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This paper presents a Markov decision process (MDP) formulation for a transaction-based system with software aging and rejuvenation. In our formulation, the arrival process of transactions is described as a Markovian arrival process (MAP). In addition, we introduce a probabilistically degrading processing rate to model the software aging. Furthermore, the paper focuses on two performance criteria to determine the optimal rejuvenation strategy: the long-run average reward and the power efficiency. Under these performance criteria, we formulate the optimality equations of MDPs for the maximization of the long-run average reward and power efficiency. Numerical experiments show that the optimal rejuvenation policy has the monotone property, and can be characterized by a threshold policy with the number of transactions through the sensitivity and statistical analysis using real traffic and aging data.

This paper proposes a quantitative security evaluation for software system from the vulnerability data consisting of discovery date, solution date and exploit publish date based on a stochastic model. More precisely, our model considers a vulnerability life-cycle model and represents the vulnerability discovery process as a non-homogeneous Poisson process. In a numerical example, we show the quantitative measures for contents management system of an open source project.

In this article we summarize some aperiodic checkpoint placement algorithms for a software system over infinite and finite operation time horizons, and compare them in terms of computational accuracy. The underlying problem is formulated as the maximization of steady-state system availability and is to determine the optimal aperiodic checkpoint sequence. We present two exact computation algorithms in both forward and backward manners and two approximate ones; constant hazard approximation and fluid approximation, toward this end. In numerical examples with Weibull system failure time distribution, it is shown that the combined algorithm with the fluid approximation can calculate effectively the exact solutions on the optimal aperiodic checkpoint sequence.

In this paper, we propose a probabilistic approach to finding failure-causing inputs based on Bayesian estimation. According to our probabilistic insights of software testing, the test case generation algorithms are developed by Markov chain Monte Carlo (MCMC) methods. Dissimilar to existing random testing schemes such as adaptive random testing, our approach can also utilize the prior knowledge on software testing. In experiments, we compare effectiveness of our MCMC-based random testing with both ordinary random testing and adaptive random testing in real program sources. These results indicate the possibility that MCMC-based random testing can drastically improve the effectiveness of software testing.

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. key words: software aging, software rejuvenation, time-triggered policy, opportunity-based policy, renewal process, Markovian arrival process, optimization

Computer security has become an increasingly important hot topic in computer and communication industry, since it is important to support critical business process and to protect personal and sensitive information. Computer security is to keep security attributes (confidentiality, integrity and availability) of computer systems, which face the threats such as deny-of-service (DoS), virus and intrusion. To ensure high computer security, the intrusion tolerance technique based on fault-tolerant scheme has been widely applied. This paper presents the quantitative performance evaluation of a virtual machine (VM) based intrusion tolerant system. Concretely, two security measures are derived; MTTSF (mean time to security failure) and the effective traffic intensity. The mathematical analysis is achieved by using Laplace-Stieltjes transforms according to the analysis of M/G/1 queueing system.

This paper deals with the transient analysis of software rejuvenation model. Concretely, we apply the phase expansion to the basic software rejuvenation model by Garg et al. (1995). The phase expansion is the approximation technique which utilizes the phase-type approximation. After applying the phase expansion, we formulate the interval reliability. In a numerical example, we investigate the accuracy of the approximation for the interval reliability.

Computer systems face the threat of deliberate security intrusions due to malicious attacks that exploit security holes or vulnerabilities. In practice, these security holes or vulnerabilities still remain in the system and applications even if developers carefully execute system testing. Thus it is necessary and important to develop the mechanism to prevent and/or tolerate security intrusions. As a result, the computer systems are often evaluated with confidentiality, integrity and availability (CIA) criteria from the viewpoint of security, and security is treated as a QoS (Quality of Service) attribute at par with other QoS attributes such as capacity and performance. In this paper, we present the method for quantifying a security attribute called mean time to security failure (MTTSF) of a VM-based intrusion tolerant system based on queueing theory.

This chapter provides a comprehensive survey of PH (phase-type) distribution and MAP (Markovian arrival process) fitting. The PH distribution and MAP are widely used in analytical model-based performance evaluation because they can approximate non-Markovian models with arbitrary accuracy as Markovian models. Among a number of past research results on PH/MAP fitting, we present the mathematical definition of the PH distribution and MAP, and summarize the most recent state-of-the-art results on the fitting methods. We also offer an overview of the software tools for PH/MAP fitting.

Most exposure levels of flavor in food are considered to be extremely low. If at all, genotoxic properties should be taken into account in safety evaluations. We have recently established a (quantitative) structure–activity relationship, (Q)SAR, combination system, which is composed of three individual models of mutagenicity prediction for industrial chemicals. A decision on mutagenicity is defined as the combination of predictive results from the three models. To validate the utility of our (Q)SAR system for flavor evaluation, we assessed 367 flavor chemicals that had been evaluated mainly by JECFA and for which Ames test results were available. When two or more models gave a positive evaluation, the sensitivity was low (19.4%). In contrast, when one or more models gave a positive evaluation, the sensitivity increased to 47.2%. The contribution of this increased sensitivity was mainly due to the result of the prediction by Derek for Windows, which is a knowledge-based model. Structural analysis of false negatives indicated some common sub-structures. The approach of improving sub-structural alerts could effectively contribute to increasing the predictability of the mutagenicity of flavors, because many flavors possess categorically similar functional sub-structures or are composed of a series of derivatives.

This paper proposes an improved expectation–maximization (EM) algorithm for phase-type (PH) distributions with grouped and truncated data. Olsson (1996) derived an EM algorithm for PH distributions under censored data, and the similar technique can be utilized to the PH fitting even under grouped and truncated data. However, it should be noted that Olsson's algorithm has a drawback in terms of computation speed. Because the time complexity of the algorithm is a cube of number of phases, it does not work well in the case where the number of phases is large. This paper proposes an improvement of the EM algorithm under grouped and truncated observations. By applying a uniformization-based technique for continuous-time Markov chains, it is shown that the time complexity of our algorithm can be reduced to the square of number of phases. In particular, when we consider the PH fitting using a canonical form of PH distributions, the time complexity is linear in the number of phases. Copyright © 2012 John Wiley & Sons, Ltd.

The extraction constant and the two-phase stability constant ( K D,M β 3 ) of tris(2-thenoyltrifluoroacetonato)europium(III) between 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C 4 mim][Tf 2 N]) as an ionic liquid and an aqueous phase were determined by considering the extraction equilibria including anionic tetrakis(2-thenoyltrifluoroacetonato)europate(III). Specific solute–solvent interactions between the neutral Eu(III) chelate and [C 4 mim][Tf 2 N] molecules were revealed from the relationships between the distribution constant of the enol form of 2-thenoyltrifluoroacetone (Htta) as a proton chelate and the distribution constant ( K D,M ) of the neutral Eu(III) chelate because the [C 4 mim][Tf 2 N] system gave the high K D,M β 3 value compared with those in conventional molecular solvents such as benzene and 1,2-dichloroethane. The coordination environment of Eu 3+ in the neutral Eu(III) chelate in [C 4 mim][Tf 2 N] was investigated by time-resolved laser-induced fluorescence spectroscopy and infrared absorption spectroscopy. Both methods consistently indicated that not only the Eu(III) chelate extracted but also Eu(tta) 3 (H 2 O) 3 synthesized as a solid crystal were almost completely dehydrated in [C 4 mim][Tf 2 N] saturated with water. Consequently, the higher K D,M or extractability of the neutral Eu(III) chelate in the [C 4 mim][Tf 2 N] system can be ascribed to the dehydration of the Eu(III) chelate, which is caused by the specific solvation with [C 4 mim][Tf 2 N] molecules.

Of the main interest in practical software testing would be the prediction of the number of detected faults in future rather than the estimation of the quantitative reliability function, which is defined as the probability that the software does not fail during a pre-specified time interval after release. In other words, practitioners wish to know the number of remaining faults and the saturated level of the cumulative number of faults, in order to control the software testing process. In not only such a situation but also the case where the likelihood information of statistical models is not fully available, the least squares estimation (LSE) may be simple but very useful in estimating model parameters. Hence, the LSE methods should be comprehensively studied in the context of software reliability engineering. In this paper we examine four LSE methods with application to the software reliability prediction. In real data analyses based on several software fault data, we show that LSE methods are s...

SUMMARY 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 proposes an improved computation method of maximum likelihood (ML) estimation for phase-type (PH) distributions with a number of phases. We focus on the EM (expectation-maximization) algorithm proposed by Asmussen et al. [27] and refine it in terms of time complexity. Two ideas behind our method are a uniformization-based procedure for computing a convolution integral of the matrix exponential and an improvement of the forward–backward algorithm using time intervals. Compared with the differential-equation-based EM algorithm discussed in Asmussen et al. [27] , our approach succeeds in the reduction of computation time for the PH fitting with a moderate to large number of phases. In addition to the improvement of time complexity, this paper discusses how to estimate the canonical form by applying the EM algorithm. In numerical experiments, we examine computation times of the proposed and differential-equation-based EM algorithms. Furthermore, the proposed EM algorithm is also compared with the existing PH fitting methods in terms of computation time and fitting accuracy.

With the aim of clarifying roles of the 3NFs in nuclei experimental programs with the polarized deuteron beam at intermediate energies are in progress at RIKEN RI Beam Factory. As the first step, we have measured a complete set of deuteron analyzing powers in deuteron–proton elastic scattering at 250 and 294 MeV/nucleon. The obtained data are compared with the Faddeev calculations based on the modern nucleon–nucleon forces together with the Tucson–Melbourne’99, and UrbanaIX three nucleon forces.

Selective synergism for the extraction of lanthanoids(III) (Ln) with β-diketones such as 2-thenoyltrifluoroacetone, 2-naphthoyltrifluoroacetone, and benzoylacetone has been investigated in the presence of trioctylphosphine oxide as a hydrophobic neutral ligand in 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide as an ionic liquid. The extractability of heavier Ln was remarkably enhanced, resulting in a significant improvement in the separation of Ln. It was found that the present synergism is ascribed to the formation of cationic ternary complexes, followed by ion exchange into the ionic liquid.

Software safety can be defined as the probability that any software hazard does not occur during a pre-specified time period. This paper proposes a new software safety assessment model based on a subordinated Markov chain, which consists of both non-homogeneous Poisson process (NHPP) and discrete time Markov chain (DTMC). In the model, NHPP and DTMC indicate the cumulative number of software errors experienced in testing phase and their impact, respectively. Using the data set of three types of software errors (critical, major and minor errors) collected in an actual software development project, we examine the effectiveness of the proposed model by compared with two existing models. Through the experiment, it is shown that the proposed model is superior to the existing ones in terms of fitting ability.

This paper examines comprehensive evaluation of aperiodic time-based checkpointing and rejuvenation schemes maximizing the steady-state system availability in an operational software system. We consider two kinds of maintenance policies: checkpointing prior to rejuvenating (CPTR) and rejuvenating prior to checkpointing (RPTC). These schemes are complementary from each other to schedule checkpoints and rejuvenation points. In addition, under a periodic full maintenance operation, we show that aperiodic checkpointing or rejuvenation scheme is optimal to maximize the steady-state system availability by applying the dynamic programming. In numerical examples, CPTR and RPTC are comparatively examined with same overhead parameters, and the effects of CPTR and RPTC on maximizing the steady-state system availability are investigated.

This article proposes a fast algorithm for estimating parameters of a mixture of Erlang (MER) distribution from empirical samples. In particular, we develop a variational approach for approximately computing posterior distributions of parameters of MER distribution in the Bayesian context. Computation speed of the proposed method becomes up to 200 times faster than that of the Markov chain Monte Carlo (MCMC) method. The estimates of proposed method are almost same as those of MCMC method. Moreover, we discuss how to estimate shape parameters of Erlang distribution based on a certain goodness-of-fit criterion in the proposed variational Bayes method.

This paper addresses a parameter estimation problem of Markovian arrival process (MAP). In network traffic measurement experiments, one often encounters the group data where arrival times for a group are collected as one bin. Although the group data are observed in many situations, nearly all existing estimation methods for MAP are based on nongroup data. This paper proposes a numerical procedure for fitting a MAP and a Markov-modulated Poisson process (MMPP) to group data. The proposed algorithm is based on the expectation-maximization (EM) approach and is a natural but significant extension of the existing EM algorithms to estimate parameters of the MAP and MMPP. Specifically for the MMPP estimation, we provide an efficient approximation based on the proposed EM algorithm. We examine the performance of proposed algorithms via numerical experiments and present an example of traffic analysis with real traffic data.

Gompertz Curve has been used to estimate the number of residual faults in testing phases of software development, especially by Japanese software development companies. Since the Gompertz curve is a deterministic function, the curve cannot be applied to estimating software reliability which is the probability that software system does not fail in a prefixed time period. In this article, we propose a stochastic model called the Gompertz software reliability model based on non-homogeneous Poisson processes. The proposed model can be derived from the statistical theory of extreme-value, and has a similar asymptotic property to the deterministic Gompertz curve. Also, we develop an EM algorithm to determine the model parameters effectively. In numerical examples with software failure data observed in real software development projects, we evaluate performance of the Gompertz software reliability model in terms of reliability assessment and failure prediction.

The polymerization shrinkage values of commercial flowable and conventional composites were measured with a newly developed laser displacement sensor. Compressive strength and filler content were also measured. Compared to conventional composites, the flowable composites required a longer time - not exceeding 4 minutes - to reach a constant polymerization shrinkage rate. In terms of shrinkage ratio, it was less than 1.5% for conventional composites at 90 minutes, which was lower than that of flowable composites, i.e. more than 2.0%. The compressive strength of conventional composites was higher than that of flowable composites. A highly significant correlation between filler content and polymerization shrinkage at 90 minutes was observed, and polymerization shrinkage tended to decrease as filler content increased. In light of the results obtained in this study, the newly developed displacement meter with a laser displacement sensor proved to be effective for in-depth investigation of the polymerization shrinkage of dental composites.

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.

The 116Cd(p,n) experiment at 300 MeV has been performed for deducing the Gamow-Teller (GT) transition strengths B(GT−) in 116In. For the transition to the ground state, the B(GT−) value of 0.26 ± 0.02 is obtained. From this B(GT−) value and the B(GT+) value by a beta-decay experiment, the contribution of the intermediate ground state of 116In to the nuclear matrix element is deduced to be 0.070 ± 0.003. The B(GT−) value obtained herein is a factor of 8 less than that obtained from a previous (3He,t) measurement. This discrepancy, as well as differences in the distribution of low energy GT strength, and the width and peak energy of the GT giant resonance may be explained if the target used in the (3He,t) measurement is a Cd target with natural abundance.

Border effect in communication network area is one of the most important problems to quantify accurately the performance/dependability of wireless ad hoc networks (WAHNs), because the assumption on uniformity of network node density is often unrealistic to describe the actual communication area. This problem appears in modeling the node behavior of WAHNs and in quantification of their network survivability. In this paper we focus on the border effects, and reformulate the network survivability models based on a semi-Markov process, where two kinds of communication network areas are considered, square area and circular area. Based on some geometric ideas, we improve the quantitative network survivability measures for three stochastic models taking account of the border effects. In numerical examples, we compare our new models with the existing ones without border effects in both steady-state and transient network survivability analyses. We show through a simulation study that the border effects are significant factors in quantifying network survivability.

Component importance analysis is to measure the effect on system reliability of component reliabilities, and it can be used to the design of system from the reliability point of view. In this paper, we consider the component importance analysis of real-time computing systems in the presence of common-cause failures (CCFs) (i.e., failure dependencies). Although the CCFs are known as a risk factor of degradation of system reliability, it is difficult to evaluate the component importance measures in the presence of CCFs analytically. This paper introduces a continuous-time Markov chain (CTMC) model for real-time computing system, and applies the CTMC-based component-wise sensitivity analysis which can evaluate the component importance measures without any structure function of system. Also, in numerical experiments, we evaluate the effect of CCFs by the comparison of system performance measures and component importance in the case of system with CCFs with those in the case that there is no CCF in the system.

Dynamic power management (DPM) plays a significant role to save the power consumption effectively in both design and operational phases of computer-based systems. Especially, it is well known that the state-dependent control policy by monitoring the energy state in each component or the whole system is efficient for power saving in server systems whose system state such as the number of transaction requests can be completely observed. In this paper we consider an optimal power-aware design in a cluster system and formulate the DPM problem by means of a Markov decision process. We derive the dynamic programming equation for the optimal control policy which maximizes the expected reward per unit electrical power, called the power effectiveness, and give a policy iteration algorithm to determine the optimal control policy sequentially. In a numerical example, we consider a cluster system with two service nodes and describe the arrival stream of the transaction request process by a Markov modulated Poisson process. It is shown that the optimal control policy maximizing the power effectiveness is given in the form of decision table.

This paper considers the model-based software reliability evaluation using the information on software testing inputs. Concretely, we define the distance between two software test cases by means of their testing inputs, and estimate the probability that the domain for a test input has already been covered by already-executed test cases. Based on the probability, we formulate the fault-detection probability in the software reliability growth model. In numerical experiments, we compare the proposed model with an existing non-homogeneous Poisson process based model with the distance of 5,000 test inputs in a real software application, and discuss the effect of test information on the software reliability evaluation.

With the aim of clarifying roles of the 3NFs in nuclei experimental programs with the polarized deuteron beam at intermediate energies are in progress at RIKEN RI Beam Factory. As the first step, we have measured a complete set of deuteron analyzing powers in deuteron–proton elastic scattering at 250 and 294 MeV/nucleon. The obtained data are compared with the Faddeev calculations based on the modern nucleon–nucleon forces together with the Tucson–Melbourne’99, and UrbanaIX three nucleon forces.

In this paper, we present a tool for estimating parameters of phase-type distribution PH and Markovian arrival process MAP on the statistical analysis package R. PH and MAP are useful for the analysis of non-Markovian models approximately. By approximating general distributions and point processes with PH and MAP, the non-Markovian models is reduced to continuous-time Markov chains CTMCs that can be solved by analytical approaches. The significant features of our tool are i PH/MAP fitting from grouped data and ii PH fitting from probability density functions.

In this paper, we consider computation algorithms for checkpoint placement in real-time applications. Under the condition that the processing time is bounded by a time limit, we derive sequentially the optimal checkpoint time based on the dynamic programming. In numerical examples, we examine the dependence of optimal checkpoint sequence on both failure time and processing time distributions, and investigate the effectiveness of sequential checkpoint placement.

Recently, a complementary approach to handle transient software failures, called software rejuvenation, is becoming popular as a proactive fault management technique in operational software systems. In this study, we develop the optimal scheduling algorithms to trigger software rejuvenation in distributed computation circumstance. In particular, we focus on two different computation circumstances in terms of detection of failures. Based on the dynamic programming, we derive the optimal software rejuvenation schedule which minimizes the expected total time of computation. In numerical examples, we examine the sensitivity of model parameters characterizing the failure phenomenon to the resulting optimal rejuvenation schedule.

In this paper, we consider discrete software reliability models to assess the software reliability in discrete time circumstance, and develop a unified parameter estimation method based on the EM (Expectation-Maximization) principle. In numerical examples, the effectiveness of the EM algorithm to estimate the model parameters in the discrete software reliability models is investigated with real software error data. It is shown that the proposed method can provide accurate estimates of the model parameters effectively.

A complete set of polarization transfer observables has been measured for the 90 Zr( p , n ) reaction at T p = 295 MeV and θ lab = 0°. The measurement can yield the total spin transfer Σ(0°) which is independent of nuclear reaction mechanisms such as the effective nucleon–nucleon interaction or distortions. The deduced Σ(0°) values indicate the strong spin-flip characteristics of the continuum up to 50 MeV excitation. A predominance of unnatural-parity transitions in the continuum is also observed from polarization transfer observables.

Propylene carbonate (PC) is known as one of the cure accelerators for alkaline phenol–formaldehyde resins. To elucidate the cure-acceleration mechanisms, the effects of PC on the condensation reactions of monomeric hydroxymethylphenols (HMPs) were investigated and compared with those of PC hydrolysate, sodium bicarbonate (NaHCO3) and ethyl formate. Immediately after the reaction started, PC, decomposing itself simultaneously, accelerated the formation of the ortho-para methylene-bonded dimer of 2,4,6-trihydroxymethylphenol. This effect of PC was very similar to that of ethyl formate. To the contrary, PC hydrolysate accelerated the formation of the para-para methylene-bonded dimer throughout the course of the reaction. This effect of PC hydrolysate was identical to that of NaHCO3. These results indicate that PC increases the reactivity of the ortho-hydroxymethyl group, presumably through transesterification. On the other hand, NaHCO3 is formed by the hydrolysis of PC or decomposition of the transesterified HMPs and it increases the reactivity of the para-hydroxymethyl group.

This paper presents a probabilistic model for evaluating the reliability of software having modular structure. In particular, it proposes a new reliability-evaluating model based on the structure of software by integrating the Jelinski–Moranda model, which is the most basic black box model, and the Littlewood model, which is a representative white box model. The performance of the proposed model is compared and studied in reference to the benchmark model of Cheung and the dependency of the architecture and the reliability growth in software reliability evaluation is discussed. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(5): 43–53, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20075

Software safety can be defined as the probability that any software hazard does not occur during a pre-specified time period. This paper proposes a new software safety assessment model based on a subordinated Markov chain, which consists of both non-homogeneous Poisson process (NHPP) and discrete time Markov chain (DTMC). In the model, NHPP and DTMC indicate the cumulative number of software errors experienced in testing phase and their impact, respectively. Using the data set of three types of software errors (critical, major and minor errors) collected in an actual software development project, we examine the effectiveness of the proposed model by compared with two existing models. Through the experiment, it is shown that the proposed model is superior to the existing ones in terms of fitting ability.

This paper addresses the problem of how to determine optimal sleep timing when the computer user should turn the hard disk or the display off in order to save electric power after the computer has not been used. We propose a stochastic model to obtain an optimal sleep timing strategy which minimizes the expected power consumed per unit time in the steady state, where access requirements of the system occur in a renewal process and processing is described by a general service time. Phase type approximation is proposed to represent the expected power consumed per unit time. We investigate the performance of this approximation through a simulation study, and design an optimal auto-sleep schedule for a computer workstation system using real data.

This paper addresses a problem of energy reduction on computer systems, namely the problem of determining the optimal auto-sleep schedule on which the system is changed into a low-power state. For this problem, we provide a stochastic model for a computer system with autosleep function. In our modeling framework, user requests arrive at the system in accordance with a general renewal process and are served by generally distributed service times. To obtain the optimal auto-sleep schedule minimizing the expected power consumption per unit time in the steady state, the phase-type approximation is applied to the renewal arrival process. In numerical examples, we investigate accuracy of the phase-type approximation through a simulation study.

In this paper, a new estimation method is proposed for the model parameters of a software reliability model based on the EM (Expectation-Maximization) principle. The debugging of the software including finite faults can be described by a generalized order statistics model. The generalized order statistics model is expressed by a nonhomogeneous Poisson process (NHPP) and the maximum likelihood method can usually be used for estimation of model parameters. However, since in this method the simultaneous logarithmic likelihood equation is numerically solved, it is not always effective from the viewpoints of algorithm stability and computation effort. The EM algorithm proposed here is a simple iteration method, which consists of several updating equations. The algorithm can accurately and stably obtain the maximum likelihood estimates. In this paper, specific EM algorithms are also derived for the cases where the occurrence of a software failure follows the exponential distribution, second-order Erlang distribution, Rayleigh distribution, Pareto distribution, and log normal distribution. Further, by using real data, the EM algorithm is compared with the method based on the simultaneous logarithmic likelihood equation in terms of the stability of the solution. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(6): 29–37, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10058

Genetic algorithm (GA) is a probabilistic algorithm for solving optimization problems, which is modeled on a genetic evolution process in biology, and is focused as an effective algorithm to find the global optimal solutions for many types of problems. Most research results on GAs are related to the design for some specific GAs and the simulation-based study for their applicability. It has not been established yet how to evaluate the performance of specific GAs in a general framework. In this paper, we give two theoretical results on the performance evaluation of GAs by using the Markovian analysis. First, we discuss convergence properties of GAs, and derive an associated performance measure, called the relaxation time for the Markov chain. Secondly, we develop an alternative Markovian analysis with rewards for real-coded GAs having real-vector individuals.

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 reconsider the non-homogeneous Markovian models for a single-server type of software system with rejuvenation in Garg et al. (1998), and revisit them from the theoretical view point. More precisely, it is assumed in these models that software failures can occur with positive probability during idle periods in transaction systems, but we exclude this unreasonable situation in our refined models.

In the reflow soldering process, the IC package is heated over 270°C by the infrared rays. In a delamination interface, the stress field near a crack tip will always be in a mixed-mode state. It was assumed that the initial defects were generated among the corner part of die pad and epoxy molding compound. The 3-D finite element analysis was carried out to evaluate the strain energy release rate of delamination interface in IC packages subjected to non-steady thermal stress. The strain energy release rate of mixed mode was evaluated by the modified crack-closure integral and virtual crack extension method. The maximum difference of strain energy release rate between the modified crack-closure integral and virtual crack extension method was about 8%. Therefore, it is considered that the modified crack-closure integral is useful as a simple evaluation method of the strain energy release rate. The stress intensity factor K was examined from 3-D and 2-D virtual crack extension method. The virtual crack extension method can evaluate stress intensity factors of the interface crack under a mixed-mode loading accurately.

This paper discusses parallel algorithms for transient analysis of continuous-time Markov chains (CTMCs). In dependable computing, it is used for evaluating the rare events such as failure based on CTMC models. The uniformizaton is a well-known algorithm for obtaining the transient solution of CTMC. However, the computation cost of uniformization is not low in the case of large-sized and stiff CTMCs. This paper considers parallelization of the uniformization algorithm. Particularly, we propose a coarse-grained parallel uniformization which is appropriate for multicore processors. This method enables us to analyze the large-sized and stiff CTMCs efficiently. In numerical examples, we examine the effectiveness of the proposed parallel algorithms with multicore processors.