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On the design of component test plans based on system reliability objectives
Component test plans are often designed by allocating a system's reliability goal among the system's components, then designing individual component test plans suitable for demonstrating achievement of each component's reliability goal. One use of the resulting component test data is the calculation of estimated system reliability, based on a model linking the component reliabilities to system reliability. The statistical precision of this system estimate depends on the component test plans (numbers of each component tested and the type of tests, e.g., variables or attributes) and, hence, is determined by the component test planners. Because system reliability may be of considerable interest, we feel an integrated view of component testing is required to assure that the ensemble of component tests will provide an adequate system reliability estimate. This paper considers the case of a series system of different components and binomial component data. For the case of equal numbers of units tested of each component (which can be shown to minimize total cost, subject to the risk constraints) the O.C. envelope is readily derived and from this envelope component test plans that satisfy the specified risks can be derived from equations that involve the cumulative binomial distribution function. Existing tables pertaining to acceptance sampling plans based on the binomial distribution can be used to determine the required number of component tests. 10 refs., 2 figs.