably influenced by dynamic indeterministic fluctuations such as the testing effort expenditure, testing efficiency and skill, testing method, and strategy. To model these dynamic fluctuations, several probability theory-based SRGMs are proposed. However, probability theory is suitable for dealing with aleatory uncertainty, but fails to deal with epistemic uncertainty widely existing in software faults. Therefore, this article considers software reliability from a new perspective under the framework of uncertainty theory, which is a new mathematical system different from probability theory, and proposes a software belief reliability growth model (SBRGM) based on uncertain differential equations for the first time. Based on this SBRGM, properties of essential software reliability metrics are investigated under belief reliability theory, which is a brand-new reliability theory. Parameter estimations for unknown parameters in SBRGM are presented. Furthermore, some numerical examples and real data analyses illustrate our methodology in detail, and show that it performs better than several famous probability-based SRGMs in terms of fitting ability and prediction ability. Finally, an optimal software release policy is discussed.

A software reliability growth model for imperfect debugging

In general, software reliability growth models (SRGMs) are often developed based on the assumptions of perfect debugging, single error type, and consistent testing environment. However, such the assumptions may be unrealistic for testing projects because new errors are always introduced during the debugging process, software errors are not alike, and the testing environment may change as the workforce escalates. Furthermore, the learning effect of the debugging process is taken under advisement, and assumes that it is unstable since the process of the error removal is also imperfect, which may cause a fluctuation of errors in the system. Therefore, the study is based on the Non-Homogeneous Poisson Process with considerations of the phenomenon of imperfect debugging, varieties of errors and change points during the testing period to extend the practicability of SRGMs. Furthermore, the error fluctuation rate is described by a sine cyclical function with a decreasing fluctuation breadth during the detection period, which indicates that the influence of increasing new errors during the testing period will be gradually unremarkable as the testing time elapses. Besides, the expected time of removing simple or complex errors is assumed to be different truncated exponential distributions. Finally, the optimal software release policies are proposed with considerations of the costs which occur in the testing and warranty period under an acceptable threshold of software reliability.

NASH EQUILIBRIUM STRATEGIES REVISITED IN SOFTWARE RELEASE GAMES

A software release game was formulated by Zeephongsekul and Chiera [Zeephongsekul, P. & Chiera, C. (1995). Optimal software release policy based on a two-person game of timing. Journal of Applied Probability 32: 470–481] and was reconsidered by Dohi et al. [Dohi, T., Teraoka, Y., & Osaki, S. (2000). Software release games. Journal of Optimization Theory and Applications 105(2): 325–346] in a framework of two-person nonzero-sum games. In this paper, we further point out the faults in the above literature and revisit the Nash equilibrium strategies in the software release games from the viewpoints of both silent and noisy type of games. It is shown that the Nash equilibrium strategies in the silent and noisy of software release games exist under some parametric conditions.

Software reliability prediction and management: A multiple change‐point model approach

AbstractIt is commonly recognized that software development is highly unpredictable and software quality may not be easily enhanced after software product is finished. During the software development life cycle (SDLC), project managers have to solve many technical and management issues, such as high failure rate, cost over‐run, low quality, and late delivery. Consequently, in order to produce robust and reliable software product(s) on time and within budget, project managers and developers have to appropriately allocate limited time, manpower, development, and testing effort. In the past, the distribution of testing effort or manpower can typically be described by the Weibull or Rayleigh model. Practically, it should be noticed that development environments or methods could be changed due to some reasons. Thus, when we plan to perform software reliability modeling and prediction, these changes or variations occurring in the development process have to be taken into consideration. In this paper, we will study how to use the Parr‐curve model with multiple change‐points to depict the consumption of testing effort and how to perform further software reliability analysis. Some mathematical properties of proposed model will be given and discussed. The applicability and performance of our proposed model will be demonstrated and assessed through real software failure data. Experimental results are analyzed and compared with other existing models to show that our proposed model gives better predictions. Finally, an optimal software release policy based on cost‐reliability criteria is proposed and studied. The main purpose is aimed at minimizing the total cost of software development when a reliability objective is given.

Impacts of networking effects on software reliability growth processes: A multi‐attribute utility theory approach

AbstractSoftware reliability growth models, which are based on nonhomogeneous Poisson processes, are widely adopted tools when describing the stochastic failure behavior and measuring the reliability growth in software systems. Faults in the systems, which eventually cause the failures, are usually connected with each other in complicated ways. Considering a group of networked faults, we raise a new model to examine the reliability of software systems and assess the model's performance from real‐world data sets. Our numerical studies show that the new model, capturing networking effects among faults, well fits the failure data. We also formally study the optimal software release policy using the multi‐attribute utility theory (MAUT), considering both the reliability attribute and the cost attribute. We find that, if the networking effects among different layers of faults were ignored by the software testing team, the best time to release the software package to the market would be much later while the utility reaches its maximum. Sensitivity analysis is further delivered.

An Ideal Software Release Policy for an Improved Software Reliability Growth Model Incorporating Imperfect Debugging with Fault Removal Efficiency and Change Point

This paper presents a general software reliability growth model (SRGM) based on non-homogeneous Poisson process (NHPP) and optimal software release policy with cost and reliability criteria. The main motive of this study is to develop a software release time decision model considering maintenance cost and warranty cost under fuzzy environment. In previous studies, maintenance cost has been defined either in terms of warranty cost or fault debugging cost. In reality, maintenance cost includes the cost of free patches, updates, technical support and future enhancement. Also, it is possible that maintenance process causes the removal of software faults in the operational phase including the faults which occur outside the warranty period or warranty definition. In other words, warranty action may be included the maintenance action, but not the converse. Considering this fact, maintenance cost and warranty cost are defined separately in the proposed study. Initially, an SRGM has been proposed with the revised concept of imperfect debugging phenomenon considering fault removal efficiency (FRE). Furthermore, the effect of changes in various environmental factors on models parameters has been taken into account. Numerical examples based on real software failure data sets have been given to analyze the performance of the proposed models.

Cost optimization of a software reliability growth model with imperfect debugging and a fault reduction factor

In modern society people depend on both hardware and software systems. A software system is embedded in every activity of a computer system. The desired performance of a software system is an important issue for many critical systems. Over the past decades, many software models were proposed for estimating the growth of reliability. To improve software quality, software reliability growth models (SRGM) play an important role. The present investigation deals with a SRGM with imperfect debugging, change points and a fault reduction factor (FRF). A FRF is the net number of faults removed in proportion to the failures experienced. This article proposes a new scheme for constructing a SRGM based on a non-homogeneous Poisson process by considering a constant FRF. The main focus is to provide an efficient parametric decomposition for a SRGM. Numerical examples are given to illustrate the validity of analytical results. References Ahmad, N., Khan, M. G. M. and Rafi, L. S. Analysis of an inflection S-shaped software reliability model considering log-logistic testing-effort and imperfect debugging, Int. J. Comput. Sci. Net. Sec. , 11(1)161–171, 2011. http://paper.ijcsns.org/07_book/201101/20110125.pdf . Chang, Y.-C. and Liu, C. A generalized JM model with applications to imperfect debugging in software reliability, Appl. Math. Model. , 33(9)3578–3588, 2009. doi:10.1016/j.apm.2008.11.018 . Goel, A. L. and Okumoto, K. Time-dependent error-detection rate model for software reliability and other performance measures, IEEE T. Reliab. , 28(3):206–211, 1979. doi:10.1109/TR.1979.5220566 . Hsu, C.-J., Huang, C.-Y. and Chang, J.-R. Enhancing software reliability modelling and prediction through the introduction of time-variable fault reduction factor, Appl. Math. Model. , 35(1):506–521, 2011. doi:10.1016/j.apm.2010.07.017 . Jha, P. C., Gupta, D., Yang, B. and Kapur, P. K. Optimal testing resource allocation during module testing considering cost, testing effort and reliability, Comput. Int. Eng. , 57(3):1122–1130, 2009. doi:10.1016/j.cie.2009.05.001 . Kapur, P. K., Kumar, A., Yadav, K. and Khatri, S. K. Software reliability growth modelling for errors of different severity using change point, Int. J. Qual., Reliab., Safe. Eng. , 14(4):311–326, 2007. doi:10.1142/S0218539307002672 . Lyu, M. R. Handbook of Software Reliability Engineering, McGraw-Hill, New York, 1996. Lyu, M. R. and Nikora, A. Applying reliability models more effectively (software), IEEE Software , 9(4):43–52, 1992. doi:10.1109/52.143104 . Musa, J. D. A theory of software reliability and its application, IEEE T. Software Eng. , 3(1):312–327, 1975. doi:10.1109/TSE.1975.6312856 . Musa, J. D. The measurement and management of software reliability, P. IEEE , 68(9):1131–1143, 1980. doi:10.1109/PROC.1980.11812 . Musa, J. D., Lamino, A. and Okumoto, K. Software reliability: Measurement, Prediction, Application, McGraw-Hill, New York, 1987. Okumoto, K. and Goel, A. L. Optimum release time for software system based on reliability and cost criteria, J. Syst. Software , 1:315–318, 1980. doi:10.1016/0164-1212(79)90033-5 . Pham, H. Software Reliability, Springer-Verlag, Singapore, 2000. Pham, H. A software cost model with imperfect debugging, Random life cycle and penalty cost, Int. J. Syst. Sci. , 27(5):455–463, 1996. doi:10.1080/00207729608929237 . Quadri, S. M. K. and Ahmad, N. Software reliability growth modelling with new modified Weibull testing- effort and optimal release policy, Int. J. Comput. Appl. , 6(12), 2010. doi:10.5120/1127-1477 . Quadri, S. M. K., Ahmad, N. and Farooq, S. U. Software reliability growth modelling with generalized exponential testing-effort and optimal software release policy, Global J. Comput. Sci. Tech. , 11(2):27–42, 2011. http://computerresearch.org/stpr/index.php/gjcst/article/view/605 . Shyur, H.-J. A stochastic software reliability model with imperfect debugging and change-point, J. Syst. Software , 66(2):135–141, 2003. doi:10.1016/S0164-1212(02)00071-7 . Xie, M. Software Reliability Modelling, World Scientist, Singapore, 1991. Xie, M. and Yang, B. A study of the effect of imperfect debugging on software development cost model, IEEE T. Software Eng. , 29(5):471–473, 2003. doi:10.1109/TSE.2003.1199075 . Li, X., Xie. M. and Szu H. N. Sensitivity analysis of release time of software reliability models incorporating testing effort with multiple change-points, Appl. Math. Model. , 34(11):3560–3570, 2010. doi:10.1016/j.apm.2010.03.006 . Zhao, J., Liu, H.-W., Cui, G. and Yang, X.-Z. Software reliability growth model with change-point and environmental function, J. Syst. Software , 79(11):1578–1587, 2006. doi:10.1016/j.jss.2006.02.030 .

OPTIMAL SOFTWARE SHIPPING TIME ESTIMATION BASED ON A CHANGE-POINT HAZARD RATE MODEL

Software failure-occurrence or the fault-detection phenomenon is changed notably in an actual testing phase or an operational phase due to the changes of factors influencing the software reliability growth process. Taking into consideration of the effect of the change in software reliability growth modeling is expected to conduct more accurate software reliability assessment because it is said that such approach enables us to conduct more plausible software reliability assessment reflecting an actual testing-environment. We develop a framework for developing software hazard rate models with effect of change-point, and discuss change-point detection methods for applying our model to quantitative software reliability assessment. Additionally, we discuss an optimal software release problem for estimating optimal shipping time with the effect of the change as one of the application problems of our model in software project management. Finally, we show numerical examples for software reliability assessment and our optimal software release policy based on our change-point model by using actual data.

Risk-based software release policy under parameter uncertainty

The determination of the optimal release time is a significant problem in the software development process. Most existing research on this problem is based on the assumption that the model parameters are either known or can be accurately estimated. Due to the uncertainties associated with parameter estimation created by the very limited amount of software failure data that is generally available, the accuracy of the optimum release time determined by traditional approaches is questionable. When the mean value of the optimal release time is used, for example, there is only a 50 per cent chance that the reliability target is met at the time of release. In this paper, an optimal software release policy under parameter uncertainty is studied. To take parameter uncertainty into consideration, an optimal risk-based software release time determination approach is introduced. Application examples are given to illustrate this approach and simulation studies are carried out. The presented results can help management to consider multiple risk levels in order to reach a more reasonable decision.

The Comparative Study of Software Optimal Release Time Based on Burr Distribution

It is great practical interest to decide when to stop testing a software system in development phase and transfer it to the user. This problem is called as the optimal software release policies. In this research, it was studied about this software release problem. Because of the possibility of introducing new faults when correcting or modifying the software, infinite failure NHPP models presented and propose an optimal release policies of the life distribution applied Burr distribution which makes out efficiency application for software reliability. In this paper, discuss optimal software release policies which minimize a total software cost of development and maintenance under the constraint of satisfying a software reliability requirement. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data (Lyu, M. R. [13]), make out estimating software optimal release time.

강도함수 특성에 근거한 소프트웨어 최적 방출시기에 관한 비교 연구

Abstract In this paper, we were researched decision problem called an optimal release policies after testing a software system in development phase and transferring it to the user. The applied model of release time exploited infinite failure non-homogeneous Poisson process This infinite failure non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The intensity function used Gompertz, Preto and Log-logstic pattern which has the efficient various property. Thus, optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time. Key Words : Software Release Policies, Infinite Non-Homogeneous Poisson Process, Intensity Function Property

와이블 분포 특성에 근거한 소프트웨어 최적 방출시기에 관한 비교 연구

본 연구에서는 소프트웨어 제품을 개발하여 테스팅을 거친 후 사용자에게 인도하는 시기를 결정하는 방출문제에 대하여 연구하였다. 인도시기에 관한 모형은 무한 고장수에 의존하는 비동질적인 포아송 과정을 적용하였다. 이러한 포아송 과정은 소프트웨어의 결함을 제거하거나 수정 작업 중에도 새로운 결함이 발생될 가능성을 반영하는 모형이다. 고장발생 수명분포는 여러 분포들을 적합시키는데 효율적인 특성을 가진 와이블분포를 이용하였다. 따라서 소프트웨어 요구 신뢰도를 만족시키고 소프트웨어 개발 및 유지 총비용을 최소화시키는 방출시간이 최적 소프트웨어 방출 정책이 된다. 본 논문의 수치적인 예에서는 고장 간격 시간 자료를 적용하고 모수추정 방법은 최우추정법과 추세분석을 통하여 자료의 효율성을 입증한 후 최적 방출시기를 추정하였다. In this paper, we were researched decision problem called an optimal release policies after testing a software system in development phase and transferring it to the user. The applied model of release time exploited infinite failure non-homogeneous Poisson process This infinite failure non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used the Weibull distribution which has the efficient various property which has the place efficient quality. Thus, optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.

A study of software reliability growth from the perspective of learning effects

For the last three decades, reliability growth has been studied to predict software reliability in the testing/debugging phase. Most of the models developed were based on the non-homogeneous Poisson process (NHPP), and S-shaped type or exponential-shaped type of behavior is usually assumed. Unfortunately, such models may be suitable only for particular software failure data, thus narrowing the scope of applications. Therefore, from the perspective of learning effects that can influence the process of software reliability growth, we considered that efficiency in testing/debugging concerned not only the ability of the testing staff but also the learning effect that comes from inspecting the testing/debugging codes. The proposed approach can reasonably describe the S-shaped and exponential-shaped types of behaviors simultaneously, and the results in the experiment show good fit. A comparative analysis to evaluate the effectiveness for the proposed model and other software failure models was also performed. Finally, an optimal software release policy is suggested.

Software Reliability Analysis by Considering Fault Dependency and Debugging Time Lag

Over the past 30 years, many software reliability growth models (SRGM) have been proposed. Often, it is assumed that detected faults are immediately corrected when mathematical models are developed. This assumption may not be realistic in practice because the time to remove a detected fault depends on the complexity of the fault, the skill and experience of personnel, the size of debugging team, the technique(s) being used, and so on. During software testing, practical experiences show that mutually independent faults can be directly detected and removed, but mutually dependent faults can be removed iff the leading faults have been removed. That is, dependent faults may not be immediately removed, and the fault removal process lags behind the fault detection process. In this paper, we will first give a review of fault detection & correction processes in software reliability modeling. We will then illustrate the fact that detected faults cannot be immediately corrected with several examples. We also discuss the software fault dependency in detail, and study how to incorporate both fault dependency and debugging time lag into software reliability modeling. The proposed models are fairly general models that cover a variety of known SRGM under different conditions. Numerical examples are presented, and the results show that the proposed framework to incorporate both fault dependency and debugging time lag for SRGM has a better prediction capability. In addition, an optimal software release policy for the proposed models, based on cost-reliability criterion, is proposed. The main purpose is to minimize the cost of software development when a desired reliability objective is given

Bayesian Approach to Optimal Release Policy of Software System

In this paper, we propose a new software reliability growth model which is the mixture of two exponential reliability growth models, one of which has the reliability growth and the other one does not have the reliability growth after the software is released upon completion of testing phase. The mixture of two such models is characterized by a weighted factor p, which is the proportion of reliability growth part within the model. Firstly, this paper discusses an optimal software release problem with regard to the expected total software cost incurred during the warranty period under the proposed software reliability growth model, which generalizes Kimura, Toyota and Yamada's (1999) model with consideration of the weighted factor. The second main purpose of this paper is to apply the Bayesian approach to the optimal software release policy by assuming the prior distributions for the unknown parameters contained in the proposed software reliability growth model. Some numerical examples are presented for the purpose of comparing the optimal software release policies depending on the choice of parameters by the non-Bayesian and Bayesian methods.

Analysis of incorporating logistic testing-effort function into software reliability modeling

This paper investigates a SRGM (software reliability growth model) based on the NHPP (nonhomogeneous Poisson process) which incorporates a logistic testing-effort function. SRGM proposed in the literature consider the amount of testing-effort spent on software testing which can be depicted as an exponential curve, a Rayleigh curve, or a Weibull curve. However, it might not be appropriate to represent the consumption curve for testing-effort by one of those curves in some software development environments. Therefore, this paper shows that a logistic testing-effort function can be expressed as a software-development/test-effort curve and that it gives a good predictive capability based on real failure-data. Parameters are estimated, and experiments performed on actual test/debug data sets. Results from applications to a real data set are analyzed and compared with other existing models to show that the proposed model predicts better. In addition, an optimal software release policy for this model, based on cost-reliability criteria, is proposed.

OPTIMAL SOFTWARE RELEASE POLICY BASED ON MARKOVIAN PERFECT DEBUGGING MODEL

In this paper we consider a Markovian perfect debugging model for which the software failure is caused by two types of faults, one which is easily detected and the other which is difficult to detect. When a failure occurs, a perfect debugging is immediately performed and consequently one fault is reduced from fault contents. We also treat the debugging time as a variable to develop a new debugging model. Based on the perfect debugging model, we propose an optimal software release policy that satisfies the requirements for both software reliability and expected number of faults which are required to achieve before releasing the software. Several measures, including the distribution of first passage time to the specified number of removed faults, are also obtained using the proposed debugging model.