Decisions Under Uncertainty: Probabilistic Analysis for Engineering Decisions

Uncertainty is an essential and inescapable part of life. During the course of our lives, we inevitably make a long series of decisions under uncertainty – and suffer the consequences. Whether it be a question of deciding to wear a coat in the morning, or of deciding which soil strength to use in the design of a foundation, a common factor in these decisions is uncertainty. One may view humankind as being perched rather precariously on the surface of our planet, at the mercy of an uncertain environment, storms, movements of the earth’s crust, the action of the oceans and seas. Risks arise from our activities. In loss of life, the use of tobacco and automobiles pose serious problems of choice and regulation. Engineers and economists must deal with uncertainties: the future wind loading on a structure; the proportion of commuters who will use a future transportation system; noise in a transmission line; the rate of inflation next year; the number of passengers in the future on an airline; the elastic modulus of a concrete member; the fatigue life of a piece of aluminium; the cost of materials in ten years; and so on. In order to make decisions, we weigh our feelings of uncertainty, but our decision-making involves quite naturally another concept – that of utility, a measure of the desirability, or otherwise, of the various consequences of our actions. The two fundamental concepts of probability and utility are related dually, as we shall see. They are both subjective, probability since it is a function of our information at any given time, and utility – perhaps more obviously so – since it is an expression of our preferences. The entire theory is behavioural, because it is motivated by the need to make decisions and it is therefore linked to the exigencies of practical life, engineering and decision-making.