Abstract
Modeling correlated component failures poses a unique challenge for reliability researchers because it requires ingenuity to devise an approach free from the assumption that components fail in a statistically independent manner. Several studies have addressed this problem with models that introduce additional parameters to describe the correlated failure of components. However, these earlier techniques often require the correlations to be positive and almost always introduce an exponential number of correlation parameters. These restrictions limit the scalability of existing approaches for conducting sensitivity analysis on the correlation parameters, which could identify correlation reductions that would improve system reliability. This paper presents a technique for reliability and sensitivity analysis that requires only a quadratic number of correlation parameters, encompassing systems with both negative and positive component correlations. Unlike previous research, the proposed approach places no unnecessary restrictions on a system's correlation parameters. A series of examples illustrates the flexibility of the approach. The results quantitatively confirm that negative component correlation assists fault-tolerant systems to attain levels of reliability even higher than systems of statistically independent redundant components. Thus, the techniques introduced here offer a methodology to concisely measure the utility of negative component correlations on system reliability improvement.