An Improved Estimation of Multiple-Point Fault Probabilities if the Faults Have Different Periodic Latencies

Abstract

Fault tree analysis (FTA), reliability block diagrams (RBD) and event tree analysis (ETA) are established methods for assessing potential risks of hazardous events, in particular when resulting from coincidental events. Combining the Boolean algebra, probability theory and reliability data, they allow quantitative estimation of intrinsic risks from technical equipment like machinery control, aerospace systems or vehicle functions, among many others.

The quantitative reliability theory was mainly developed between the 1960s and the 1980s. At that time, simplifications and approximations for the mathematical formulae were needed to achieve calculation results within acceptable time, regarding restricted computer resources.

Our investigation revealed that some of these simplifications and approximations, often assumed as precise calculations in secondary literature, can lead to wrong results in quantitative risk assessment. When faults are combined, and individual latency periods exist, the currently established approximations may lead to results which are too optimistic in comparison with a precise probabilistic approach.

This publication proposes a new approximation for the computation of the related probabilities. The approach provides an upper-bound estimation. Using the developed formulae, the under-estimation of multipleevent probabilities can be avoided.

In addition, certain vagueness and over-simplification in the probabilistic treatment of events with latency periods can be eliminated. Examples of related shortcomings in the literature can be found, down to the early roots of reliability theory.