A markov process model for software reliability analysis

Software reliability is a rapidly developing discipline. In this paper we model the fault-detecting processes by Markov processes with decreasing jump intensity. The intensity function is suggested to be a power function of the number of the remaining faults in the software. The models generalize the software reliability model suggested by Jelinski and Moranda (‘Software reliability research’, in W. Freiberger (ed.), Statistical Computer Performance Evaluation, Academic Press, New York, 1972. pp. 465–497). The main advantage of our models is that we do not use the assumption that all software faults correspond to the same failure rate. Preliminary studies suggest that a second-order power function is quite a good approximation. Statistical tests also indicate that this may be the case. Numerical results show that the estimation of the expected time to next failure is both reasonable and decreases relatively stably when the number of removed faults is increased.     

Flexible software reliability growth model with testing effort dependent learning process

A lot of importance has been attached to the testing phase of the Software Development Life Cycle (SDLC). It is during this phase it is checked whether the software product meets user requirements or not. Any discrepancies that are identified are removed. But testing needs to be monitored to increase its effectiveness. Software Reliability Growth Models (SRGMs) that specify mathematical relationships between the failure phenomenon and time have proved useful. SRGMs that include factors that affect failure process are more realistic and useful. Software fault detection and removal during the testing phase of SDLC depend on how testing resources (test cases, manpower and time) are used and also on previously identified faults. With this motivation a Non-Homogeneous Poisson Process (NHPP) based SRGM is proposed in this paper which is flexible enough to describe various software failure/reliability curves. Both testing efforts and time dependent fault detection rate (FDR) are considered for software reliability modeling. The time lag between fault identification and removal has also been depicted. The applicability of our model is shown by validating it on software failure data sets obtained from different real software development projects. The comparisons with established models in terms of goodness of fit, the Akaike Information Criterion (AIC), Mean of Squared Errors (MSE), etc. have been presented.     

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 Markov modulated Poisson model for software reliability

In this paper, we consider a latent Markov process governing the intensity rate of a Poisson process model for software failures. The latent process enables us to infer performance of the debugging operations over time and allows us to deal with the imperfect debugging scenario. We develop the Bayesian inference for the model and also introduce a method to infer the unknown dimension of the Markov process. We illustrate the implementation of our model and the Bayesian approach by using actual software failure data.     

Skill-based framework for optimal software project selection and resource allocation

This paper presents a conceptual framework and a mathematical formulation for software resource allocation and project selection at the level of software skills. First, we introduce a skill-based framework that considers universities, software companies, and potential projects of a country. Based on this framework, we formulate a linear integer program PMax which determines the selection of projects and the allocation of human resources that maximize profit for a certain company. We show that PMax is NP-complete. Therefore, we devise a meta-heuristic, called Tabu Select and Greedily Allocate (TSGA), to overcome the computational complexities. When compared to PMax running on CPLEX, TSGA performs 15 times faster with an accuracy of 98% on small to large size problems where CPLEX converges. On larger problems where CPLEX does not return an answer, TSGA computes a feasible solution in the order of minutes.     

Practical stopping criteria for validating safety-critical software by estimating impartial reliability

In this research, we investigate stopping rules for software testing and propose two stopping rules from the aspect of software reliability testing based on the impartial reliability model. The impartial reliability difference (IRD-MP) rule considers the difference between the impartial transition-probability reliabilities estimated for both software developer and consumers at their predetermined prior information levels. The empirical–impartial reliability difference (EIRD-MP) rule suggests stopping a software test when the computed empirical transition reliability is tending to its estimated impartial transition reliability. To insure the high-standard requirement for safety-critical software, both rules take the maximum probability (MP) of untested paths into account.     

Optimal asset allocation for a general portfolio of life insurance policies

Asset liability matching remains an important topic in life insurance research. The objective of this paper is to find an optimal asset allocation for a general portfolio of life insurance policies. Using a multi-asset model to investigate the optimal asset allocation of life insurance reserves, this study obtains formulae for the first two moments of the accumulated asset value. These formulae enable the analysis of portfolio problems and a first approximation of optimal investment strategies. This research provides a new perspective for solving both single-period and multiperiod asset allocation problems in application to life insurance policies. The authors obtain an efficient frontier in the case of single-period method; for the multiperiod method, the optimal asset allocation strategies can differ considerably for different portfolio structures.     

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.     

Optimal allocation of reliability tasks to mitigate faults during system development

^** Email: walter.johnston{at}baesystems.com^*** Email: j.quigley{at}strath.ac.uk^**** Email: lesley.walls{at}strath.ac.uk This paper considers reliability planning for a concept designfor a new system where a portfolio of possible reliability developmenttasks exists; the goal is to find a selection and sequence oftasks to achieve reliability targets subject to time constraintsat minimal cost. This is non-trivial given that each task potentiallycan expose several different weaknesses and each weakness potentiallycan be exposed by several different tasks. We use a Bayesianpoint process model to estimate the system reliability. Theprior distribution maps to a fault register and relates directlyto a set of potential engineering modifications.The likely impactof each task can be assessed using the point process model.An integer programming approach is used to sequence and scheduletasks under the constraint that contractual reliability requirementsmust be met. An illustrative example is provided and an extensionto system availability is proposed.     

Optimal resource allocation for security in reliability systems

Recent results have used game theory to explore the nature of optimal investments in the security of simple series and parallel systems. However, it is clearly important in practice to extend these simple security models to more complicated system structures with both parallel and series subsystems (and, eventually, to more general networked systems). The purpose of this paper is to begin to address this challenge. While achieving fully general results is likely to be difficult, and may require heuristic approaches, we are able to find closed-form results for systems with moderately general structures, under the assumption that the cost of an attack against any given component increases linearly in the amount of defensive investment in that component. These results have interesting and sometimes counterintuitive implications for the nature of optimal investments in security.     

A discrete time model for software reliability with application to a flight control software

This work is motivated by a particular software reliability problem in a unit of flight control software developed by the Indian Space Research Organization (ISRO), in which the testing of the software is carried out in multiple batches, each consisting of several runs. As the errors are found during the runs within a batch, they are noted, but not debugged immediately; they are debugged only at the end of that particular batch of runs. In this work, we introduce a discrete time model suitable for this type of periodic debugging schedule and describe maximum likelihood estimation for the model parameters. This model is used to estimate the reliability of the software. We also develop a method to determine the additional number of error‐free test runs required for the estimated reliability to achieve a specific target with some high probability. We analyze the test data on the flight control software of ISRO. Copyright © 2011 John Wiley & Sons, Ltd.     

A generalized DEA model for centralized resource allocation

In this paper, we introduced a new generalized centralized resource allocation model which extends Lozano and Villa’s and Asmild et al.’s models to a more general case. In order to uncover the sources of such total input contraction in the generalized centralized resource allocation model, we applied the structural efficiency to further decompose it into three components: the aggregate technical efficiency, the aggregate allocative efficiency and re-transferable efficiency components. The proposed models are not only flexible enough for the central decision-maker to adjust the inputs and outputs to achieve the total input contraction but also identify the sources of such total input contraction, thereby giving rise to an important interpretation and understanding of the generalized centralized resource allocation model. Finally, an empirical example is used to illustrate the approach.     

关于一种新模型对软件总体可靠度的估计

本文在对文[4]中软件可靠度的估计进行研究的基础上,提出了软件总体可靠性的一个新模型,对软件总体的可靠度进行了讨论,利用点估计方法,得到软件可靠度的点估计值,证明了软件总体失效率λ估计解的唯一性,并对缺陷数进行了估计,从而给出了新模型下软体总体可靠性的估计.     

Stackelberg strategy solution for optimal software release policies

We present a software release policy which is based on the Stackelberg strategy solution concept. The model formulated assumes the existence of two type of producers in the market, the leader and follower. The resulting release policy combines both cost factors and a loss of opportunity factor which is the result of competition between the rival producers. We define a Stackelberg strategy pair in the context of our model and, through a series of preliminary results, show that an optimal strategy pair exists. We also present a numerical example which utilizes a software reliability growth model based on the nonhomogeneous Poisson process. Finally, we explore the relative leadership property of the optimal strategies.This work was supported in part by a FOAS Research Grant provided by RMIT. The author would like to thank the referees for constructive suggestions which helped to improve a previous version of this paper.     

具有内生基础设施分配的城市经济增长模型

In this paper, an urban economic growth model with endogenous infrastructure allocation is given by introducing the two-variable utility function for city＇s inhabitant. A twodimensional dynamical system is obtained by solving the utility maximization problem and it is proved that this system has the unique non-zero equilibrium which is a saddle. The model has the unique optimal growth and an optimal rate of infrastructure allocation.     

A note on “Optimal resource allocation for security in reliability systems”

In a recent paper by Azaiez and Bier [Azaiez, M.N., Bier, V.M., 2007. Optimal resource allocation for security in reliability systems. European Journal of Operational Research 181, 773–786], the problem of determining resource allocation in series-parallel systems (SPSs) is considered. The results for this problem are based on the results for the least-expected cost failure-state diagnosis problem. In this note, it is demonstrated that the results for the least-expected cost failure-state diagnosis problem for SPSs in Azaiez and Bier (2007) are incorrect. In addition relevant results that were not cited in the paper are summarized.     

Fixed cost and resource allocation based on DEA cross-efficiency

In many managerial applications, situations frequently occur when a fixed cost is used in constructing the common platform of an organization, and needs to be shared by all related entities, or decision making units (DMUs). It is of vital importance to allocate such a cost across DMUs where there is competition for resources. Data envelopment analysis (DEA) has been successfully used in cost and resource allocation problems. Whether it is a cost or resource allocation issue, one needs to consider both the competitive and cooperative situation existing among DMUs in addition to maintaining or improving efficiency. The current paper uses the cross-efficiency concept in DEA to approach cost and resource allocation problems. Because DEA cross-efficiency uses the concept of peer appraisal, it is a very reasonable and appropriate mechanism for allocating a shared resource/cost. It is shown that our proposed iterative approach is always feasible, and ensures that all DMUs become efficient after the fixed cost is allocated as an additional input measure. The cross-efficiency DEA-based iterative method is further extended into a resource-allocation setting to achieve maximization in the aggregated output change by distributing available resources. Such allocations for fixed costs and resources are more acceptable to the players involved, because the allocation results are jointly determined by all DMUs rather than a specific one. The proposed approaches are demonstrated using an existing data set that has been applied in similar studies.     

Resource allocation model and double-sphere crowding distance for evolutionary multi-objective optimization

Convergence speed and diversity of nondominated solutions are two important performance indicators for Multi-Objective Evolutionary Algorithms (MOEAs). In this paper, we propose a Resource Allocation (RA) model based on Game Theory to accelerate the convergence speed of MOEAs, and a novel Double-Sphere Crowding Distance (DSCD) measure to improve the diversity of nondominated solutions. The mechanism of RA model is that the individuals in each group cooperate with each other to get maximum benefits for their group, and then individuals in the same group compete for private interests. The DSCD measure uses hyper-spheres consisting of nearest neighbors to estimate the crowding degree. Experimental results on convergence speed and diversity of nondominated solutions for benchmark problems and a real-world problem show the efficiency of these two proposed techniques.     

A software framework based on a conceptual unified model for evolutionary multiobjective optimization: ParadisEO-MOEO

This paper presents a general-purpose software framework dedicated to the design and the implementation of evolutionary multiobjective optimization techniques: ParadisEO-MOEO. A concise overview of evolutionary algorithms for multiobjective optimization is given. A substantial number of methods has been proposed so far, and an attempt of conceptually unifying existing approaches is presented here. Based on a fine-grained decomposition and following the main issues of fitness assignment, diversity preservation and elitism, a conceptual model is proposed and is validated by regarding a number of state-of-the-art algorithms as simple variants of the same structure. This model is then incorporated into the ParadisEO-MOEO software framework. This framework has proven its validity and high flexibility by enabling the resolution of many academic, real-world and hard multiobjective optimization problems.