A confidence-based approach to reliability design considering correlated failures

To maintain a competitive edge, technology manufacturers must produce systems that are reliable enough to satisfy customers yet cheap enough to engineer so that they are profitable. This paper presents an optimization model to maximize the statistical confidence in product profitability, permitting flexibility in the design and number of the units manufactured. This is unlike traditional approaches, which focus on the two cases that optimize the reliability of a single unit or the s-expected profit obtained from a very large number of units. These two extremes disregard a practical concern, namely the negative impact that a larger than s-expected number of failures will exert on product profitability. This paper formulates an optimization problem to mitigate this risk. Virtually all reliability optimization problems also assume that component failures are s-independent. The present paper does not impose this assumption. The utility of the approach is demonstrated through a series of examples which compare the reliability of systems designed with and without the assumption of s-correlated component failures. The results indicate that explicitly considering s-correlation consistently mitigates the risk to profitability more effectively than the same method when component failures are assumed to be s-independent.