Interactive effects of a quantitative and broadened interpretation of the double contingency principle

Implementation of the Double Contingency Principle (DCP) for defense-in-depth depends upon measures taken to prevent single failure cause of a criticality accident. In previously published work, the Markov method was shown to be useful for analyzing concurrency, and the independence of changes in process conditions was shown to be expressible quantitatively in terms of a correlation coefficient. Also in previously published work, interpretation of the correlation coefficient was broadened to include the augmentations of negative-definite values and of non-commutativity. In addition, previously published work examined the precepts of reliability analysis and the precepts of correlation analysis to show that the well-trodden path of the former can lead to more perceptive implementation of the latter, while the broadening of the latter can introduce new pathways to the former. In this paper, interactive effects of quantitative assessments of the likelihood, independence, and concurrency aspects of the DCP are examined. When such interactive effects are considered, the quantitative approach becomes more complex, and the use of related approaches, such as reliability analysis, becomes more limited. An illustrative example of the augmentations introduced in previous work is shown with consideration of interactive effects. (authors)