Component-Based System Reliability Considering Positive and Negative Correlation

Most methods to model system reliability assume component failures are statistically independent. A smaller number of studies propose methods to characterize various forms of correlation or dependence but the majority of these consider only positive correlation or dependence. To fill this gap, this paper presents an approach to quantify the reliability of component-based systems subject to positive and negatively correlated component failures. The approach enables the derivation of algebraic system reliability expressions containing a vector of non-identical component reliabilities and matrix of non-identical pairwise correlations representing the correlation between the failures of the components. The approach is demonstrated through a series of examples, which quantify the impact of positive and negatively correlated component failures on system reliability. Our results indicate that the approach can quantify the negative and positive impact of correlation on system reliability. Thus, the approach can be used to identify correlations detracting from system reliability.