Evaluation of operational system structures based on reliability data

Systems of components have a structure that plays an important role in determining how the reliability of the individual components relates to the reliability of the system. The system reliability can be computed from component reliabilities using results from basic probability theory in the simplest case with all of the components assumed to act independently of one another. However, in the case of dependence, such calculations can be much more involved. When reliability data have been independently collected on both the system and each component in the system, it can be difficult to model any possible dependence between components. Established methods use the known structure of a system, along with these data, to assess whether the reliability of the individual components are mutually independent. In this paper, we expand this methodology to include an assessment of the type of dependence that may exist between the components. This is based on finding the system structure that would most likely produce the observed reliability data, under independence. In the frequentist setting, the likelihood approach is used to find these structures and an observed confidence measure is used to assess the strength of the statistical evidence in favor of each possible structure. In the Bayesian setting, posterior probabilities along with Bayes factors are used. An example demonstrates how these methods can be used in an applied setting.