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Guest Editorial:
Multi-State System Reliability

Volume 7, Number 3, May 2011, pp.203-204


Université Laval, Canada


      In this special issue of IJPE, we would like to present eight impressive papers on the subject of multi-state systems reliability. In classical binary reliability analysis, a system and its constituent components and subsystems are assumed to be either in a working state or in a failed one. However, in many real-life situations, this two-state assumption may not be adequate and appropriate. The system may, in fact, have more than two levels of performance varying from perfect functioning to complete failure. For example, the presence of degradation is a common realistic situation, in which a system should be considered to be a multi-state system. Degradation can be caused by system deterioration or by variable ambient conditions. Fatigue, failures of non-essential components, and number of random shocks on the system are all examples of system degradation causes. In this case, the failure rate depends on the status of the system which can degrade gradually. The reliability analysis of such degraded systems should consider multiple operational states to take into account multiple degradation levels and a multi-state system may perform at different intermediate states between working perfectly and complete failure.


      As a relatively new emerging discipline, the reliability of multi-state systems has received increasing and extensive attention during past few years. At the junction of binary reliability and performance analysis, it gives new opportunities towards many promising research directions. The papers selected for this special issue on multi-state systems cover some of the important problems that are currently being addressed by the engineering community. They demonstrate the vibrant research in the area of multi-state systems reliability analysis and optimization. The papers included in this special issue are:


      Paper 1 (Defence and Attack of Multi-State Systems, by K. Hausken, Norway) develops a game-theoretical model for a two component system. Each component is protected by a defender which maximizes its reliability weighted against the defense costs, and attacked by an attacker which maximizes its unreliability weighted against the attack costs.

      Paper 2 (Multi-state Reliability Modelling of a Manufacturing Cell, by M. Savsar, Kuwait) develops a stochastic model to analyze performance measures of a flexible manufacturing cell. The later is modelled as a multi-state system to take into account degraded functioning modes.     

      Paper 3 (A Component Importance Measure Suitable for Flow Transmission Multi-State System, by Fares Innal and Y. Dutuit, France) uses stochastic Petri net models with predicates to deal with the performance evaluation of a multi-state system and its components. A Monte Carlo simulation approach is used to show the interest of the importance factors.

      Paper 4 (Models and Measures for Fuzzy Reliability and Its Relationship to Multi-State Reliability, by Z. Li and K. C. Kapur, U.S.A.) is based on the theory and methods for fuzzy sets. The authors illustrate how fuzzy modelling of the states of the components/system can capture more realistic performance of the system for its evaluation and decision making processes by the system designer as well as the customer.

      Paper 5 (Analytical Uncertainty Propagation for Availability Assessment of Stochastic Multi-State Systems, by M. El Falou and E. Châtelet, France) generalizes uncertainty propagation methods to multi-state systems. The proposed method is based on an analytical calculation of the probability of the system states. It is able to deduce analytically the availability of the system with the associated uncertainty.

      Paper 6 (Optimal Assignment of a Two Types of Components in a Multi-state Stochastic-flow Network, Y.-K. Lin and C.-T. Yeh, Taiwan) models a system as a network with edges and nodes, in which each component (edge/node) is multi-state due to complete failure, partial failure, maintenance, etc. To maximize the system reliability according to the optimal two-type component assignment under a budget constraint, a genetic algorithm is developed. The system reliability is evaluated in terms of minimal paths and recursive sum of disjoint products (RSDP).  

      Paper 7 (Planning Inspections in the Case of Damage Tolerance Approach to Service of Fatigued Aircraft Structures, by N. Nechval et al., Latvia) uses a damage tolerance approach to determine appropriate decreasing intervals between inspections of fatigue-sensitive aircraft structures modelled as multi-state systems. The proposed stochastic model evaluates the crack probability, and the probability of random time to reach a specified crack size.   


      Paper 8 (Sustainable Reuse Approaches based on Residual Lifetime : A Case Study in Assistive Technology, S. H. Mohammadian et al., Canada) deals with the selection of qualified-for-reuse components for returned systems. Physical properties and age are used to assess the multi-state degraded components’ residual lifetimes. The proposed approach has been applied to the end of life of electric-powered wheelchair batteries.


      In concluding this editorial, I would like to thank all contributing authors for their outstanding papers and my sincere thanks are due to referees whose timely help in reviewing these papers was always available. I am also grateful to the Editor-in-Chief, Professor Krishna B. Misra, for his support and help in realizing this project.     



Mustapha Nourelfath is a full professor of Industrial Engineering at Université Laval (Canada), in the Department of Mechanical Engineering at the Faculty of Science and Engineering. Before his current position, he was Professor at UQAT (Université du Québec en Abitibi-Témiscamingue, Canada). After graduating from ENSET-Mohammedia (Morocco), Professor Nourelfath obtained a DEA and a Ph.D. in industrial automation and industrial engineering from INSA (National Institute of Applied Science) of Lyon (France), in 1994 and 1997, respectively. Dr. Nourelfath is member of the organizing and scientific committees of different international conferences, and regularly acts as a referee for many scientific journals. He is a member of CIRRELT (Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation). His specific topics of interest are operations research and artificial intelligence applications in reliability, logistics, manufacturing, and supply chain management problems. He serves editorial boards of International Journal of Performability Engineering and Reliability Engineering and System Safety.


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