Search

In this paper, we propose a new non-homogeneous Poisson process (NHPP) based software reliability model (SRM), where the software debug rate is given by a local polynomial function. The main feature of this semi-parametric SRM is to control the goodness-of-fit by changing the polynomial degree. Numerical examples with 16 actual software development project data are devoted to comparing our SRM with the well-known existing NHPP-based SRMs in terms of goodness-of-fit and predictive performances.

In this chapter, we introduce a stochastic framework to evaluate the system availability of an intrusion tolerant system (ITS), where the system undergoes patch management with a periodic vulnerability checking strategy, i.e., pull-type patch management. In particular, a composite stochastic reward net (SRN) is developed to capture the overall system behaviors, including vulnerability discovery, intrusion tolerance, and reactive maintenance operations. Furthermore, two kinds of availability criteria, the interval availability and the steady-state availability of the system, are formulated by applying the phase-type (PH) approximation to solve the Markov regenerative process (MRGP) model derived from the composite SRN. Numerical experiments are conducted to investigate the effects of the vulnerability checking interval on the system availability.

Intrusion tolerance is an ability to keep the correct service by masking the intrusion based on fault-tolerant techniques. With the rapid development of virtualization, the virtual machine (VM)-based intrusion tolerance scheme has been developed according to the concept of state machine replication with Byzantine fault tolerant technique. In this article, we present the quantitative security evaluation of the VM-based intrusion tolerant system with the time to security failure. We assume that the arrival stream follows a Markovian arrival process (MAP), which is one of the most general stochastic processes, and analytically derive the Laplace–Stieltjes transform of time to security failure based on the analysis of the $\text{MAP}/G/1/\infty$ queue.

We compare the extraction and separation performance of a newly developed fluorous extractant, tris(4,4,5,5,6,6,7,7,7-nonafluoroheptyl) phosphate (TFP) in a fluorinated diluent perfluorohexane, for trivalent lanthanide ions (LnIII) with a conventional organic extractant, tri-n-butyl phosphate (TBP) in n-octane. Interestingly, the fluorinated extractant TFP exhibits a superior extraction performance for LnIII than the organic extractant TBP, despite the tendency of hydrocarbon fluorination to reduce the extraction performance. Furthermore, the high separation factors among LnIII by TFP suggest that the separation performance of TFP is superior to that of TBP. We proved the superior extraction and separation performance of TFP by comparing the coordination environment of the extracted TFP and TBP complexes, the fluorous phase, and the organic phase. From a microscopic perspective, luminescence lifetime measurements and extended X-ray absorption fine structure spectroscopy revealed the near coordination environment of EuIII in the extracted complex of the extracting phase. Hydrating water scarcely exists in the EuIII-TFP complex, while the EuIII-TBP complex has at least one hydrating water molecule. On the other hand, from a macroscopic perspective, water and nitrate anion transport into the extracting phase during EuIII extraction are revealing. The large amounts of water and NO3− anions in the organic phase compared to those in the fluorous phase suggest that the extraction of water and NO3− anions somehow impairs the extraction of EuIII into the organic phase. Hence, TFP in a fluorinated diluent can be used as an alternative extraction and separation system for LnIII.

In this paper, we consider a two-unit parallel redundant system with deterioration on a lattice, where each unit has multi-stage deterioration levels, say, n levels. The transition from one deterioration level to the subsequent level occurs following the well-known Marshall-Olkin bivariate exponential distribution. We derive the closed form of the Laplace transform of the time to system failure in the two-unit parallel redundant system with deterioration on n×n lattice without repair and simultaneous failure, as well as the simple system on 3×3 lattice.

This review summarizes recent progress in solvent extraction of rare earth elements (REEs) using an ionic liquid (IL) as the extraction solvent. These IL extraction systems are advantageous owing to the affinity of ILs for both charged and neutral hydrophobic species, in contrast to conventional organic solvent extraction systems. Herein, REE extraction studies using ILs are detailed and classified based on the type of extraction system, namely extraction using anionic ligands, extraction using neutral ligands, synergistic extraction, extraction without extractants, and a specific system using task-specific ionic liquids (TSILs). In IL extraction systems, the extracted complexes are often different from those in organic solvent systems, and the REE extraction and separation efficiencies are often significantly enhanced. Synergistic IL extraction is an effective approach to improving the extractability and separability of REEs. The development of novel TSILs suitable for IL extraction systems is also effective for REE separation.

PurposeIn this paper, the authors propose two construction methods to estimate confidence intervals of the time-based optimal software rejuvenation policy and its associated maximum system availability via a parametric bootstrap method. Through simulation experiments the authors investigate their asymptotic behaviors and statistical properties.Design/methodology/approachThe present paper is the first challenge to derive the confidence intervals of the optimal software rejuvenation schedule, which maximizes the system availability in the sense of long run. In other words, the authors concern the statistical software fault management by employing an idea of process control in quality engineering and a parametric bootstrap.FindingsAs a remarkably different point from the existing work, the authors carefully take account of a special case where the two-sided confidence interval of the optimal software rejuvenation time does not exist due to that fact that the estimator distribution of the optimal software rejuvenation time is defective. Here the authors propose two useful construction methods of the two-sided confidence interval: conditional confidence interval and heuristic confidence interval.Research limitations/implicationsAlthough the authors applied a simulation-based bootstrap confidence method in this paper, another re-sampling-based approach can be also applied to the same problem. In addition, the authors just focused on a parametric bootstrap, but a non-parametric bootstrap method can be also applied to the confidence interval estimation of the optimal software rejuvenation time interval, when the complete knowledge on the distribution form is not available.Practical implicationsThe statistical software fault management techniques proposed in this paper are useful to control the system availability of operational software systems, by means of the control chart.Social implicationsThrough the online monitoring in operational software systems, it would be possible to estimate the optimal software rejuvenation time and its associated system availability, without applying any approximation. By implementing this function on application programming interface (API), it is possible to realize the low-cost fault-tolerance for software systems with aging.Originality/valueIn the past literature, almost all authors employed parametric and non-parametric inference techniques to estimate the optimal software rejuvenation time but just focused on the point estimation. This may often lead to the miss-judgment based on over-estimation or under-estimation under uncertainty. The authors overcome the problem by introducing the two-sided confidence interval approach.

This paper focuses on the so-called proportional intensity-based software reliability models (PI-SRMs), which are extensions of the common non-homogeneous Poisson process (NHPP)-based SRMs, and describe the probabilistic behavior of software fault-detection process by incorporating the time-dependent software metrics data observed in the development process. The PI-SRM is proposed by Rinsaka et al. in the paper “PISRAT: Proportional Intensity-Based Software Reliability Assessment Tool” in 2006. Specifically, we generalize this seminal model by introducing eleven well-known fault-detection time distributions, and investigate their goodness-of-fit and predictive performances. In numerical illustrations with four data sets collected in real software development projects, we utilize the maximum likelihood estimation to estimate model parameters with three time-dependent covariates (test execution time, failure identification work, and computer time-failure identification), and examine the performances of our PI-SRMs in comparison with the existing NHPP-based SRMs without covariates. It is shown that our PI-STMs could give better goodness-of-fit and predictive performances in many cases.

In software reliability engineering, software-rejuvenation and -checkpointing techniques are widely used for enhancing system reliability and strengthening data protection. In this paper, a stochastic framework composed of a composite stochastic Petri reward net and its resulting non-Markovian availability model is presented to capture the dynamic behavior of an operational software system in which time-based software rejuvenation and checkpointing are both aperiodically conducted. In particular, apart from the software-aging problem that may cause the system to fail, human-error factors (i.e., a system operator’s misoperations) during checkpointing are also considered. To solve the stationary solution of the non-Markovian availability model, which is derived on the basis of the reachability graph of stochastic Petri reward nets and is actually not one of the trivial stochastic models such as the semi-Markov process and the Markov regenerative process, the phase-expansion approach is considered. In numerical experiments, we illustrate steady-state system availability and find optimal software-rejuvenation policies that maximize steady-state system availability. The effects of human-error factors on both steady-state system availability and the optimal software-rejuvenation trigger timing are also evaluated. Numerical results showed that human errors during checkpointing both decreased system availability and brought a significant effect on the optimal rejuvenation-trigger timing, so that it should not be overlooked during system modeling.

Software reliability models (SRMs) are widely used for quantitative evaluation of software reliability by estimating model parameters from failure data observed in the testing phase. In particular, non-homogeneous Poisson process (NHPP)-based SRMs are the most popular because of their mathematical tractability. In this paper, we focus on the parameter estimation algorithm for NHPP-based SRMs and discuss the EM algorithm for generalized fault count data. The presented algorithm can be applied for failure time data, failure count data, and their mixture. The paper derives the EM-step formulas for basic 12 NHPP-based SRMs and demonstrate a numerical experiment to present the convergence property of our algorithms. The developed algorithms are suitable for an automatic tool for software reliability evaluation.

Utilization data are defined as the time series data consisting of time fractions of busy periods in fixed time intervals and are practically used to represent server conditions, such as CPU utilization. In general, it is more challenging to estimate the model parameters from the utilization data since we do not know the exact job arrival time and the service time from the utilization data. In this paper, we consider an approach to estimate the model parameters from the utilization data by assuming a few model assumptions. In particular, we suppose an Mt/M/1/K queueing system whose job arrival follows a Non-homogeneous Poisson Process (NHPP) and propose a parameter estimation method for the NHPP approximately from the utilization data based on the maximum likelihood estimation (MLE) via the expectation maximization (EM) algorithm. In numerical experiments, we generate the simulated utilization data of an Mt/M/1/K queueing system and investigate the effectiveness of our method. Also, we use the real CPU utilization data to exhibit the performance evaluation.

Component importance analysis is to measure the effect on system reliability of component reliabilities, and is used to the system design from the reliability point of view. On the other hand, to guarantee high reliability of real-time computing systems, redundancy has been widely applied, which plays an important role in enhancing system reliability. One of commonly used type of redundancy is the standby redundancy. However, redundancy increases not only the complexity of a system but also the complexity of associated problems such as common-mode error. In this paper, we consider the component importance analysis of a real-time computing system with warm standby redundancy in the presence of Common-Cause Failures (CCFs). 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. In numerical experiments, we evaluate the effect of CCFs by the comparison of system performance measure and component importance in the case of system without CCF with those in the case of system with CCFs. Also, we compare the effect of CCFs on the system in warm and hot standby configurations.

Mobile cloud computing (MCC) is a state-of-the-art architecture that integrates the cloud computing into the mobile environment and overcomes obstacles, such as processing capability, battery life, storage, and availability. Also the MCC is expected to be a key technology for cyber physical systems by connecting to vehicular systems, medical systems, and other mission-critical systems. Therefore, it is a critical issue for MCC to guarantee the high reliability. In this paper, we consider the component importance analysis of an MCC with common-cause failures (CCFs) by using a Markov reward model-based componentwise sensitivity approach. The component importance analysis is capable of quantifying the criticality of components and helps us to design the highly reliable system. In particular, this paper examines the effect of CCFs on the MCC. Our experimental results show that the preferred action to improve the availability of system with CCFs efficiently is to decrease the failure rate of the cloud node in the cloud infrastructure.

Software rejuvenation is one of the proactive fault management techniques to prevent system performance degradation, which may lead to the system failure caused by software aging. In the design of software rejuvenation, it is important to determine the optimal timing of triggering the rejuvenation in terms of the system overhead. In this paper, we consider six software rejuvenation policies, which are categorized into time-based and workload-based policies, under the environment where the arrival stream of system follows a Markovian arrival process (MAP). After building the stochastic models with respective rejuvenation policies, we formulate the loss probability of transaction and the upper bound of mean response time as the system performance indices. In the numerical illustrations, we exhibit a comprehensive study to compare six software rejuvenation policies numerically and show that the proposed rejuvenation policies called wait-time policies are superior to the others under the MAP arrival stream.

We performed a safety evaluation using the procedure devised by the Joint FAO/WHO Expert Committee on Food Additives (JECFA) of the following four flavouring substances that belong to the class of ‘aliphatic primary alcohols, aldehydes, carboxylic acids, acetals, and esters containing additional oxygenated functional groups’ and are uniquely used in Japan: butyl butyrylacetate, ethyl 2-hydroxy-4-methylpentanoate, 3-hydroxyhexanoic acid and methyl hydroxyacetate. Although no genotoxicity study data were found in the published literature, none of the four substances had chemical structural alerts predicting genotoxicity. All four substances were categorised as class I by using Cramer’s classification. The estimated daily intake of each of the four substances was determined to be 0.007–2.9 μg/person/day by using the maximised survey-derived intake method and based on the annual production data in Japan in 2001, 2005 and 2010, and was determined to be 0.250–600.0 μg/person/day by using the single-portion exposure technique and based on average-use levels in standard portion sizes of flavoured foods. Both of these estimated daily intake ranges were below the threshold of toxicological concern for class I substances, which is 1800 μg/person/day. Although no information from in vitro and in vivo toxicity studies for the four substances was available, these substances were judged to raise no safety concerns at the current levels of intake.

The role of bis(trifluoromethanesulfonyl)imide (Tf2N−) anions in the ionic liquid–water distribution systems of Eu(III) chelates with 2-thenoyltrifluoroacetone (Htta) was investigated by liquid–liquid distribution and time-resolved laser-induced fluorescence spectroscopy (TRLFS). The extraction constants of neutral Eu(tta)3 and anionic Eu(tta)4− chelates in 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([Cnmim][Tf2N]) were determined by analyzing the distribution equilibrium. The effect of the ionic liquids on the distribution constant of the neutral Eu(tta)3 chelate was evaluated by the regular solution theory. The distribution constant of Eu(tta)3 in [Cnmim][Tf2N] was increased dramatically by the solvation effects of Eu(tta)3 in [Cnmim][Tf2N]. TRLFS for [Eu(tta)3(H2O)3] synthesized revealed that the Eu(tta)3 chelate was almost completely dehydrated in a series of [Cnmim][Tf2N] (n = 2–10). The Eu(tta)3 chelate exists as di- or tri-hydrates in 1-ethyl-3-methylimidazolium perchlorate ([C2mim][ClO4]) containing 20 mol dm−3 water, whereas mono-hydrated chelate was formed in [C2mim][Tf2N, ClO4] in the presence of 0.50 mol dm−3 Tf2N− and 20 mol dm−3 water. These results show that the coordinated water molecules of [Eu(tta)3(H2O)3] were replaced by the Tf2N− anions. In fact, an anionic adduct, [Eu(tta)3(Tf2N)]−, was observed by electrospray ionization mass spectrometry in the presence of [C4mim][Tf2N].

This article presents parameter estimation of phase-type (PH) distribution. PH distribution is widely used in model-based performance evaluation such as reliability and queueing system, and is defied by an absorbing continuous-time Markov chain (CTMC). Since non-Markovian model can be approximated by a CTMC by replacing general distributions with PH distributions, the parameter estimation is a challenging issue in stochastic modeling. We focus on the statistical inference algorithms to estimate not only the parameters of PH distribution with grouped, truncated and missing data but also the probability density function, and give two examples of PH fitting in reliability engineering.

In this paper, we extend the existing opportunity-based age replacement policies by taking account of dependency between the failure time and the arrival time of a replacement opportunity for one-unit system. Based on the bivariate probability distribution function of the failure time and the arrival time of the opportunity, we focus on two opportunity-based age replacement problems and characterize the cost-optimal age replacement policies which minimize the relevant expected costs, with the hazard gradient, which is a vector-valued bivariate hazard rate. Through numerical examples with the Farlie–Gumbel–Morgenstern bivariate copula and the Gaussian bivariate copula having the general marginal distributions, we investigate the dependence of correlation between the failure time and the opportunistic replacement time on the age replacement policies.

The distribution constants of 4-benzoyl-3-phenyl-5-isoxazolone (HPBI) and deprotonated one (PBI-) between hydrophobic ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C1C4im][Tf2N]) and aqueous phases were determined, together with the acid-dissociation constant of HPBI. The solvent extraction of three selected lanthanoid ions (La3+, Eu3+, and Lu3+) with HPBI from aqueous nitrate phase into [C1C4im][Tf2N] has been investigated. Application of the ionic liquid as the extracting phase greatly enhanced the extraction performance of HPBI for lanthanoid ions compared with that in the chloroform system. A slope analysis was conducted in order to compare the results of the solution 4f-ion coordination chemistry in ionic and molecular media. The composition of the extracted species was established to be anionic tetrakis entities, Ln(PBI)4-, for light, middle, and heavy lanthanoid ions in an ionic environment (Ln denotes lanthanoid ion). Nevertheless, the typical neutral chelate lanthanoid complexes of the type Ln(PBI)3 have been detected when the conventional molecular diluent chloroform was applied as an organic phase.

In the management of software testing, testing-recourse allocation is one of the most important problems due to the tradeoff between development cost and reliability of released software. This paper presents the model-based approach to design the testing-resource allocation. In particular, we employ the architecture-based software reliability model with operational profile to estimate the quantitative software reliability in operation phase and formulate the multiobjective optimization problems with respect to cost, testing effort, and software reliability. In numerical experiment, we investigate the difference of the presented optimization problem from the existing testing-resource allocation model.

Using the procedure devised by the Joint FAO/WHO Expert Committee on Food Additives (JECFA), we performed safety evaluations on five acetal flavouring substances uniquely used in Japan: acetaldehyde 2,3-butanediol acetal, acetoin dimethyl acetal, hexanal dibutyl acetal, hexanal glyceryl acetal and 4-methyl-2-pentanone propyleneglycol acetal. As no genotoxicity study data were available in the literature, all five substances had no chemical structural alerts predicting genotoxicity. Using Cramer’s classification, acetoin dimethyl acetal and hexanal dibutyl acetal were categorised as class I, and acetaldehyde 2,3-butanediol acetal, hexanal glyceryl acetal and 4-methyl-2-pentanone propyleneglycol acetal as class III. The estimated daily intakes for all five substances were within the range of 1.45–6.53 µg/person/day using the method of maximised survey-derived intake based on the annual production data in Japan from 2001, 2005, 2008 and 2010, and 156–720 µg/person/day using the single-portion exposure technique (SPET), based on the average use levels in standard portion sizes of flavoured foods. The daily intakes of the two class I substances were below the threshold of toxicological concern (TTC) – 1800 μg/person/day. The daily intakes of the three class III substances exceeded the TTC (90 μg/person/day). Two of these, acetaldehyde 2,3-butanediol acetal and hexanal glyceryl acetal, were expected to be metabolised into endogenous products after ingestion. For 4-methyl-2-pentanone propyleneglycol acetal, one of its metabolites was not expected to be metabolised into endogenous products. However, its daily intake level, based on the estimated intake calculated by the SPET method, was about 1/15 000th of the no observed effect level. It was thus concluded that all five substances raised no safety concerns when used for flavouring foods at the currently estimated intake levels. While no information on in vitro and in vivo toxicity for all five substances was available, their metabolites were judged as raising no safety concerns at the current levels of intake.

This paper introduces a phase-type software reliability model (PH-SRM) and develops parameter estimation algorithms with grouped data. The PH-SRM is one of the most flexible models, which contains the existing non-homogeneous Poisson process (NHPP) models, and can approximate any type of NHPP-based models with high accuracy. Hence PH-SRM is promising to reduce the effort to select the best models in software reliability assessment. However, PH-SRM may involve many parameters compared to typical NHPP models. Thus the efficient parameter estimation algorithm is required. This paper enhances the parameter estimation algorithms for PH-SRM, so that they can handle grouped data. The grouped data is commonly applied to collect the data such as the number of bugs per day in practice. Thus the presented algorithms are helpful for the reliability assessment in practical software development project. Concretely, we consider the EM (expectation–maximization) algorithm for PH-SRM with both fault-detection time and grouped data. Finally, we examine performance of PH-SRM from the viewpoints of fitting ability.

This paper presents component importance analysis for virtualized system with live migration. The component importance analysis is significant to determine the system design of virtualized system from availability and cost points of view. This paper discusses the importance of components with respect to system availability. Specifically, we introduce two different component importance analyses for hybrid model (fault trees and continuous-time Markov chains) and continuous-time Markov chains, and show the analysis for existing probabilistic models for virtualized system. In numerical examples, we illustrate the quantitative component importance analysis for virtualized system with live migration.

Dynamic power management (DPM) plays a significant role to save power consumption effectively in both the design and operational phases of computer-based systems. It is well known that the state-dependent control policy by monitoring energy states in each component or the whole system is efficient for power saving in server systems whose system state, such as transaction request, 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 the Markov decision process. We derive the dynamic programming equation for the optimal control policy, which maximizes the expected reward per unit electrical power, which is called the power effectiveness, and give the policy iteration algorithm to determine the optimal control policy sequentially. In numerical experiments, we show the optimal control policy for an example of a cluster system with two service nodes, where the arrival stream of the transaction request is described as a Markov modulated Poisson process. In addition, based on the access data of an enterprise system, the optimal power-aware control for the cluster system and its effectiveness is examined.

The ultrasonic wave velocities in wood impregnated with a fire-retardant chemical were measured via a non-contact method. An air-coupled ultrasonic wave was made to propagate along the radial direction of the wood. The wave velocities in the wood samples after chemical impregnation were larger than those before impregnation. With increased chemical concentration, the relative changes in the velocities increased to a maximum of 16.3%, and these velocity changes exhibited a strong correlation with the chemical retention. These findings suggest that it is possible to evaluate the uniformity distributions of chemicals in fire-retardant-treated wood via a non-contact and nondestructive method based on air-coupled ultrasonics.

We report on the acid dissociation constants (Ka) of diglycolamic acid-type ligands together with comprehensive data on the extraction performance of N,N-dioctyldiglycolamic acid (DODGAA) for 54 metal ions. The pKa of the diglycolamic acid framework was determined to be 3.54 ± 0.03 in water (0.1 M LiCl, 25°C) by potentiometric titration, indicating that DODGAA is strongly acidic compared with acetic acid. DODGAA can quantitatively transfer various metal ions among the 54 metal ions through a proton-exchange reaction, and provides excellent extraction performance and separation ability for rare-earth metal ions, In(III), Fe(III), Hg(II), and Pb(II) among the 54 metal ions.

Database systems are widely used in many fields. As the scale of database systems increases, more firms decide to deploy the database system in a distributed environment for the sake of data integrity fault tolerance. For guaranteeing the consistency of data, database management systems adopt isolation policies. This paper discusses probabilistic models for snapshot isolation of database management system. Snapshot isolation is an effective method to enhance the consistency of database system, although it degrades the system performance where the system has large network latency such as distributed database system. Also, under the failure-prone environment, a restart scheme is considered as one countermeasure. This paper proposes probabilistic models for the dynamics of snapshot isolation of database system and exhibits the optimization of system performance with respect to updating interval of snapshot isolation within the failure-prone environment from the analytical point of view. Numerical experiments are conducted to validate the effectiveness of analytical results by using real traffic data.

Liquid-liquid extraction of lanthanide ions (Ln(3+)) using N,N-dioctyldiglycolamic acid (DODGAA) was comprehensively investigated, together with fluorescence spectroscopic characterization of the resulting extracted complexes in the organic phase. DODGAA enables the quantitative partitioning of all Ln(3+) ions from moderately acidic solutions, while showing selectivity for heavier lanthanides, and provides remarkably high extraction separation performance for Ln(3+) compared with typical carboxylic acid extractants. Furthermore, the mutual separation abilities of DODGAA for light lanthanides are higher than those of organophosphorus extractants. Slope analysis, loading tests, and electrospray ionization mass spectrometry measurements demonstrated that the transfer of Ln(3+) with DODGAA proceeded through a proton-exchange reaction, forming a 1:3 complex, Ln(DODGAA)3. The stripping of Ln(3+) from the extracting phase was successfully achieved under acidic conditions. Time-resolved laser-induced fluorescence spectroscopy revealed that the extracted Eu(3+) ions were completely dehydrated by complexation with DODGAA.

Using the procedure devised by the Joint FAO/WHO Expert Committee on Food Additives (JECFA), we performed safety evaluations on four flavoring substances structurally related to menthol (L-menthyl 2-methylbutyrate, DL-menthyl octanoate, DL-menthyl palmitate, and DL-menthyl stearate) uniquely used in Japan. While no genotoxicity study data were available in the literature, all four substances had no chemical structural alerts predictive of genotoxicity. Moreover, they all four are esters consisting of menthol and simple carboxylic acids that were assumed to be immediately hydrolyzed after ingestion and metabolized into innocuous substances for excretion. As menthol and carboxylic acids have no known genotoxicity, it was judged that the JECFA procedure could be applied to these four substances. According to Cramer's classification, these substances were categorized as class I based on their chemical structures. The estimated daily intakes for all four substances were within the range of 1.54-4.71 μg/person/day and 60-1250 μg/person/day, using the methods of Maximized Survey-Derived Intake and Single Portion Exposure Technique, respectively, based on the annual usage data of 2001, 2005, and 2010 in Japan. As the daily intakes of these substances were below the threshold of concern applied to class I substances viz., 1800 μg/person/day, it was concluded that all four substances raise no safety concerns when used for flavoring foods under the currently estimated intake levels.

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.