The focus of this research is on estimation of the reliability of large systems. Reliability models previously used for space operations and maintenance schedules suffer from one or more of the following weaknesses.

1. Standard reliability models fail to accurately model multiple causal stresses leading to component failure, and they tend to focus on time to failure as the only variable of interest. The purpose of this research is to develop multivariate models accounting for several input variables affecting component survival functions. As an example, multivariate models might improve prediction of failure times for the oxidizer valves in the Shuttle's reaction control system. Let t1 and t2 denote soak and cycle times of an RCS valve and let R(t1,t2) be the corresponding probability that the valve is operating at those times. We are interested in estimating R under censorship of both the soak and cycle times to failure. More generally, we would like to estimate the component survival function R(t1,...,tn) with several causal stresses, expressed either in terms of the times those stresses have been operating or in terms of their magnitudes.

Some of the mathematical tools, e.g., multiple logistic binary response models and proportional hazards models, are already well established, although not in the context of system reliability.

2. Experience has shown that hazard rates of system components do not behave like simple textbook models. Even in cases where components have survived a "burn in" period before being placed in operation, it is sometimes observed that the hazard rate decreases for an initial period of time. This research aims at a better understanding of this phenomenon through randomized failure rates and mixtures of increasing failure rate models. A possible application would be early failure modeling of orbital replacement units on the International Space Station.

3. System reliability models usually treat component failures as independent events. For complex systems this can lead to unrealistic estimates of failure probability. The solution is to adequately model dependence in stress processes. The simplest models after independent component models are those obtained as mixtures of them. Their system survival functions can be expressed in terms such as

,

where Ri(ti,ui), the survival function of the ith component, depends on parameters ui and G is a multivariate distribution function. These models retain some of the tractability of systems with independent components. It remains to be seen whether they are practically useful.

References
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