This paper addresses the optimal allocation of reliability among components that are to be assembled into a system. While it is a generally accepted notion that a component's cost is an increasing function of its reliability, most research to date adopts exponentially increasing, closed-form functions to relate cost and reliability. However, in practice such functions are often unknown or difficult to construct, and it is often more reasonable to describe cost-reliability relationships via discrete data sets. We consider such situations, where each component is available at several reliability levels with corresponding costs. The design optimization problem results in a nonlinear integer program. Because every system configuration has an equivalent representation as either a series connection of parallel subsystems or a parallel connection of series subsystems, we provide formulations, linear relaxations, and algorithms for these two.
Since mathematical models based on component reliabilities are frequently used for prediction of system reliability, it stands to reason that cost-eective inferences on the reliability of a system could be made on the basis of tests of its constituent components. Prior research in the area of system-based component testing has for the most part addressed the development of plans that test only the components. From a practitioner's point of view, this is an issue of concern since system failures are often caused by imperfect interfaces and other causes that are not directly attributable to component failures. The exclusion of system tests may thus be an erroneous approach. This paper addresses the development of test plans that explicitly consider the possibility of interface failures. The paper analyzes a series system to determine when testing should be performed on the system alone, on the components only, and on both, depending on test costs and interface reliabilities. Optimum test plans are derived by solving a twostage mathematical program.
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