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This paper offers several contributions to the area of discrete reliability growth projection. We present a new, logically derived model for estimating the reliability growth of complex, one-shot systems (i.e., the reliability following implementation of corrective actions to known failure modes). Multiple statistical estimation procedures are utilized to approximate this exact expression. A new estimation method is derived to approximate the vector of failure probabilities associated with a complex, one-shot system. A mathematically-convenient functional form for the s -expected initial reliability of a one-shot system is derived. Monte-Carlo simulation results are presented to highlight model accuracy with respect to resulting estimates of reliability growth. This model is useful to program managers, and reliability practitioners who wish to assess one-shot system reliability growth.