Test-analyze-and-fix (TAAF) is the most commonly recognized method of improving system reliability. The work presented here addresses the question of when to stop testing during TAAF programs involving one-shot systems when the number of systems to be produced is predetermined and the probabilities of identifying and successfully correcting each failure mode are less than one. The goal here is to determine when to cease testing to maximize utility where utility is defined as the number of systems expected to perform successfully in the field after deployment of the lot. Two TAAF stopping rules are presented. Simulation is used to model TAAF execution under different reliability growth conditions. Four discrete reliability growth models (DRGM's) are used to generate "real world" reliability growth and to estimate reliability growth using hypothetical observed success/failure data. Ranges for the following parameters are considered: starting reliability, growth rate, maximum achievable reliability, number of systems to be produced, probability of incorrectly identifying a failure mode, and probability of an unsuccessful design modification. Conclusions are drawn regarding stopping rule performance in terms of stopping rule signal location, utility loss, achieved reliability, and fraction tested. Both rules perform well and are implementable from a practical standpoint. Specific recommendations for stopping rule implementation are given based on the controllable factors, estimation methodology and lot size. / Master of Science