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.

This paper proposes a dynamic capture-recapture (DCR) model to estimate not only the total number of software faults but also quantitative software reliability from observed data. Compared to conventional static capture-recapture (SCR) model and usual software reliability models (SRMs) in the past literature, the DCR model can handle dynamic behavior of software fault-detection processes and can evaluate quantitative software reliability based on capture-recapture sampling of software fault data. This is regarded as a unified modeling framework of SCR and SRM with the Bayesian estimation. Simulation experiments under some plausible testing scenarios show that our models are superior to SCR and SRMs in terms of estimation accuracy.

This paper considers two simulation models for simple unreliable file systems with checkpointing and rollback recovery. In Model 1, the checkpoint is generated at a pre-specified time and the information on the main memory since the last checkpoint is back-uped in a secondary medium. On the other hand, in Model 2, the checkpointing is executed at the time when the number of transactions completed for processing is achieved at a pre-determined level. However, it is difficult to treat such models analytically without employing any approximation method, if queueing effects related with arrival and processing of transactions can not be ignored. We apply the generalized stochastic Petri net (GSPN) to represent the stochastic behaviour of systems under two checkpointing schemes. Throughout GSPN simulation, we evaluate quantitatively the maintainability of checkpoint models under consideration and examine the dependence of model parameters in the optimal checkpoint policies and their associated system availabilities.

In this paper, we present non-Markovian availability models for capturing the dynamics of system behavior of an operational software system that undergoes aperiodic time-based software rejuvenation and checkpointing. Two availability models with rejuvenation are considered taking account of the procedure after the completion of rollback recovery operation. We further proceed to investigate whether there exists the optimal rejuvenation schedule that maximizes the steady-state system availability, which is derived by means of the phase expansion technique, since the resulting models are not the trivial stochastic models such as semi-Markov process and Markov regenerative process, so that it is hard to solve them by using the common approaches like Laplace-Stieltjes transform and embedded Markov chain techniques. The numerical experiments are conducted to determine the optimal rejuvenation trigger timing maximizing the steady-state system availability for each availability model, and to compare both two models.

Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this paper, we consider both the periodic and non-periodic software rejuvenation policies under different dependability measures. As is well known, the steady-state system availability is the probability that the software system is operating in the steady state and, at the same time, is often regarded as the mean up rate in the system operation period. We show that the mean up rate should be defined as the mean value of up rate, but not as the mean up time per mean operation time. We derive numerically the optimal software rejuvenation policies which maximize the steady-state system availability and the mean up rate, respectively, for each periodic or non-periodic model. Numerical examples show that the real mean up rate is always smaller than the system availability in the steady state and that the availability overestimates the ratio of operative time of the software system.

Long running software systems are known to experience an aging phenomenon called software aging, one in which the accumulation of errors during the execution of software leads to performance degradation and eventually results in failure. To counteract this phenomenon a proactive fault management approach, called software rejuvenation, is particularly useful. It essentially involves gracefully terminating an application or a system and restarting it in a clean internal state. In this paper, we evaluate dependability performance of a communication network system with the software rejuvenation under the assumption that the requests arrive according to a Markov modulated Poisson process (MMPP). Three dependability measures, steady-state availability, loss probability of requests and mean response time on tasks, are derived through the hidden Markovian analysis based on the time-based software rejuvenation scheme. In numerical examples, we investigate the sensitivity of some model parameters to the dependability measures.

In recent years, considerable attention has been devoted to continuously running software systems whose performance characteristics are smoothly degrading in time. Software aging often affects the performance of a software system and eventually causes it to fail. A novel approach to handle transient software failures due to software aging is called software rejuvenation, which can be regarded as a preventive and proactive solution that is particularly useful for counteracting the aging phenomenon. In this paper, we focus on a high assurance software system with fault-tolerance and preventive rejuvenation, and analyze the stochastic behavior of such a highly critical software system. More precisely, we consider a fault-tolerant software system with two-version redundant structure and random rejuvenation schedule, and evaluate quantitatively some dependability measures like the steady-state system availability and MTTF based on the familiar Markovian analysis. In numerical examples, we examine the dependence of two fault tolerant techniques; design and environment diversity techniques, on the system dependability measures.

The software rejuvenation is one of the most effective preventive maintenance technique for operational software systems with high assurance requirement. In this paper, we propose the workload-based software rejuvenation scheme for a server type of software system, and develop stochastic models to determine the optimal software rejuvenation schedules for some dependability measures. In numerical examples, we evaluate quantitatively the performance of workload-based software rejuvenation scheme and compare it with the time-based rejuvenation scheme.

This paper considers how to evaluate the resiliency for virtualized system with software rejuvenation. The software rejuvenation is a proactive technique to prevent the failure caused by aging phenomenon such as resource exhaustion. In particular, according to Gohsh et al. (2010), we compute a quantitative criterion to evaluate resiliency of system by using continuous-time Markov chains (CTMC). In addition, in order to convert general state-based models to CTMCs, we employ PH (phase-type) expansion technique. In numerical examples, we investigate the resiliency of virtualized system with software rejuvenation under two different rejuvenation policies.

This article considers a hybrid data backup model for a file system, which combines both conventional magnetic disk (MD) and write-once, read-many optical disk (OD). Since OD recently is a lower cost medium as well as a longer life medium than the ordinary MD, this kind of backup configuration is just recognized to be important. We mathematically formulate the hybrid data backup model and obtain the closed-form average cost rate when the system failure time and the recovery time follow exponential distributions. Numerical calculations are carried out to obtain the optimal backup policy, which is composed of two kinds of backup sizes from the main memory to MD and from MD to OD and minimizes the average cost rate. In numerical examples, the dependence of the optimal backup policy on the failure and the recovery mechanism is examined.