A time-dependent methodology for fault tree evaluation

Abstract A methodology is developed by which exact and detailed probabilistic information is obtained for any fault tree. The methodology, called “Kinetic Tree Theory”, is believed to be a major advancement in the field of reliability and safety analysis and is expected to have far-reaching ramifications. The first assumption of Kinetic Tree Theory is that the primary failures, or components, of the fault tree are independent; one primary failure may occur at any number of places in the fault tree, but those primary failures which are unique are assumed independent. Inter-dependent primary failures can be handled by extension of the methods presented. The second and last assumption of Kinetic Tree Theory is that the mode failures (critical paths) of the fault tree are known. These are obtainable in a straightforward manner from the fault tree as is demonstrated. Fault trees of any structure and of any complexity are handled. General failure and repair distributions are handled; there is no limitation to these distributions as in other methodologies. Complete probabilistic information is first obtained for each primary failure of the fault tree, then for each mode failure (critical path), and finally for the top failure itself. The information is obtained as a function of time, and hence, with regard to reliability and safety; complete kinetic behavior is obtained. The expressions developed are in a simple form, and as is shown, application to yield numerical results is both efficient and straightforward — with an average computer time on the order of one minute required for a 500 primary failure fault tree (on an IBM 360/75 computer).