Recently, the wavelet-based estimation method has gradually been becoming popular as a new tool for software reliability assessment. The wavelet transform possesses both spatial and temporal resolution which makes the wavelet-based estimation method powerful in extracting necessary information from observed software fault data, in global and local points of view at the same time. This enables us to estimate the software reliability measures in higher accuracy. However, in the existing works, only the point estimation of the wavelet-based approach was focused, where the underlying stochastic process to describe the software-fault detection phenomena was modeled by a non-homogeneous Poisson process. In this paper, we propose an interval estimation method for the wavelet-based approach, aiming at taking account of uncertainty which was left out of consideration in point estimation. More specifically, we employ the simulation-based bootstrap method, and derive the confidence intervals of software reliability measures such as the software intensity function and the expected cumulative number of software faults. To this end, we extend the well-known thinning algorithm for the purpose of generating multiple sample data from one set of software-fault count data. The results of numerical analysis with real software fault data make it clear that, our proposal is a decision support method which enables the practitioners to do flexible decision making in software development project management.

Utilization data (a kind of incomplete data) is defined as the fraction of a fixed period in which the system is busy. In computer systems, utilization data is very common and easily observable, such as CPU utilization. Unlike inter-arrival times and waiting times, it is more significant to consider the parameter estimation of transaction-based systems with utilization data. In our previous work [7], a novel parameter estimation method using utilization data for an Mt/M/1/K queueing system was presented to estimate the parameters of a non-homogeneous Poisson process (NHPP). Since NHPP is classified as a simple counting process, it may not fit actual arrival streams very well. As a generalization of NHPP, Markovian arrival process (MAP) takes account of the dependency between consecutive arrivals and is often used to model complex, bursty, and correlated traffic streams. In this paper, we concentrate on the parameter estimation of an MAP/M/1/K queueing system using utilization data. In particular, the parameters are estimated by using maximum likelihood estimation (MLE) method. Numerical experiments on real utilization data validate the proposed approach and evaluate the effective traffic intensity of the arrival stream of MAP/M/1/K queueing system. Besides, three kinds of utilization datasets are created from a simulation to assess the effects of observed time intervals on both estimation accuracy and computational cost. The numerical results show that MAP-based approach outperforms the exiting method in terms of both the estimation accuracy and computational cost.

Non-homogeneous Poisson processes (NHPPs) have gained much popularity in actual software testing phases to estimate the software reliability, the number of remaining faults in software and the software release timing. In this paper, we propose a new modeling approach for the NHPP-based software reliability models (SRMs) to describe the stochastic behavior of software fault-detection processes. The fundamental idea is to apply the equilibrium distribution to the fault-detection time distribution in NHPP-based modeling. We also develop efficient parameter estimation procedures for the proposed NHPP-based SRMs. Through numerical experiments, it can be concluded that the proposed NHPP-based SRMs outperform the existing ones in many data sets from the perspective of goodness-of-fit and prediction performance.

This paper considers a transaction-based multi-server system with rejuvenation, and derive the optimal software rejuvenation policies under some system dependability measures; the steady-state availability, the probability of transaction loss and the upper bound of mean response time on transactions. We compare the system configuration based on a single-server with that based on a multi-server in terms of the software rejuvenation scheme. In numerical examples, we calculate the optimal software rejuvenation timing and its associated dependability measure, and refer to the effect of preventive maintenance in the transaction-based multi-server software systems.

In this paper, we consider the similar software cost models with periodic rejuvenation to Garg, Puliafito, Telek and Trivedi (1995) under the cost effectiveness criteria. First, an alternative model as well as the original one are analyzed by Markov regenerative processes. We derive analytically the optimal periodic software rejuvenation policies which maximize the cost-effectiveness in the steady state for two models. Further, we develop statistical non-parametric algorithms to estimate the optimal software rejuvenation policies, provided that the sample data to characterize the system failure times are given. Then, the total time on test (TTT) concept is used. In numerical examples, we compare the periodic software rejuvenation policy with the non-periodic one, and investigate the asymptotic properties of the non-parametric estimators for the optimal software rejuvenation policies through a simulation experiment.

In this paper we consider two non-parametric estimation methods for software reliability assessment without specifying the fault-detection time distribution, where the underlying stochastic process to describe software fault-counts in the system testing is given by a non-homogeneous Poisson process. The resulting data-driven methodologies can give the useful probabilistic information on the software reliability assessment under the incomplete knowledge on fault-detection time distribution. Throughout examples with real software fault data, it is shown that the proposed methods provide more accurate estimation results than the common parametric approach.

In this letter we develop a software reliability modeling framework by introducing the Burr XII distributions to software fault-detection time. An extension to deal with software metrics data characterizing the product size, program complexity or testing expenditure is also proposed. Finally, we investigate the goodness-of-fit performance and compare our new models with the existing ones through real data analyses.

This paper proposes the test case prioritization in regression testing. The large size of a test suite to be executed in regression testing often causes large amount of testing cost. It is important to reduce the size of test cases according to prioritized test sequence. In this paper, we apply the Markov chain Monte Carlo random testing (MCMC-RT) scheme, which is a promising approach to effectively generate test cases in the framework of random testing. To apply MCMC-RT to the test case prioritization, we consider the coverage-based distance and develop the algorithm of the MCMC-RT test case prioritization using the coverage-based distance. Furthermore, the MCMC-RT test case prioritization technique is consistently comparable to coverage-based adaptive random testing (ART) prioritization techniques and involves much less time cost.

Software rejuvenation is a proactive fault management technique that has been extensively studied in the recent literature. In this paper, we focus on an example for a telecommunication billing application considered in Huang et al. (1995) and develop the discrete-time stochastic models to estimate the optimal software rejuvenation schedule. More precisely, two software availability models with rejuvenation are formulated via the discrete semi-Markov processes, and the optimal software rejuvenation schedules which maximize the steady-state availabilities are derived analytically. Further, we develop statistically non-parametric algorithms to estimate the optimal software rejuvenation schedules, provided that the complete sample data of failure times are given. Then, a new statistical device, called the discrete total time on test statistics, is introduced. Finally, we examine asymptotic properties for the statistical estimation algorithms proposed in this paper through a simulation experiment.

This paper proposes a statistical method to estimate the optimal software release time which minimizes the expected total software cost incurred in both testing and operation phases. It is shown that the underlying cost minimization problem can be reduced to a graphical one. This implies that the software release problem under consideration is essentially equivalent to a time series forecasting for the software fault-occurrence time data. In order to predict the future fault-occurrence time, we apply three extraordinary auto-regressive models by Singpurwalla and Soyer (1985) as the prediction devices as well as the well-known AR and ARIMA models. Numerical examples are devoted to illustrate the predictive performance for the proposed method. We compare it with the classical exponential software reliability growth model based on the non-homogeneous Poisson process, using actual software fault-occurrence time data.

In this paper, we develop an effective smoothing technique to estimate the optimal software release schedule which minimizes the total software cost. The optimal software release problem is essentially reduced to a statistical estimation problem for the software failure rate, but the resulting estimator based on both the fault-detection time data observed in testing phase and its estimate in future is discontinuous and does not always function well for determining the optimal release schedule. We estimate the smoothed software failure rate using the usual quadratic programming approach and generate the optimal software release schedule with higher accuracy.

The non-homogeneous Poisson process (NHPP) has been applied successfully to model nonstationary counting phenomena for a large class of problems. In software reliability engineering, the NHPP-based software reliability models (SRMs) are of a very important class. Since NHPP is characterized by its rate (intensity) function, which is known as the software failure rate of NHPP-based SRM, it is of great interest to estimate accurately the rate function from observed software failure data. In the existing work the same authors introduced a Haar-wavelet-based technique for this problem and found that the Haar wavelet transform provided a very powerful performance in estimating software failure rate. In this paper, we consider the application potentiality of a Daubechies wavelet estimator in the estimation of software failure rate, given the software failure time data. We give practical solutions by overcoming technical difficulties in applying the Daubechies wavelet estimator to the real software failure time data.

An exponential regression-based model with stochastic intensity is developed to describe the software reliability growth phenomena, where the software testing metrics depend on the intensity process. For such a generalized modeling framework, the common maximum likelihood method cannot be applied any more to the parameter estimation. In this paper, we propose to use the pseudo maximum likelihood method for the parameter estimation and to seek not only the model parameters but also the software reliability measures approximately. It is shown in numerical experiments with real software fault data that the resulting software reliability models based on four parametric approximations provide the better goodness-of-fit performance than the common non-homogeneous Poisson process models without testing metric information.

This paper discusses how to compute the parametric sensitivity function in continuous-time Markov chains (CTMC). The sensitivity function is the first derivative of the steady-state probability vector regarding a CTMC parameter. Since the sensitivity function is given as a solution of linear equations with a sparse matrix, several linear equation solvers are available to obtain it. In this paper, we consider Jacobi and successive-over relaxation as variants of the Gauss-Seidel algorithm. In addition, we develop an algorithm based on the Takahashi method for the sensitivity function. In numerical experiments, we comprehensively evaluate the performance of these algorithms from the viewpoint of computation time and accuracy.

Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this article, we consider periodic software rejuvenation models based on the expected cost per unit time in the steady state under discrete-time operation circumstance. By applying the discrete renewal reward processes, we describe the stochastic behavior of a telecommunication billing application with a degradation mode, and determine the optimal periodic software rejuvenation schedule minimizing the expected cost. Similar to the earlier work by the same authors, we develop a statistically non-parametric algorithm to estimate the optimal software rejuvenation schedule, by applying the discrete total time on test concept. Numerical examples are presented to estimate the optimal software rejuvenation schedules from the simulation data. We discuss the asymptotic behavior of estimators developed in this paper.

This paper considers a probabilistic model for a database recovery action with checkpoint generations when system failures occur according to a renewal process whose renewal density depends on the cumulative operation period since the last checkpoint. Necessary and sufficient conditions on the existence of the optimal checkpoint interval which maximizes the ergodic availability are analytically derived, and solvable examples are given for the well-known failure time distributions. Further, several methods to be needed for numerical calculations are proposed when the information on system failures is not sufficient. We use four analytical/tractable approximation methods to calculate the optimal checkpoint schedule. Finally, it is shown through numerical comparisons that the gamma approximation method is the best to seek the approximate solution precisely.

Survivability is the capability of a system to provide its services in a timely manner even after intrusion and compromise occur. In this paper, we focus on the quantitative analysis of survivability of virtual machine (VM) based intrusion tolerant system in the presence of Byzantine failures due to malicious attacks. Intrusion tolerant system has the ability of a system to continuously provide correct services even if the system is intruded. This paper introduces a scheme of the intrusion tolerant system with virtualization, and derives the success probability for one request by a Markov chain under the environment where VMs have been intruded due to a security hole by malicious attacks. Finally, in numerical experiments, we evaluate the performance of VM-based intrusion tolerant system from the viewpoint of survivability.

This paper presents the opportunity-based software rejuvenation policy and the optimization problem of software rejuvenation trigger time maximizing the system performance index. Our model is based on a basic semi-Markov software rejuvenation model by Dohi et al. 2000 under the environment where possible time, called opportunity, to execute software rejuvenation is limited. In the paper, we consider two stochastic point processes; renewal process and Markovian arrival process to represent the opportunity process. In particular, we derive the existence condition of the optimal trigger time under the two point processes analytically. In numerical examples, we illustrate the optimal design of the rejuvenation trigger schedule based on empirical data.

In the present paper, we propose a novel cyber-attack detection model based on two multivariate-analysis methods to the audit data observed on a host machine. The statistical techniques used here are the well-known Hayashi's quantification method IV and cluster analysis method. We quantify the observed qualitative audit event sequence via the quantification method IV, and collect similar audit event sequence in the same groups based on the cluster analysis. It is shown in simulation experiments that our model can improve the cyber-attack detection accuracy in some realistic cases where both normal and attack activities are intermingled.