Chapter 2 - Mathematics for Probabilistic Safety

Abstract

This chapter gives an account of the uses of mathematics in probabilistic safety. Probabilistic safety evaluates the harmful effects of an artificial construct on human beings. This construct can be called an airplane, a plant, a facility, or a system, depending on the degree of its complexity. A logical system model consists of the important components of a system and the effects that the component failure has on the system's operability. This model treats each component as either working or not working. Hence, the state of the system may be represented by a logical equation composed of the states of its components. The chapter uses a set theory and a Venn diagram to show relationships between components and the system and to show the importance of the mincutset to calculate system probability. A system's risk is the product of its failure probability and the consequences of its failure. This chapter focuses on logic modeling and probabilities. Logic modeling uses the Boolean algebra that is based on two-state variables, whose reduction rules are explained in detail. Other concepts discussed in this chapter include definitions of probability, methods for combining probabilities, calculating failure rates from inspection and incident data by classical and Bayes statistics, treating of uncertainties as distributed variables, and calculating confidence intervals.