Bounding the times to failure of 2-component systems

Characterizing the distribution of times to failure in 2-component systems is an important special case of a more general problem, finding the distribution of a function of random variables. Advances in this area are relevant to reliability as well as other fields, and influential papers on the topic have appeared in the reliability field over a span of many years. Using failure times of 2-component systems as a vehicle, this report begins by reviewing a technique for characterizing distributions of functions of random variables when the dependency relationship between the random variables used as inputs to the function is unknown. The technique addressed is called Distribution Envelope determination (DEnv). Using this review as a foundation, an extension to DEnv is described which applies to cases where means and variances of the input distributions are known, and partial information about dependency is available in the form of a value for correlation. Pearson correlation is used because it is the most commonly encountered correlation measure. This reason is important because the assumption of independence, while common, is frequently problematic. Yet the opposite extreme of no assumption about dependency may mean ignoring available information which could affect the analysis.