Reliability evaluation of complex systems is of interest to engineers of all disciplines. The techniques for reliability evaluation depend upon the logic diagram of the system. System reliability evaluation is straight forward in case of series-parallel systems; while this is not so in general nonseries parallel systems. In this paper, many different techniques for reliability evaluation of general systems have been presented. Merits and demerits of every method are discussed. An example is solved by all the methods to have a comparison of computational labour involved and the size of final derived reliability expression.
"Alternatively, statisticians have emphasized both the point and interval estimations of the network reliability given failure data of individual component or the system. The Bayesian approach     is frequently used to derive the posterior reliability distribution based on prior information of components or the system. The Bayesian approach is quite limited and it is only effective to simple moments of the network reliability estimate based on component test data. "
[Show abstract][Hide abstract] ABSTRACT: A new algorithm is proposed to approximate the terminal-pair network reliability based on minimal cut theory. Unlike many existing models that decompose the network into a series–parallel or parallel–series structure based on minimal cuts or minimal paths, the new model estimates the reliability by summing the linear and quadratic unreliability of each minimal cut set. Given component test data, the new model provides tight moment bounds for the network reliability estimate. Those moment bounds can be used to quantify the network estimation uncertainty propagating from component level estimates. Simulations and numerical examples show that the new model generally outperforms Esary-Proschan and Edge-Packing bounds, especially for high reliability systems.
[Show abstract][Hide abstract] ABSTRACT: Fault (or success) trees constructed from circuit diagrams having multiple inputs and outputs and/or bridged circuits are equivalent Boolean representations which do not, necessarily, bear any resemblance to the original circuit diagram. In this paper we show how this problem can be avoided and how a sequenced-fault tree, in which the events are arranged in the order in which they appear on the flow sheet, can be constructed.The construction of the tree is preceded by the development of an “Event Diagram” which is more convenient than a reliability block diagram if common mode failures or multiple prerequisite events are involved in system failure.
[Show abstract][Hide abstract] ABSTRACT: An algorithm for optimum allocation of redundancies in a general system is presented. The method is applicable to problems having any number of constraints which need not be linear. For selecting the subsystem where redundancy is to be added, a heuristic criterion is introduced which takes into account the relative increment in reliability versus increments in constraints. The method is applicable for any system configuration where subsystems are composed of identical parallel elements. The algorithm is simple, requires little computation effort, and is easily programmed for a computer. An example of a nonseries system illustrates the procedure.
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