Once again, we present in this issue nine papers. First seven of them are part of the special issue guest-edited by Professor Joh Tadashi Dohi of Hiroshima University, Japan and Professor Won Young Yun, Pusan National University, South Korea.
Realizing the importance of the subject of Stochastic Modeling and Optimization Techniques, in performance assessment of large complex systems, when Professor Dohi approached me for bringing out a special issue of International Journal of Performability Engineering on this this subject, in which some recent results can be presented, I readily agreed to his suggestion We hope the readers of this journal will find some ideas and approaches useful for them on the subject of system performability analysis.

Only five papers (50 % of those presented) were selected from the papers presented at a special session on Stochastic Reliability Modeling and Optimization organized by the Guest Editors at the Conference QR2MSE 2014 which was held in Dalian, China, on July 22-25, 2014. These papers were invited from the authors based on the significance and discussion that followed the presentation of their papers at this conference and the authors were asked to submit an extended version of their papers for the special issue of International Journal of Performability Engineering. In addition to the five papers selected, two more papers were invited by the Guest Editors from well-known researchers which in their opinion would be supplementing the theme. All papers were once again peer-reviewed and revised based on the comments of the referees following the IJPE norms. The result of this exercise is before the readers. We would welcome comments from the readers of IJPE and researchers to initiate an academic discussion on the papers included in this special issue.

In addition to the above seven papers of the special issue section, we have included two more papers from the regular stream of IJPE.

The eighth paper, of this issue, Economic, Robust and Quality Design of Engineering Systems using a Hybrid Six Sigma-second Moment Approach, the authors claim to present a new approach to allocate means and tolerances while designing engineering systems Useful features of second-moment methods and design for Six Sigma methods are combined. The approach presented obviates the shortcomings of Taguchi’s expected loss function and the need to integrate over the failure region in probabilistic methods.

The ninth paper, Application of ANN to Monitor the Correlated Process using Higher Sample Size, claims that the modified chart, based on sum of chi-squares theory is able to counter the autocorrelation in the observations. Various optimal schemes of modified chart for sample size (n) of 10 are proposed at different levels of correlation (F). The ARLs of the modified chart are also validated and compared with the ARLs obtained by Artificial Neural networks (ANNs).

Besides these nine papers included in this issue, reviews of two latest books are provided in this issue for the benefit of IJPE readers.

I would like to express my sincere thanks to the Guest editors for making all the efforts to bring out the special issue and I also like to thank reviewers who helped us in this task of selecting papers. My thanks are also due to all the authors whose contributions are included in this issue.

Stochastic Reliability Modeling and Optimization is the most fundamental topic in the board area of reliability and maintenance engineering, and still plays a significant role in industrial applications. In past, we have organized the similar titled special sessions in several locations such as The 2009 International Conference on Advanced Software Engineering & Its Applications (ASEA-2009), Jeju Island, Korea, December 10-12, 2009, The 2nd International Conference on Advanced Computer Science and Information Technology (AST-2010), Miyazaki, Japan, June 23-25, 2010, International Conference on Quality, Reliability, Maintenance, and Safety (QR2MSE 2011), Xi'an, China, June 17-19, 2011, The 7th International Conference on Mathematical Methods in Reliability - Methodology and Practice (MMR-2011), Beijing, China, June 20-14, 2011. Especially, the selected papers from the last two conferences were included in the monograph; Stochastic Reliability and Maintenance Modeling (T. Dohi and T. Nakagawa, eds.), Springer, 2013, and the special issue in Reliability Engineering and System Safety (vol. 116, 2013).

QR2MSE 2014 was held in Dalian, China, on July 22-25, 2014. At this well-attended conference, we organized a special session on Stochastic Reliability Modeling and Optimization, and accepted ten papers from China, Japan and Korea, through the peer-review process. Based on these conference papers and detailed discussion at the conference venue, we called for the extended papers with significant extension, in the Special Issue on Stochastic Reliability Modeling and Optimization, for inclusion in the International Journal of Performability Engineering (IJPE). Finally, we selected five submissions from the QR2MSE conference papers, in addition to two tutorial/invited papers from distinguished researchers.

All papers included in this special issue of IJPE have been peer reviewed by at least two referees. We are much pleased to accept seven high quality papers for this special issue and to provide the most recent research results in Stochastic Reliability Modeling and Optimization. It is known that stochastic modeling and optimization techniques are very useful for quantification and analysis of complex systems in real world, and are commonly used in both design and operational phases of engineering systems. We believe that the readers of this journal may be able to find new ideas and problems in the area of system performability analysis.

The first paper, which is an invited contribution, viz., Largeness Avoidance in Availability Modelling Using Hierarchical & Fixed-point Iterative Techniques’’ by H. Sukhwani, A. Bobbio, and K. S. Trivedi treats a practically important issue in availability modeling with large scaled Markov chains and proposes a sophisticated technique based on hierarchical modeling approach and Brouwer’s fixed-point algorithm.

The second invited paper, Survey of Replacement Policies for Parallel Systems with Newly Proposed Approaches by T. Nakagawa and X. Zhao is an excellent survey on some optimal replacement policies for parallel system with random number of components. It deals with the situation where the number of active components is known in advance and provides a new paradigm for optimal maintenance decision.

The remaining five papers are the extended versions and refereed contributions selected from the QR2MSE 2014 conference papers.

The third paper of this special issue, Converting a Multi-state System into a Family of Binary State Systems by F. Ohi concerns a mathematical theory to convert a multi-state system into a family of binary state systems. Since the multi-state system is essentially difficult through analytical treatment, the result will be useful to analyze complex multi-state systems.

The fourth paper, Magnitude Relation of the All-terminal Reliability of Network Systems by X. Xiao, Y. Chen, N. Takahashi, and H. Yamamoto describes the magnitude relation of the all-terminal reliability of network systems. Because it is useful to focus on the special property of complex network in computing the network reliability, their approach is validated theoretically and experimentally.

In the fifth paper, Optimal Data Transfer Strategies for the Automatic Hierarchized Storage within a Server System, the authors X. Zhao, S. Nakamura, and T. Nakagawa address the optimal data transfer strategies for automatic hierarchized storage within a server system. It is a good application of optimal maintenance theory to real computer systems and is related to the fault-tolerant computing.

The sixth paper, A Simulation-based Multi-Level Redundancy Allocation for a Multi-Level System, Y. J. Han, W. Y. Yun and J. Y. Lee considers a simulation-based multi-level redundancy allocation for a multi-level system. Though the underlying problem is difficult to treat analytically, the authors apply the well-defined simulation scheme and provide realistic solutions with application to the reliability engineering practice.

The final paper, M-SRAT: Metrics-based Software Reliability Assessment Tool by K. Shibata, K. Rinsaka, and T. Dohi develops a metrics-based software reliability assessment tool, called M-SRAT, and show through some illustrative examples that it is useful to assess the software reliability when not only software fault count data but also software metrics data are observed.

All the papers included in this special issue are the original contributions and are well-balanced between theoretical contributions and practical application.

Lastly, we like to thank Professor Krishna B. Misra, Editor-in-Chief of IJPE, for kind guidance, warm encouragement and his help from time to time to edit this special issue.

Guest Editors
Tadashi Dohi, Hiroshima University, Japan
Won Young Yun, Pusan National University, Korea

ABOUT THE GUEST AUTHORS

Tadashi Dohi has been working as a full Professor in the Department of Information Engineering, Graduate School of Engineering, Hiroshima University since 2002. He received the B.S.E., M.S. and Ph.D. degrees in Engineering from Hiroshima University, Japan, in 1989, 1991and 1995, respectively. During 1992 and 2000, he was a Visiting Researcher in the Faculty of Commerce and Business Administration, University of British Columbia, Canada, and Hudson School of Engineering, Duke University, USA, respectively, on leave of absence from Hiroshima University. His research areas include reliability engineering, software reliability, dependable computing, performance evaluation and high assurance systems design. Professor Dohi has authored numerous publications in these areas. He is a member of IEICE, ORSJ, JAMS, ISCIE and IEEE. He also serves as a member of editorial boards of several international journals.

Won Young Yun is a Professor in the Department of Industrial Engineering, Pusan National University, Busan, Korea. He received his B.S. from Seoul National University in 1982 and an M.E. and Ph.D. from the Department of Industrial Engineering, Korea Advanced Institute of Science and Technology (KAIST) in 1984 and 1988, respectively. He was a Visiting Researcher in the University of Birmingham, U.K. and Queensland University of Technology, Australia, in 1993 and 1999 respectively. His research interests include optimization problems in system reliability, maintenance, warranty, and inland container repositioning in which simulation and meta-heuristics are used to find optimal solutions.

Accurate modeling of availability is a practical problem in today’s complex high-availability systems. But as the system gets more complex, the state-space required for accurate modeling tends to grow very fast. In order to mitigate the largeness in model generation / solution, the system model could be divided into subsystem models, and solution for sub-models can be combined to yield overall model solution. Such hierarchical composition techniques reduce the state-space tremendously. But simple hierarchical techniques provide exact results only when sub-model solutions are independent. In many scenarios, some components or procedures are shared across subsystems, which violate independence in sub-model solution. Hence approximation techniques like nearly independent systems are required to model systems where sub-model solutions are dependent. This paper demonstrates approximation techniques for availability modeling for a fluid pressure control system using the concepts of nearly independent subsystems and fixed-point iteration.

This paper surveys several replacement policies for parallel systems, where three newly proposed notions in our research are considered: (i) Random number of units, (ii) excess and shortage costs, and (iii) approach of “whichever occurs last”. First, we take up replacement policies for a parallel system when its number of units could be constantly predetermined and randomly estimated. Next, we introduce excess and shortage costs used in scheduling problems into models and derive optimal replacement times, where the case of random number of units is also considered. Third, when a parallel system is operating for successive jobs with a random working time, we plan two kinds of policies of replacement first and replacement last that are formulated by using two respective approaches of “whichever occurs first” and “whichever occurs last”. All discussions are given analytically and optimal replacement polices are computed numerically.

In this paper we show mutual relationships between a multi-state system and a family of binary state systems and show some relationships among minimal state vectors of the systems, which give us how to construct the structure function of the multi-state system by using the structure functions of the binary state systems. But the state spaces of multi-state systems are assumed to be totally ordered set, because of simplicity for our first examination about the transformation.

We concern the minimization problem of the total construction cost subject to the condition that the all-terminal reliability is not less than a reliability threshold. Although algorithm for solving this problem has been developed based on the so-called branch and bound method, it is known that the implement of the existing algorithm requires a fair amount of time, especially in the case that the number of edges is quite greater than the number of nodes. To reduce the computational time, we apply factoring method to classify network systems into several types (groups), and specify the type which has greater all-terminal reliability than the other types. Furthermore, we derive the exact maximum all-terminal reliability of the network systems with n+4 edges. Our proposal directly leads to a significant improvement of the overall efficiency of the optimization algorithm.

Under the technique of Hierarchical Storage Management (HSM), this paper discusses optimal times of data transfers for enormous data within a server system. First of all, we propose three classifications in storage, i.e., Solid State Drive (SSD), Serial Attached SCSI (SAS) HDD, and Serial ATA (SATA) HDD, which are used for frequent accessed, inactive, and long-term preserved data blocks. To save the total time for data scans and data transfers, we secondly formulate two models in which the times when data transfers should be made: 1) Number N of data transfers from SSD to SAS; 2) Time T of data transfers from SAS to SATA. We suppose that data scans occur at non-homogeneous and homogeneous Poisson processes, and optimize respective models in number N and time T. Finally, two cases of numerical examples are given to illustrate the proposed models.

In this paper, we deal with a multi-level redundancy allocation problem for a multi-level system and system, modules and component levels in the system are simultaneously considered as candidates for redundancy. System availability and life cycle cost are used as the constraint and objective function, respectively, and are estimated by simulation. The level and degree of redundancy are determined that minimize the life cycle cost and satisfy the target system availability. An estimation of distribution algorithm is used to determine best solutions, and numerical examples are studied in order to compare module redundancy with component redundancy.

In this paper we develop a software reliability assessment tool, called M-SRAT: Metrics-based Software Reliability Assessment Tool, by using several testing metrics data as well as software fault data observed in the testing phase. The fundamental idea is to use the metrics-based software reliability models proposed by the same authors. M-SRAT is written in Java language with 54 classes and 8.0 KLOC, where JDK1.5.0 9 and JFreeChart are used as the development kit and the chart library, respectively. This tool can support (i) the parameter estimation of software reliability models via the method of maximum likelihood, (ii) the goodness-of-fit test under several optimization criteria, (iii) the assessment of quantitative software reliability and prediction performance.

This paper presents a new approach to rationally allocate means and tolerances in engineering systems at the design stage. Features of second-moment methods and Design for Six Sigma methods are combined. Either point or global variance methods may be invoked to model the uncertainty in the design variables. Shortcomings of Taguchi’s expected loss function and the need to integrate over the failure region in probabilistic methods are obviated. Multiple responses, each with any of the performance metrics including target-is-best, smaller-is-best and larger-is-best, are handled. The novelty of the approach is that cost or quality may serve as an objective with the other serving as a constraint in the optimization process. The impact of the method is that it reinforces quality concepts from Six Sigma design while ensuring that robustness is maximized. Two diverse case studies justify the methodology.

The Average run lengths (ARLs) of the modified x? chart are computed by simulation using MATLAB software in this paper. The modified x? chart, based on sum of chi-squares theory is able to counter the autocorrelation in the observations. Various optimal schemes of modified x? chart for sample size (n) of 10 are proposed at different levels of correlation (Φ). The ARLs of the modified x? chart are also validated and compared with the ARLs obtained by Artificial Neural networks (ANNs). It is found that when the level of correlation (Φ) increases for a particular sample size (n), the performance of all the schemes deteriorates. It is concluded that the modified chart offers more robustness compared to Shewhart x? chart for autocorrelated data at various levels of correlation (Φ) and shifts in the process mean.