An efficient method for reliability evaluation of multistate networks given all minimal path vectors
نویسندگان
چکیده
The multistate networks under consideration consist of a source node, a sink node, and some independent failure-prone components in between the nodes. The components can work at different levels of capacity. For such a network, we are interested in evaluating the probability that the flow from the source node to the sink node is equal to or greater than a demanded flow of d units. A general method for reliability evaluation of such multistate networks is using minimal path (cut) vectors. A minimal path vector to system state d is called a d-MP. Approaches for generating all d-MPs have been reported. Given that all d-MPs have been found, the issue becomes how to evaluate the probability of the union of the events that the component state vector is greater than or equal to at least one of the d-MPs. There is a need for a more efficient method of determining the probability of this union of events. In this paper, we report an efficient recursive algorithm for this union probability evaluation based on the Sum of Disjoint Products (SDP) principle, and name it the Recursive Sum of Disjoint Products (RSDP) algorithm. The basic idea is that, based on the SDP principle and a specially defined “maximum” operator, “⊕”, the probability of a union with L vectors can be calculated via calculating the probabilities of several unions with L − 1 vectors or less. The correctness of RSDP is illustrated. The efficiency of this algorithm is investigated by comparing it with an existing algorithm that is generally accepted to be efficient. It is found that RSDP is more efficient than the existing algorithm when the number of components of a system is not too small. RSDP provides us with an efficient, systematic and simple approach for evaluating multistate network reliability given all d-MPs.
منابع مشابه
Reliability Evaluation of Multicommodity Limited-Flow Networks with Budget Constraints
Many real-world systems such as manufacturing systems, transportation systems and logistics/distribution systems that play important roles in our modern society can be regarded as multicommodity flow networks whose arcs have independent, finite and multi-valued random capacities. Such a flow network is a multistate system with multistate components and its reliability for level (d;c), i.e., the...
متن کاملReliability Evaluation of Stochastic-flow Network through Two Minimal Intersecting Paths under Budget and Time Constraints
A stochastic flow network (SFN) is more suitable than a general network to describe some real systems as it is composed of multistate links as well as multistate nodes. As the nodes and the links have different capacities at different time, the minimum transmission time through a stochastic flow network is not fixed. In order to shorten the transmission time, in this paper the data are allowed ...
متن کاملBounds for the availabilities for multistate monotone systems based on decomposition into stochastically independent modules
Multistate monotone systems are used to describe technological or biological systems when the system itself and its components can perform at different operationally meaningful levels. This generalizes the binary monotone systems used in standard reliability theory. In this paper we consider the availabilities and unavailabilities of the system in an interval, i.e. the probabilities that the sy...
متن کاملPerformance Evaluation of Infrastructure Networks with Multistate Reliability Analysis
The purpose of this paper is to present a multistate reliability approach to evaluate the performance of the infrastructure networks from the viewpoint of reliability. There are many infrastructure networks that follow the classical two-terminal network reliability problem. We present a relatively efficient algorithm to find a subset of lower boundary points and then use them to develop lower b...
متن کاملEvaluation of Network Reliability for a Computer Network Subject to a Budget Constraint
This paper constructs a multistate flow network composed of multistate edges to model a computer network. Each edge has lead time, capacity, and cost parameters. Therefore, the minimum transmission time through a single path is not a fixed number. Under the transmission protocol that the data are sent through p (p ≥ 2) minimal paths simultaneously, the minimum transmission time is also stochast...
متن کامل