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In the literature, infinite-failure software reliability models (SRMs), such as Musa-Okumoto SRM (1984), have been demonstrated to be effective in quantitatively characterizing software testing processes and assessing software reliability. This paper primarily focuses on the infinite-failure (type-II) non-homogeneous Poisson process (NHPP)-based SRMs and evaluates the performances of these SRMs comprehensively by comparing with the existing finite-failure (type-I) NHPP-based SRMs. In more specific terms, to describe the software fault-detection time distribution, we postulate 11 representative probability distribution functions that can be categorized into the generalized exponential distribution family and the extreme-value distribution family. Then, we compare the goodness-of-fit and predictive performances with the associated 11 type-I and type-II NHPP-based SRMs. In numerical experiments, we analyze software fault-count data, collected from 16 actual development projects, which are commonly known in the software industry as fault-count time-domain data and fault-count time-interval data (group data). The maximum likelihood method is utilized to estimate the model parameters in both NHPP-based SRMs. In a comparison of the type-I with the type-II, it is shown that the type-II NHPP-based SRMs could exhibit better predictive performance than the existing type-I NHPP-based SRMs, especially in the early stage of software testing.

The fire performance of fire retardant-treated wood can be evaluated based on how much of the chemical retardant is used. Therefore, methods for identifying chemical content in wood are needed. Stereo images of wood samples before and after the fire retardant treatment were captured using micro-focus X-ray computed tomography. Image brightness values, indicating concentration, were calculated using binarized images sliced from the X-ray images. Changes in integrated brightness values before and after treatment showed a strong positive correlation with chemical content at a 1% significance level. The chemical content of the retardant-treated wood was predicted based on the relationship between the two. The predicted values were in agreement with the values measured using the leaching method. Fire performance tests of the fire retardant-treated wood were conducted using a cone calorimeter. The treated wood was classified as fire-retardant and non-combustible wood. In addition, the fire performance predicted by the relationship between changes in integrated brightness values and chemical content agreed with the classification by the fire performance test. These findings suggest that X-ray computed tomography can be potentially used to predict the chemical content of fire retardant-treated wood.

With the growing demand for high reliability and safety software, software reliability prediction has attracted more and more attention to identifying potential faults in software. Software reliability growth models (SRGMs) are the most commonly used prediction models in practical software reliability engineering. However, their unrealistic assumptions and environment-dependent applicability restrict their development. Recurrent neural networks (RNNs), such as the long short-term memory (LSTM), provide an end-to-end learning method, have shown a remarkable ability in time-series forecasting and can be used to solve the above problem for software reliability prediction. In this paper, we present an attention-based encoder-decoder RNN called EDRNN to predict the number of failures in the software. More specifically, the encoder-decoder RNN estimates the cumulative faults with the fault detection time as input. The attention mechanism improves the prediction accuracy in the encoder-decoder architecture. Experimental results demonstrate that our proposed model outperforms other traditional SRGMs and neural network-based models in terms of accuracy.

With the rapid increase of software scale and complexity, the cost of traditional software testing methods will increase faster than the scale of software. In order to improve test efficiency, it is particularly important to automatically generate high-quality test cases. This paper introduces a framework for automatic test data generation based on the generative adversarial network (GAN). GAN is employed to train a generative model over execution path information to learn the behavior of the software. Then we can use the trained generative model to produce new test data, and select the test data that can improve the branch coverage according to our proposed selection strategy. Compared to prior work, our proposed method is able to handle programs under test with large-scale branches without analyzing branch expressions. In the experiment, we exhibit the performance of our method by using two modules in GNU Scientific Library. In particular, we consider the application of our method in two testing scenarios; unit testing and integration testing, and conduct a series of experiments to compare the performance of three types of GAN models. Results indicate that the WGAN-GP shows the best performance in our framework. Compared with the random testing method, the WGAN-GP based framework improves the test coverage of five functions out of the seven in the unit testing.

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.

Cloud computing and its associated virtualization have already been the most vital architectures in the current computer system design. Due to the popularity and progress of cloud computing in different organizations, performance evaluation of cloud computing is particularly significant, which helps computer designers make plans for the system’s capacity. This paper aims to evaluate the performance of a cloud datacenter Bitbrains, using a queueing model only from CPU utilization data. More precisely, a simple but non-trivial queueing model is used to represent the task processing of each virtual machine (VM) in the cloud, where the input stream is supposed to follow a non-homogeneous Poisson process (NHPP). Then, the parameters of arrival streams for each VM in the cloud are estimated. Furthermore, the superposition of estimated arrivals is applied to represent the CPU behavior of an integrated virtual platform. Finally, the performance of the integrated virtual platform is evaluated based on the superposition of the estimations.

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 modelbased 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.

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.

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.

Reliability is one of the most fundamental attributes in quality metrics, and receives considerable attentions in all engineering and computer science fields. Also, maintenance is the most useful solution for the proactive reliability management. Since modern systems in mechatronics, electronic and electrical engineering, computer science, chemical plant and process engineering, structural engineering, etc. are large scaled and much complex, efforts to assess the system reliability with maintenance are increasing as well. In fact, we often encounter mathematical modeling issues in quantitative assessment of reliability and maintenance of complex systems. The Special Interest Group on Reliability (SIGR) in Operations Research Society of Japan has continued working in Reliability and Maintenance research in Japan since 2014, and experienced to organize 18 technical seminars including 2 international symposiums and 1 special session in an international conference. We proud to have organized high quality events on reliability and maintenance modeling for the past three years and presented the latest research results in this emerging field. Based on our research activity in SIGR, we were honored to have a Special Issue on Mathematical Modeling in Reliability and Maintenance of Japan, in International Journal of Mathematical, Engineering and Management Sciences (IJMEMS). Not only the members of SIGR but also the general authors in reliability and maintenance modeling field were invited to submit their papers. Up to the paper submission deadline on March 31, 2017, we received 8 submissions from Japan and China. Each paper was strictly reviewed by two referees. Based on a few rounds of revisions, we could accept all the papers in this special issue. We thank all the referees and authors for their patient efforts to improve the papers. The paper on “A Summary of Periodic Replacement Policies with Number of Failures”, by Xufeng Zhao, Cunhua Qian, Syouji Nakamura and Toshio Nakagawa, is an excellent survey paper on periodic replacement policies, which can be categorized into block replacement. The second paper, “Note on History of Age Replacement Policies”, by Toshio Nakagawa, Mingchih Chen and Xufeng Zhao, focuses on a historical survey on another category called age replacement. Satoshi Mizutani and Toshio Nakagawa summarize “Maintenance Overtime Policy with Cumulative Damage”, which is often used in heavy industry. The above three papers would be useful for readers of this journal to understand the fundamental maintenance modeling approaches. The fourth paper on “Parametric Bootstrap Methods for Estimating Model Parameters of Non-homogeneous Gamma Process”, by Yasuhiro Saito and Tadashi Dohi, deals with statistical interval estimation procedure with bootstrap techniques under the incomplete knowledge on failure time distribution. Since the gamma process is a generalization of an nonhomogeneous Poisson process to describe minimal repair processes, the resulting statistical techniques and validation results through a simulation experiment will be useful in practice. The fifth paper “Fast Calculation Methods for Reliability of Connected-(r,s)-out-of-(m,n):F Lattice System in Special Cases”, by Taishin Nakamura, Hisashi Yamamoto and Xiao Xiao, is a challenge to compute the quantitative reliability in complex structured systems, where some specific cases are highlighted. The last three papers concern the reliability and quality issues in computer science. The paper on “Reliability Importance of Components in a Real-Time Computing System with Standby Redundancy Schemes”, by Junjun Zheng, Hiroyuki Okamura and Tadashi Dohi, treats a real-time computing system, and conducts the reliability importance analysis to investigate the impact of components. Masanari Kondo, Osamu Mizuno and Eun-Hye Choi report “Causal-Effect Analysis using Bayesian LiNGAM Comparing with Correlation Analysis in Function Point Metrics and Effort”. This is an important issue in empirical software engineering. Throughout the real project data analysis the authors succeed to improve the common causal-effect analysis. Momotaz Begum and Tadashi Dohi consider “Optimal Release Time Estimation of Software System using Box-Cox Transformation and Neural Network”, where the classical neural network approach is improved by introducing the Box-Cox data transformation. Finally, the guest editors would like to appreciate Dr. Mangey Ram, Professor of Graphic Era University, India, and Editor-in-Chief of IJMEMS. This special issue will not be published without his kind invitation and encouragement. We hope this special issue leads to further research and development in reliability and maintenance engineering.