Bounds on System Reliability by Linear Programming
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VIEW THE REPLYPublication: Journal of Engineering Mechanics
Volume 129, Issue 6
Abstract
Bounds on system probability in terms of marginal or joint component probabilities are of interest when exact solutions cannot be obtained. Currently, bounding formulas employing unicomponent probabilities are available for series and parallel systems, and formulas employing bi- and higher-order component probabilities are available for series systems. No theoretical formulas exist for general systems. It is shown in this paper that linear programming (LP) can be used to compute bounds for any system for any level of information available on the component probabilities. Unlike the theoretical bicomponent and higher-order bounds, the LP bounds are independent of the ordering of the components and are guaranteed to produce the narrowest possible bounds for the given information. Furthermore, the LP bounds can incorporate any type of information, including an incomplete set of component probabilities or inequality constraints on component probabilities. Numerical examples involving series, parallel and general structural systems are used to demonstrate the methodology.
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Copyright © 2003 American Society of Civil Engineers.
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Received: May 1, 2002
Accepted: Oct 14, 2002
Published online: May 15, 2003
Published in print: Jun 2003
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