Evaluation of Reliability Characteristics of Two Dissimilar Network Flow Systems (original) (raw)
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Reliability Comparison Between Redundant Repairable Network Flow Systems
SOP Transactions on Applied Mathematics, 2014
The importance in promoting, sustaining industries, manufacturing systems and economy through reliability measurement has become an area of interest. Reliability is one of the most important factors in any successful industries and manufacturing settings. In this paper, we study the reliability of three different repairable redundant network flow systems. First order differential equations method is used to obtain the explicit expressions for mean time to system failure, steady-state availability, busy period of repairman and profit function. Some numerical experiments are conducted in order to illustrate the effects of failure and repair rates on reliability indices such as mean time to system failure, steady-state availability and profit function. Furthermore, we compare the configurations based on reliability indices and cost benefits for the three configurations and find that configuration II is more reliable than configuration I and III.
Reliability evaluation of a stochastic-flow network (SFN) has been extensively studied in the past decades and various algorithms have been proposed. A number of graph based algorithms are in terms of minimal paths (MPs). Most MP-based algorithms have been proposed for the case of single-source single-sink SFN and a few algorithms have considered the multi-source multi-sink case. However, there are many practical networks such as communication and telecommunication networks comprised of several sources and sinks. Here, we consider a multi-source multi-sink SFN and propose an algorithm to find all the lower boundary points in terms of the MPs. The proposed algorithm is shown to be correct. Moreover, the algorithm is shown to be more efficient than some existing ones. After World War I, reliability was measured as the number of accidents per hour of flight time for one-, two-, and four-engine airplanes [1]. Afterwards, network reliability theory has extensively been applied to a variety of real-world systems such as power transmission and distribution [2], mobile ad hoc wireless [3], transportation [4], and manufacturing [5]. Moreover, in problems such as maximizing system reliability [2, 5] or optimal design of a network subject to reliability constraint [6], there has been an increasingly significant need for efficiently computing or estimating the system reliability. Thus, the system reliability problem turns to be an important challenging problem for system engineers. Evaluating the system reliability is an NP-hard problem [7], and thus the problem continues to be interesting to investigate. In a single-source single-sink stochastic-flow network (SS-SFN), system reliability is usually considered as the probability of transmitting a given amount of flow (or data) from a source node to a sink node [7−14]. A number of graph-based algorithms have been proposed in terms of minimal cuts (MCs) [7−11] or minimal paths (MPs) [2, 3, 12, 13] to evaluate the system reliability of an SS-SFN. Forghani-elahabad and Mahdavi-Amiri [8] considered an SS-SFN with budget constraint and proposed an effective algorithm to evaluate the reliability of the network. In [9], investigating several existing algorithms, their flaws were illustrated and modifying the flaws, an improved algorithm was proposed to compute the exact system reliability. In addition, Forghani-elahabad and Mahdavi-Amiri [10] presented a new data structure along with some new results to propose an improved algorithm. The authors showed the algorithm to be more efficient than the other existing algorithms theoretically and practically. In [11], an improved algorithm was proposed to determine all the upper boundary points in order to compute the system reliability. Later, the authors in [12] considered the case of sending all the flow through two separate minimal paths (SMPs), and proposed an algorithm to find the two most reliable SMPs transmitting a given amount of flow within the given time and budget constraints. They also extended the proposed algorithm to the case of q SMPs in [13]. In a multi-source multi-sink stochastic-flow network (MM-SFN), there is also a demand for flow to be transmitted from each source to its corresponding sink, and hence the system reliability in an MM-SFN is the probability of transmitting all the required demands from the sources to their corresponding sinks simultaneously. Lin and Yuan [15] considered an MM-SFN and proposed an algorithm to evaluate the system reliability in terms of minimal paths. Considering a real-world network, namely Taiwan Advanced Research and Education Network, Lin and Yen [16] proposed an algorithm
Network reliability evaluation
Wiley Interdisciplinary Reviews: Computational Statistics, 2010
This article, beyond presenting a spectrum of network reliability methods studied in the past decades, describes a scalable innovative 'overlap technique' to tackle large complex networks' reliability evaluation difficulties, which cannot be handled by straightforward reliability block diagramming (RBD) techniques used for the simple parallel-series topologies. Examples are shown on how to apply the overlap algorithm to compute the ingress-egress reliability. Monte Carlo simulations demonstrate the methods discussed. (1) Static (time independent), (2) dynamic (time dependent) using a versatile Weibull distribution to represent the multiple stages of network components from infancy to useful life period and to wearout, and (3) multistate versions to include derated behavior beyond conventional working and nonworking states, are illustrated for calculating the directional source-target (s-t) reliability of complex networks by using the Java software ERBDC: Exact Reliability Block Diagramming Calculator . 2010 John Wiley & Sons, Inc.
On reliability evaluation of a capacitated-flow network in terms of minimal pathsets
Networks, 1995
Many real-world systems such as electric power transmission and distribution systems, transportation systems, and manufacturing systems can be regarded as flow networks whose arcs have independent, finite, and multivalued random capacities. Such a flow network is indeed a multistate system with multistate components and so its reliability for the system demand d , i.e., the probability that the maximal flow is no less than d , can be computed in terms of minimal path vectors to level d (named d-MPs here). The main objective of this paper was to present a simple algorithm to generate all d-MPs of such a system for each system capacity level d in terms of minimal pathsets. Analysis of our algorithm and comparison to Xue's algorithm shows that our method has the following advantages: (1) the family of d-MP candidates that it generates is smaller in size and so d-MPs can be generated more efficiently, (2) it is expressed more intuitively and so easier to understand, and (3) whenever applied in a seriesparallel case, both algorithms are essentially the same, but in a non series-parallel case, Xue's algorithm needs the extra work to transform the system into a series-parallel in advance. Two examples are illustrated to show how all d-MPs are generated by our algorithm and then the reliability of one example is computed. 0 7995 John Wiley & Sons, Inc.
Journal of Mathematics and Statistics, 2005
Many authors have studied the effectiveness of a redundant system under two or three types of failure under the assumption that such failures are repairable. Little attention is paid on whether such repair act ion can restore the system operating condition to as good as new (perfect repair) and the effect of such perfect repair on the system performance. In this study, various measures of system effect iveness such as mean time to system failu re (MTSF), steady state availability, busy period and profit function of a 2-out-of-3 repairable system with perfect repair are analy zed using Kolmogorov's forward equation method. Some particular cases have been discussed graphically. The results have indicated that perfect repair action plays a v ital ro le on system performance. Simu lations results show that perfect repair is important part icularly in increasing mean time to system failure, availability and system performance as a whole.
Reliability analysis techniques explored through a communication network example
1996
This paper reviews general methods used to perform dependability analysis on a given system. A communication network example is used in relation to a client/server type of application to illustrate the reliability and availability modeling techniques. We review both non-state space as well as state space based methods and discuss the bene ts and limitations of each. The paper assumes a general understanding of probability theory.
Sum of disjoint product approach for reliability evaluation of stochastic flow networks
International Journal of System Assurance Engineering and Management, 2017
Computer and telecommunication networks are stochastic in nature, as each node and arc may have multiple capacity states besides complete failure. Various twoterminal reliability estimation algorithms for such stochastic flow networks are available in literature. These algorithms generate d-minimal cuts from minimal cut-sets of the network, where d is required demand. Different techniques are available in literature to evaluate exact reliability from such d-minimal cuts such as the recursive inclusion-exclusion method. The recursive inclusion-exclusion method has certain redundant computations while evaluating network reliability. This paper proposes a sum of disjoint products technique to minimize redundant computations in exact reliability computation from flow vectors. MATLAB simulation is performed to evaluate the performance of the proposed method and compare it with the existing methods for benchmark networks available in literature. Simulation results show that the proposed method require lesser computational efforts and memory.
Quantitative evaluation of network reliability
2013
The determination of the reliability value for technical systems whose components are subjected to random failure is known as an NP-hard problem. Hence, efforts to conceive efficient solutions on restricted classes of networks have been pursued since the 1960s. In this thesis, substantial contributions are made to improve the current state-of-the-art in exact terminal reliability. Moreover, the proposed model extensions additionally allow for considering dependent component failures.
American Journal of Operational Research, 2013
In this paper, we studied a series system consisting of single unit. The system is subjected to three types of failures. Type I failure is minor in which the system is imperfect ly repaired. Type II failure is majo r in which the entire system is replaced. Type III failure is called a partial failure in wh ich the system works in reduced capacity and is perfectly repaired. Failure and repair t ime are assumed exponential. We developed the explicit exp ressions for mean time to system failure (MTSF), steady-state availability, busy period and profit function using Kolmogorov forward equations method. Special cases are studied to determine the impact of various system parameters on MTSF, busy period, steady-state availability and profit function.