Fuzzy optimization approach to component selection of fault-tolerant software system

In developing software systems, a manager’s goal is to design software using limited resources and meet the user requirements. One of the important user requirements concerns the reliability of the software. The decision to choose the right software modules (components) becomes extremely difficult because of the number of parameters to be considered while making the decision. If suitable components are not available, then the decision process is further complicated with build versus buy decisions. In this paper, we have formulated a fuzzy multi-objective approach to optimal decision “build-or-buy” for component selection for a fault-tolerant modular software system under the consensus recovery block scheme. A joint optimization model is formulated where the two objectives are maximization of system reliability and minimization of the system cost with a constraint on delivery time. An example of developing a retail system for small-and-medium-size enterprises is used to illustrate the proposed methodology.     

Application of fuzzy time series in prediction of time between failures &; faults in software reliability assessment

Since last seventies, various software reliability growth models (SRGMs) have been developed to estimate different measures related to quality of software like: number of remaining faults, software failure rate, reliability, cost, release time, etc. Most of the exiting SRGMs are probabilistic. These models have been developed based on various assumptions. The entire software development process is performed by human being. Also, a software can be executed in different environments. As human behavior is fuzzy and the environment is changing, the concept of fuzzy set theory is applicable in developing software reliability models. In this paper, two fuzzy time series based software reliability models have been proposed. The first one predicts the time between failures (TBFs) of software and the second one predicts the number of errors present in software. Both the models have been developed considering the software failure data as linguistic variable. Usefulness of the models has been demonstrated using real failure data.     

一种新的基于不完全排错的最优软件发行策略

软件的最优发行管理问题是软件可靠性研究的一个关键问题.现有的最优软件发行模型大都假定软件排错过程是完全的,并且在排错过程中没有新的故障引入,这种假设在很多情况下是不合理的.本文提出了一种新的最优软件发行管理模型,该模型既考虑了软件的不完全排错过程,又考虑了在排错过程中可能会引入新的故障,同时还考虑了由于排错经验的不断积累,软件的完全排错概率会增加的情况.本文同时给出了该模型的解.     

Statistical software reliability prediction and its applicability based on mean time between failures

One of the most important issues for a development manager may be how to predict the reliability of a software system at an arbitrary testing time. In this paper, using the software failure-occurrence time data, we discuss a method of software reliability prediction based on software reliability growth models described by an NHPP (nonhomogeneous Poisson process). From the applied software reliability growth models, the conditional probability distribution of the time between software failures is derived, and its mean and median are obtained as reliability prediction measures. Finally, based on several numerical examples, we compare the performance between these measures from the view point of software reliability prediction in the testing phase.     

A generalized JM model with applications to imperfect debugging in software reliability

For their nice mathematical properties, state space models have been widely used, especially for forecasting. Over the last decades, the study of tracking software reliability by statistical models has attracted scientists’ attention. However, most of models focus on perfect debugging although practically imperfect debugging arises everywhere. In this paper, a non-Gaussian state space model is modified to predict software failure time with imperfect debugging. In fact, this model is very flexible so that we can modify the system equation in this model to satisfy the various situations. Besides, this model is suitable for tracking software reliability, and applied to two well known datasets on software failures.     

NHPP software reliability model considering the uncertainty of operating environments with imperfect debugging and testing coverage

In this paper, we propose a testing-coverage software reliability model that considers not only the imperfect debugging (ID) but also the uncertainty of operating environments based on a non-homogeneous Poisson process (NHPP). Software is usually tested in a given control environment, but it may be used in different operating environments by different users, which are unknown to the developers. Many NHPP software reliability growth models (SRGMs) have been developed to estimate the software reliability measures, but most of the underlying common assumptions of these models are that the operating environment is the same as the developing environment. But in fact, due to the unpredictability of the uncertainty in the operating environments for the software, environments may considerably influence the reliability and software's performance in an unpredictable way. So when a software system works in a field environment, its reliability is usually different from the theory reliability, and also from all its similar applications in other fields. In this paper, a new model is proposed with the consideration of the fault detection rate based on the testing coverage and examined to cover ID subject to the uncertainty of operating environments. We compare the performance of the proposed model with several existing NHPP SRGMs using three sets of real software failure data based on seven criteria. Improved normalized criteria distance (NCD) method is also used to rank and select the best model in the context of a set of goodness-of-fit criteria taken all together. All results demonstrate that the new model can give a significant improved goodness-of-fit and predictive performance. Finally, the optimal software release time based on cost and reliability requirement and its sensitivity analysis are discussed.     

Software reliability assessment models based on cumulative bernoulli trial processes

The binomial software reliability growth model (SRGM) contains most existing SRGMs proposed in earlier work as special cases, and can describe every software failure-occurrence pattern in continuous time. In this paper, we propose generalized binomial SRGMs in both continuous and discrete time, based on the idea of cumulative Bernoulli trials. It is shown that the proposed models give some new unusual discrete models as well as the well-known continuous SRGMs. Through numerical examples with actual software failure data, two estimation methods for model parameters with grouped data are provided, and the predictive model performance is examined quantitatively.     

Enhancing software reliability modeling and prediction through the introduction of time-variable fault reduction factor

Over the past three decades, many software reliability models with different parameters, reflecting various testing characteristics, have been proposed for estimating the reliability growth of software products. We have noticed that one of the most important parameters controlling software reliability growth is the fault reduction factor (FRF) proposed by Musa. FRF is generally defined as the ratio of net fault reduction to failures experienced. During the software testing process, FRF could be influenced by many environmental factors, such as imperfect debugging, debugging time lag, etc. Thus, in this paper, we first analyze some real data to observe the trends of FRF, and consider FRF to be a time-variable function. We further study how to integrate time-variable FRF into software reliability growth modeling. Some experimental results show that the proposed models can improve the accuracy of software reliability estimation. Finally, sensitivity analyses of various optimal release times based on cost and reliability requirements are discussed. The analytic results indicate that adjusting the value of FRF may affect the release time as well as the development cost.     

The cross-entropy method with patching for rare-event simulation of large Markov chains

There are various importance sampling schemes to estimate rare event probabilities in Markovian systems such as Markovian reliability models and Jackson networks. In this work, we present a general state-dependent importance sampling method which partitions the state space and applies the cross-entropy method to each partition. We investigate two versions of our algorithm and apply them to several examples of reliability and queueing models. In all these examples we compare our method with other importance sampling schemes. The performance of the importance sampling schemes is measured by the relative error of the estimator and by the efficiency of the algorithm. The results from experiments show considerable improvements both in running time of the algorithm and the variance of the estimator.     

考虑多种类型缺陷的软件可靠性模型研究

本文提出一种考虑多种类型缺陷的软件可靠性模型,并构建了缺陷检测和剔除两个过程的模型。具体分类情况,可以根据模型的检验方法(拟合准则和预测有效性度量)和模型复杂度来具体决定,如果有测试人员的分类建议或者分类数据,可以结合模型共同决定。为了说明问题,本文给出四种类型缺陷的具体模型,并对实际数据集进行了拟合。通过模型比较,验证了多种类型缺陷模型的有效性。最后,通过构建软件最优发布时间策略对模型进行了应用。研究结果为软件开发和测试提供了理论参考。     

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.     

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The hybrid censoring scheme is a mixture of type-I and type-II censoring schemes. It is a popular censoring scheme in the literature of life data analysis. Mixed exponential distribution (MED) models is a class of favorable models in reliability statistics. Nevertheless, there is no much discussion to focus on parameters estimation for MED models with hybrid censored samples. We will address this problem in this paper. The EM (Expectation-Maximization) algorithm is employed to derive the closed form of the maximum likelihood estimators (MLEs). Finally, Monte Carlo simulations and a real-world data analysis are conducted to illustrate the proposed method.     

Multi-criteria optimization model integrated with AHP for evaluation and selection of COTS components

This paper deals with COTS evaluation and selection for developing a modular software system under single application development task. We consider both quantitative and qualitative criteria which fulfils the specific needs of a software system. We use analytical hierarchy process (AHP) technique for evaluating the fitness of COTS components based upon various criteria and sub-criteria thereby providing overall score of each COTS component. We develop optimization models integrating AHP and multi-criteria decision-making, which aim at: (i) maximize the total value of purchasing (TVP) subject to budget, compatibility and reliability constraints, and (ii) maximize TVP and minimize the total cost of purchase simultaneously subject to compatibility and reliability constraints. The efficiency of the models is illustrated by means of numerical illustrations.     

Central ADER schemes for hyperbolic conservation laws

In this paper we first briefly review the very high order ADER methods for solving hyperbolic conservation laws. ADER methods use high order polynomial reconstruction of the solution and upwind fluxes as the building block. They use a first order upwind Godunov and the upwind second order weighted average (WAF) fluxes. As well known the upwind methods are more accurate than central schemes. However, the superior accuracy of the ADER upwind schemes comes at a cost, one must solve exactly or approximately the Riemann problems (RP). Conventional Riemann solvers are usually complex and are not available for many hyperbolic problems of practical interest. In this paper we propose to use two central fluxes, instead of upwind fluxes, as the building block in ADER scheme. These are the monotone first order Lax-Friedrich (LXF) and the third order TVD flux. The resulting schemes are called central ADER schemes. Accuracy of the new schemes is established. Numerical implementations of the new schemes are carried out on the scalar conservation laws with a linear flux, nonlinear convex flux and non-convex flux. The results demonstrate that the proposed scheme, with LXF flux, is comparable to those using first and second order upwind fluxes while the scheme, with third order TVD flux, is superior to those using upwind fluxes. When compared with the state of art ADER schemes, our central ADER schemes are faster, more accurate, Riemann solver free, very simple to implement and need less computer memory. A way to extend these schemes to general systems of nonlinear hyperbolic conservation laws in one and two dimensions is presented.     

On the convergence of the partial least squares path modeling algorithm

This paper adds to an important aspect of Partial Least Squares (PLS) path modeling, namely the convergence of the iterative PLS path modeling algorithm. Whilst conventional wisdom says that PLS always converges in practice, there is no formal proof for path models with more than two blocks of manifest variables. This paper presents six cases of non-convergence of the PLS path modeling algorithm. These cases were estimated using Mode A combined with the factorial scheme or the path weighting scheme, which are two popular options of the algorithm. As a conclusion, efforts to come to a proof of convergence under these schemes can be abandoned, and users of PLS should triangulate their estimation results.     

三级四阶显式辛R-K-N格式的完全构造

s级p阶辛Runge-Kutta-Nystr\"om(R-K-N)方法的一种充要条件是用关于参数的非线性方程组来表示的,辛R-K-N格式的构造问题因而转化为该方程组的求解问题. 在一些特殊的限定条件下, 已有该方程组在s=3,p=4时的两组解,即得到了两个三级四阶显式辛格式. 对于s=3,p=4情形,基于吴方法,利用计算机代数系统Maple及软件包wsolve给出了对应的非线性方程组的全部解, 这样就构造了所有的三级四阶显式辛R-K-N格式, 并证明了三级四阶显式辛R-K-N方法所满足的条件方程有冗余. 数值实验结果显示出新的辛格式在一定的条件下有着较好的误差精度.     

Optimization models for critical spare parts inventories—a reliability approach

In industries characterized by heavy utilization of equipment and machinery, such as mining, oil & gas, utilities, transportation, adequate stockholding of critical spare parts becomes essential. Insufficient stocks affect overall performance of physical assets, as lack of spares may result in gross penalties, lower availability or increased operational risks. On the other hand, oversized inventories lead to inefficient use of capital and may imply severe expenditures. This paper presents various approaches for the determination of the optimal stock size, when the stock is composed of (i) non-repairable or (ii) repairable parts. The paper is focused on spares for relatively expensive, highly reliable components, rather than on fast-moving spare parts. Optimization criteria considered are minimization of costs, maximization of equipment availability, and the achievement of a desired stock reliability (probability that a spare part request will not be rejected because of the lack of spares in stock). For stock reliability, instantaneous and interval reliability calculations are considered. In addition, models directed to the estimation of the remaining life of a given stock of spare parts (at a certain stock reliability level) are introduced. The paper describes several models subject to practical industrial application, and presents case studies from utilities and mining to illustrate their use.     

Optimization models for quality and cost of modular software systems

This study presents two optimization models for selecting the best Commercial Off-The-Shelf (COTS) software product among alternatives for each module in the development of modular software systems. The objective function of the models is to maximize quality within a budgetary constraint. The software system consists of several programs, where a specific function of each program can call upon a series of modules. Several alternative COTS products are available for each module. A weight to the modules is given by utilizing the Analytic Hierarchy Process (AHP) based on the access frequencies of the modules. A simplified example is given to demonstrate each optimization model.     

Lyapunov direct method for investigating stability of nonstandard finite difference schemes for metapopulation models

In this paper nonstandard finite difference (NSFD) schemes of two metapopulation models are constructed. The stability properties of the discrete models are investigated by the use of the Lyapunov stability theorem. As a result of this we have proved that the NSFD schemes preserve essential properties of the metapopulation models (positivity, boundedness and monotone convergence of the solutions, equilibria and their stability properties). Especially, the basic reproduction number of the continuous models is also preserved. Numerical examples confirm the obtained theoretical results of the properties of the constructed difference schemes. The method of Lyapunov functions proves to be much simpler than the standard method for studying stability of the discrete metapopulation model in our very recent paper.     

Sensitivity analysis of release time of software reliability models incorporating testing effort with multiple change-points

To accurately model software failure process with software reliability growth models, incorporating testing effort has shown to be important. In fact, testing effort allocation is also a difficult issue, and it directly affects the software release time when a reliability criteria has to be met. However, with an increasing number of parameters involved in these models, the uncertainty of parameters estimated from the failure data could greatly affect the decision. Hence, it is of importance to study the impact of these model parameters. In this paper, sensitivity of the software release time is investigated through various methods, including one-factor-at-a-time approach, design of experiments and global sensitivity analysis. It is shown that the results from the first two methods may not be accurate enough for the case of complex nonlinear model. Global sensitivity analysis performs better due to the consideration of the global parameter space. The limitations of different approaches are also discussed. Finally, to avoid further excessive adjustment of software release time, interval estimation is recommended for use and it can be obtained based on the results from global sensitivity analysis.