Environmental stress screening (ESS) is employed to reduce, if not eliminate, the occurrence of early field failures. In this dissertation, a general stochastic modeling framework is presented for multi-component systems. Environmental stress screening can be performed at one or more assembly levels for a system. Systems are modeled as a series-series collection of components and connections. Components and connections are assumed to come from good and substandard populations and their time to failure distributions are modeled with mixture distributions. ESS models currently found in the literature assume that time to failure distributions are mixtures of exponentials. This dissertation extends previous work by examining mixtures of Weibull distributions for both components and connections. The mixed Weibull distribution is used to examine how screening strategies change when wear-out mechanisms are present. A further generalization is made by modeling components and connections with mixtures of phase-type distributions. Optimal screening strategies are developed using a variety of criteria. First, a life cycle cost model is developed for a general series-series multiple assembly level system. This is the first multi-component, multi-screening level cost model with imperfect failure detection to appear in the literature. Failure detection capability is shown to have a significant impact on the optimal screening strategy. Other criteria examined includes system mean residual life and system mission reliability. Finally, the impact of a systems structure on optimal screening strategies is explored.
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