Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems
Introduction
Weighted multi-state systems are composed of multi-state components which have different performance levels and several failure modes, and such a model is much more realistic in studying system reliability [1], [2], [3], [4]. A multi-state system may have a basic architecture such as series, parallel, k-out-of-n, and network. The k-out-of-n structure is a very popular structure of the multi-state systems with wide application and research works [5], [6], [7], [8], [9], [10]. The multi-state weighted k-out-of-n system is a type of multi-state systems that has wide spread applications such as in traffic systems, telecommunication networks, and satellites [11]. Due to the importance and wide application of multi-state systems, many research works have been devoted to model the availability/reliability of these systems.
Li and Zuo [2] reviewed the methods for availability or reliability assessment of multi-state systems, and applied a recursive algorithm for availability assessment of multi-state weighted k-out-of-n system in a non-dynamic model. Most reliability/availability studies of multi-state weighted k-out-of-n system pre-assumed that the state probability of system/component does not change throughout system lifetime. However, complex systems are often subjected to aging process which implies that the system/component state probability may gradually change with time [12]. Therefore, it is of large practical value to model the state probability as a function of time. In the recursive algorithm used by Li and Zuo [2], the formula should be broken down into sub-formulas for calculation of reliability. When the factor “time” is considered in the sub-formulas, the method becomes more complex and computational. In this case, the system availability can be obtained using Universal Generating Function (UGF) [13]. UGF application can deal with the dynamic reliability evaluation.
Mostly, UGF has been used for reliability calculation of multi-state systems with different types of structures such as series-parallel and bridge [14], [15], [16], [17], [18], [19]. Application of UGF was for these types rather than multi-state k-out-of-n systems.
Liu and Kapur [20] developed reliability measures and analyzed reliability for dynamic non-repairable multistate systems. As systems become more complex, achieving an optimal design has been of great importance in recent years. The design of a system is often evaluated by four types of measures: reliability, availability, mean time to failure, and percentile life [21]. In this paper, by availability evaluation, we investigate the optimal design of a dynamic multi-state system.
Li and Zuo [11] presented a study on reliability assessment and optimal design of multi-state weighted k-out-of-n systems for a non-dynamic model. In their work, the objective was to select the component choices to minimize the system cost subject to requirement on system availability. In this paper, we modify the objective function presented by Li and Zuo [11] to minimize the cost and find the optimal system design in dynamic model. The rest of this paper is organized as follows. Section 2 presents a dynamic model to assess the availability of multi-state weighted k-out-of-n: G systems. In Section 3, a dynamic design problem is introduced to be solved by genetic algorithm. In Section 4, one real-world example from maritime transportation system is used to apply the dynamic availability model. Conclusions are provided in Section 5.
Section snippets
Dynamic availability model
In weighted k-out-of-n: G systems, each component of the system and the whole system have states: 0, 1, 2… M. In Fig. 1, a general Markov model for a system with components and with states is presented. Component in state has a capacity value of . System is in state j or above if the total capacity of all components is larger than or equal to the value . Then, this definition meansIn dynamic availability assessment of multi-state weighted
Dynamic design problem
Most optimization problems for the design of complex systems consider two goals or evaluation elements: availability/reliability and cost [22], [23], [24]. In this study, we consider these two elements in an optimal design problem for multi-state weighted k-out-of-n systems which have not yet been studied as a dynamic problem. The decision variables of this problem are probability (availability) and capacity of the components at different states. In this way, design engineers would know which
A numerical case study
Our case study is from a real world application in maritime transportation in naval shipyard Gdynia of Poland. The naval shipyard consists of two transportation systems to move the ships coming for repair to the designated location [31]. The ship-rope elevator is used to dock and undock ships coming to the Naval Shipyard in Gdynia for repairs. The elevator is composed of a steel platform carriage and 10 rope-hosting winches fed by separate motors. The rope transportation system is composed of
Conclusions
In this paper, dynamic modeling is considered for the availability assessment of multi-state weighted k-out-of-n systems. As in real world, component characteristics may change over time, we should consider most systems as dynamic system. However, most of the existing modeling in availability assessment of multi-state k-out-of-n systems has been non-dynamic. Therefore, in this paper, first we present an approach for availability modeling of dynamic systems by Markov modeling of the system and
Acknowledgments
The work in this paper is partially done under the Singapore-Poland Joint Research Project entitled “Safety and Reliability of Complex Industrial Systems and Process” ((SERC) Grant number 0721340050) granted by Singapore's Agency for Science, Technology and Research (A*STAR) and Poland's Ministry of Science and Higher Education (MSHE). The work described in this paper was also partially supported by a Grant from City University of Hong Kong (Project no. 9380058).
References (31)
- et al.
Reliability evaluation of multi-state weighted k-out-of-n systems
Reliab. Eng. Syst. Saf.
(2008) - et al.
Reliability and covariance estimation of weighted k-out-of-n multi-state systems
Eur. J. Oper. Res.
(2012) - et al.
Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down
Reliab. Eng. Syst. Saf.
(2006) - et al.
Reliability of k-out-of-n systems with phased-mission requirements and imperfect fault coverage
Reliab. Eng. Syst. Saf.
(2012) - et al.
A method for evaluation of reliability indices for repairable circular consecutive-k-out-of-n: F systems
Reliab. Eng. Syst. Saf.
(2003) - et al.
Optimal design of multi-state weighted k-out-of-n systems based on component design
Reliab. Eng. Syst. Saf.
(2008) - et al.
Reliability and risk analysis of large systems with ageing components
Reliab. Eng. Syst. Saf.
(2008) - et al.
A joint reliability-redundancy optimization approach for multi-state series-parallel systems
Reliab. Eng. Syst. Saf.
(2009) - et al.
A model for availability analysis of distributed software/hardware systems
Inf. Software Technol.
(2002) - et al.
Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization
Reliab. Eng. Syst. Saf.
(2009)
Optimal testing-resource allocation with genetic algorithm for modular software systems
J. Syst. Software
Genetic algorithm based multi-objective reliability optimization in interval environment
Comput. Ind. Eng.
Some improvements on adaptive genetic algorithms for reliability-related applications
Reliab. Eng. Syst. Saf.
The hierarchical weighted multi-state k-out-of-n system model and its application for infrastructure management
IEEE Trans. Reliab.
Optimal design of a multi-state weighted series-parallel system using physical programming and genetic algorithms
Asia Pac. J. Oper. Res.
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