基于多版本较准的软件费用模型研究

软件可靠性模型为软件的费用模型提供了很好的依据.在软件可靠性增长模型的测试阶段和操作运行阶段,环境的不同导致了两个阶段故障检测率的不同.在多版本较准的软件可靠性模型基础上,构造了一个综合了软件设计费用、软件测试费用、软件维护费用、软件失效造成的风险损失的软件费用模型.最后从软件费用出发,讨论了软件的最佳发布时间.     

A software cost model with imperfect debugging,random life cycle and penalty cost

The paper develops a cost model with an imperfect debugging and random life cycle as well as a penalty cost that is used to determine the optimal release policies for a software system. The software reliability model, based on the nonhomogeneous Poisson process, allows for three different error types: critical, major and minor errors. The model also allows for the introduction of any of these errors during the removal of an error. Using the software reliability model presented, the cost model with multiple error types and imperfect debugging is developed. This cost also considers the penalty cost due to delay for a scheduled delivery time and the length of the software life cycle is random with a known distribution. The optimal software release policies that minimize the expected software system costs (subject to the various constraints) or maximize the software reliability subject to a cost constraint, are then determined. Numerical examples are provided to illustrate the results.     

Optimal procurement, disposal and pricing policies for managing rental goods

Consider a video rental retailer who procures DVDs or video cassettes from a distributor and rents them to the customers. To meet the time‐varying rental demand, the retailer needs to develop cost‐effective procurement and disposal policies. In this paper, we first present a base model in which the underlying rental demand is decreasing over time, backorders are not allowed and the disposal price is exogenous. For this base model, we show that the optimal procurement quantity is equal to the sum of effective demands (rental demand net of returns) over an integral number of periods, and the optimal disposal policy can be determined by solving a simple dynamic program with polynomial complexity. We then analyze the case of endogenous disposal prices and derive optimal disposal policies by solving a quadratic optimization problem with tree constraints. We also extend the base model to allow for backorders and to cases where the retailer has multiple procurement opportunities and a contractual period where disposals are not allowed. We show that the qualitative nature of the procurement policy is preserved in these cases and the optimal procurement and selling policies can be determined using similar dynamic programming algorithms.     

基于时间的软件恢复策略的建模与分析

针对软件在连续运行过程中普遍发生的老化现象,提出了一种嵌套的基于时间的软件恢复策略,对恢复过程的Petri网模型分析求解,并最终得到了最优恢复时间间隔序列和最优应用级恢复次数。该策略同时考虑应用级和系统级的恢复,从而进一步减少了恢复时间,降低了恢复成本和周期性应用级恢复策略预测失败的风险,提高了系统的可靠性。对于更复杂的系统,策略还可进一步嵌套进程级的恢复,从而具有一定的可扩展性。     

A Study of Uncertainty in Software Cost and Its Impact on Optimal Software Release Time

For a development software project, management often faces the dilemma of when to stop testing the software and release it for operation, which requires careful decision-making as it has great impact on both software reliability and project cost. In most existing research on optimal software release problem, the cost considered was the expected cost (EC) of the project. However, what management concerns is the actual cost (AC) of the project rather than the EC. Treatment (such as minimization) of the EC may not ensure a desired low level of the AC, due to the uncertainty (variability) involved in the AC. In this paper, we study the uncertainty in software cost and its impact on optimal software release time in detail. The uncertainty is quantified by the variance of the AC and several risk functions. A risk-control approach to optimal software release problem is proposed. New formulations of the problem which are extensions of current formulations are developed, and solution procedures are established. Several examples are presented. Results reveal that it seems crucial to take account of the uncertainty in software cost in optimal software release problem, otherwise unsafe decision may be reached which could be a false dawn to management.     

Optimal lot size and offline inspection policy

In this study, we investigate the effects of using process status at the end of the production lot (PSPL), on determining the optimal policies for products inspection and production lot size. First, we obtain the optimal product inspection policies for different PSPL for a given lot in the in-control or out-of-control state. Properties for the inspection policy are explored. Then, the expected total cost function, which includes setup cost, process maintenance cost and quality-related control cost, is obtained. The optimal production lot size that minimizes the expected total cost per item is determined. Our proposed inspection policy is compared with the three policies of no inspection, full inspection, and disregarding the first s items policy, in which only items from s+1 until the end of the production lot are inspected. Differences in the minimum expected total cost per item between our proposed inspection policy and the other three policies are investigated with a numerical example.     

Optimal software release scheduling based on artificial neural networks

The determination of the optimal software release schedule plays an important role in supplying sufficiently reliable software products to actual market or users. In the existing methods, the optimal software release schedule was determined by assuming the stochastic and/or statistical model called software reliability growth model. In this paper, we propose a new method to estimate the optimal software release timing which minimizes the relevant cost criterion via artificial neural networks. Recently, artificial neural networks are actively studied with many practical applications and are applied to assess the software product reliability. First, we interpret the underlying cost minimization problem as a graphical one and show that it can be reduced to a simple time series forecasting problem. Secondly, artificial neural networks are used to estimate the fault-detection time in future. In numerical examples with actual field data, we compare the new method based on the neural networks with existing parametric methods using some software reliability growth models and illustrate its benefit in terms of predictive performance. A comprehensive bibliography on the software release problem is presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

Software release policies with gain in reliability justifying the costs

An important question in the developing process of software products is when to stop testing to make the gain in reliability justify the costs. In this paper, a software reliability-cost model is presented to determine the optimal release policies that maximize the expected net gain in reliability. Several software cost factors are considered in this study, such as the cost of removing detected errors and the risk cost due to software failure. The error removal cost is modeled based on a stochastic process. A software reliability model based on the non-homogeneous Poisson process is used. Numerical examples are provided to illustrate the results. This revised version was published online in June 2006 with corrections to the Cover Date.     

带有周期检测性的软件预防性再生策略

研究了软件老化过程及软件预防性再生策略问题.引入累积损伤模型,将由aging related bug引起的内存的消耗看作是由于冲击造成的内存损伤量,通过周期性的检测可以得到内存被逐步消耗而不被释放的量,当内存消耗量达到预防性再生值时在下一个检测点执行软件预防性再生策略.建立了单位时间费用模型并解析得到使单位时间期望费用最低的预防性再生值,最后通过模拟进一步验证了最优再生策略的奈件.     

基于CGOM的软件费用模型研究

软件测试是提高软件质量的重要手段，对测试数据充分的测试准则是软件测试完成的标准．目前，绝大多数的测试准则并不考虑软件费用，容易为了满足测试准则而使用户承担昂贵的测试费用．该文提出了一种随机过程类非齐次泊松过程(NHPP)中的经典模型——G-O模型的改进模型，并基于此模型构造了一个综合了软件设计费用、软件测试费用、软件维护费用、软件失效造成的风险损失的软件费用模型．最后从软件费用出发，讨论了软件的最佳发布时间．     

Bayesian updating of optimal release time for software systems

In this paper, a Bayesian method dealing with software reliability growth with consideration of the learning effect is proposed to determine an optimal release time for software systems with regard to the testing cost and experts’ prior judgments. Such an approach is able to devise an appropriate software-debugging scheme which has the best arrangement of available resources and personnel with a minimal software testing cost when lacking sufficient information for decision making. Past research on software reliability emphasized the estimation of the number of cumulative software errors or the software reliability with respect to a specific time period, yet it neglected the determination of software release time with consideration of the software testing cost, meaning that existing approaches are not entirely practical. Accordingly, the proposed method is concerned with the evaluation of the software testing cost incurred during the testing period based on experts’ prior judgments and the software testing data collected within a given duration, and is thus characterized by its practicality as well as meaningfulness with consideration of the learning effect. Finally, a numerical example is given to verify the effectiveness of the proposed approach, and sensitivity and risk analyses are performed on this example.

软件发布周期费用估算方法研究

本文对软件维护过程中的发布周期费用估算方法进行了研究,提出了基于发布规划的估算原则,并对整个基于发布规划的费用估算的抽象过程进行分析。     

Cost-oriented task allocation and hardware redundancy policies in heterogeneous distributed computing systems considering software reliability

Task allocation policy and hardware redundancy policy for distributed computing system (DCS) are of great importance as they affect many system characteristics such as system cost, system reliability and performance. In recent years, abundant research has been carried out on the optimal task allocation and/or hardware redundancy problem, most of which took a reliability-oriented approach, i.e., the optimization criterion was system reliability maximization. Nevertheless, besides system reliability, other system characteristics such as system cost may be of great concern to management. In this paper, we take a cost-oriented approach to the optimal task allocation and hardware redundancy problem for DCS, which addresses both system cost and system reliability issues. A system cost model which could reflect the impact of system unreliability on system cost is developed, and by minimizing the total system cost, a satisfactory level of system reliability could be reached simultaneously. In the reliability modeling and analysis of DCS, we take both hardware reliability and software reliability into account. Two numerical examples are given to illustrate the formulation and solution procedures, in which genetic algorithm is used. Results show that based on the developed system cost model, appropriate decision-makings on task allocation and hardware redundancy policies for DCS could be made, and the result obtained seems to be a fairly good trade-off between system cost and system reliability.     

Stochastic software safety/reliability measurement and its application

Safety and reliability have become important software quality characteristics in the development of safety-critical software systems. However, there are so far no quantitative methods for assessing a safety-critical software system in terms of the safety/reliability characteristics. The metrics of software safety is defined as the probability that conditions that can lead to hazards do not occur. In this paper, we propose two stochastic models for software safety/reliability assessment: the data-domain dependent safety assessment model and the availability-related safety assessment model. These models focus on describing the time- or execution-dependent behavior of the software faults which can lead to unsafe states when they cause software failures. The application of one of these models to optimal software release problems is also discussed. Finally, numerical examples are illustrated for quantitative software safety assessment and optimal software release policies. This revised version was published online in June 2006 with corrections to the Cover Date.     

Does information security attack frequency increase with vulnerability disclosure? An empirical analysis

Research in information security, risk management and investment has grown in importance over the last few years. However, without reliable estimates on attack probabilities, risk management is difficult to do in practice. Using a novel data set, we provide estimates on attack propensity and how it changes with disclosure and patching of vulnerabilities. Disclosure of software vulnerability has been controversial. On one hand are those who propose full and instant disclosure whether the patch is available or not and on the other hand are those who argue for limited or no disclosure. Which of the two policies is socially optimal depends critically on how attack frequency changes with disclosure and patching. In this paper, we empirically explore the impact of vulnerability information disclosure and availability of patches on attacks targeting the vulnerability. Our results suggest that on an average both secret (non-published) and published (published and not patched) vulnerabilities attract fewer attacks than patched (published and patched) vulnerabilities. When we control for time since publication and patches, we find that patching an already known vulnerability decreases the number of attacks, although attacks gradually increase with time after patch release. Patching an unknown vulnerability, however, causes a spike in attacks, which then gradually decline after patch release. Attacks on secret vulnerabilities slowly increase with time until the vulnerability is published and then attacks rapidly decrease with time after publication.

Two-echelon stochastic inventory system with returns and partial backlogging

This paper investigates a two-echelon stochastic inventory system with returns and partial backlogging; our proposed model, which is realistic for practical situations, might be applicable in many manufacturing planning situations. The objective is to find a continuous-review inventory control policy that minimises the total expected annual cost of the system. A computer code using the software Mathematica 5.2 is developed to derive the optimal solution. Additionally, we discuss the sensitivity of the optimal solution together with the changes of the values of the parameters associated with the model for decision-making. The results are illustrated with the help of four numerical examples.     

按单装配系统中组件生产和库存分配控制策略研究

针对由两种组件、三类顾客需求组成的按单装配系统, 本文研究了其中的组件生产控制与库存分配问题. 在各类顾客需 求是泊松到达过程, 各种组件加工时间服从指数分布的假设下, 我们运用马尔科夫决策理论建立了无限期折扣总成本模型, 根据Lippman转换得到了相应归一化后的离散最优方程, 在此基础之上分析了生产和库存分配联合最优控制策略的结构性质. 本文证明了最优策略是依赖于系统状态的动态策略. 组件的最优生产策略是动态基库存策略, 其中基库存水平是关于系统中其他组件库存水平的非减函数. 而最优的分配策略是动态的阈值策略, 对于只需一种组件构成的顾客需求, 组件的分配阈值是系统中另一组件库存水平的增函数; 而对于同时需要两种组件组成的顾客需求, 其各组件的分配阈值是另一组件库存水平的减函数. 最后通过数值试验给出了各个参数对联合最优控制策略的影响, 并得到了相应的管理启示.     

Fuzzy age-dependent replacement policy and SPSA algorithm based-on fuzzy simulation

An increase in the performance of deteriorating systems can be achieved through the adoption of suitable maintenance policies. One of the most popular maintenance policies is the age-dependent replacement policy. In this paper, a fuzzy age-dependent replacement policy is considered in which the lifetimes of components are treated as fuzzy variables. To minimize the long-term expected cost per unit time, a programming model is formulated. Also, a theorem for optimal solution existence is proposed. In order to solve the proposed model, a fuzzy simulation technique is designed which estimates the expected value of the objective function. The simultaneous perturbation stochastic approximation (SPSA) algorithm is then used to determine a solution. Finally, a numerical example is presented to illustrate the effectiveness of this technique.     

需求和退货与供应中断相关环境下库存控制

需求和退货与供应中断相关会引发库存剧烈波动,从而导致库存控制非常困难.在采用Markov调制Lévy过程描述库存水平变化条件下,利用水平穿越法、更新过程和鞅理论确定循环期望时间和费用函数,据此构建系统长程平均费用率模型.在此基础上,通过仿真实验研究需求(退货)与供应中断相关度对最优库存控制策略的影响,并分析不同中断和退货类型下最优控制策略的变化,从而为该环境下有效管理库存提供新启示.     

Stochastic scheduling on parallel machines to minimize discounted holding costs

We study stochastic scheduling on m parallel identical machines with random processing times. The cost involved in the problem is discounted to the present value and the objective is to minimize the expected discounted holding cost, which covers in a unified framework many performance measures discussed in the literature as special cases, including discounted rewards, flowtime, and makespan. We prove that the SEPT rule is optimal, on a fairly general ground, in the class of preemptive dynamic policies, the class of nonpreemptive dynamic policies, and the class of nonpreemptive static list policies. The LEPT rule, on the other hand, is optimal to minimize the expected discounted makespan only under certain restrictive conditions. Without such conditions, the LEPT rule is found no longer optimal for discounted makespan by a counterexample, in contrast to the case without discounting. This research was partially supported by the National Natural Science Foundation of China under Grant No. 70671043, Research Grants Council of Hong Kong Under Project No. 410208, NSFC/RGC Joint Research Grant No. N-CUHK442/05 (NSFC Ref: 70518002), and Macquarie University Research Development Grant.