Confidence Limits for Highly Reliable Coherent Systems with Exponentially Distributed Component Life
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A method for constructing upper confidence limits (UCL's) for parametric functions of type g(λ) = Σ j Π i∈Ij λ i is considered. It is based on maximization of g(λ) over a confidence set of type {λ | Σ λiTi ≤ Λα & λ i ≥ 0} obtained by pooling statistical data received from separate testing of system components. An asymptotic representation of the reliability function of an arbitrary coherent system is given assuming that the element failure rates are low. It has the form R(t) ≈ 1 - exp (– trg(λ)) and, therefore, a UCL g* for g(λ) provides a lower confidence limit (LCL) for R(t). Explicit formulas are presented for parallel, series-parallel, and k-out-of-n systems, for two types of statistical test data, namely, testing over a given time period and testing until a prescribed number of failures appear. The performance of the method is discussed in terms of two characteristics: the average value of g*/g(λ) and the true confidence coefficient P{g* ≥ g(λ)}.