Overview

Probabilistic thinking is based on very old ideas which go back to De Mere [1], La Place [2], and Bayes [3]. What is probability and how does it relate to frequency, statistics and, finally, machinery reliability? The word probability has several meanings. At least three will be considered here.

One definition of probability has to do with the concept of equal likelihood. If a situation has N equally likely and mutually exclusive outcomes, and if n of these outcomes are event E, then the probability P( E) of event E is:

(3.1)

This probability can be calculated a priori and without doing experiments.

The example usually given is the throw of an unbiased die, which has six equally likely outcomes the probability of throwing a one is 1:6. Another example is the withdrawal of a ball from a bag containing four white balls and two red ones the probability of picking a red one is 1:3. The concept of equal likelihood applies to the second example also, because, even though the likelihoods of picking a red ball and a white one are unequal, the likelihoods of withdrawing any individual ball are equal.

This definition of probability is often of limited usefulness in engineering because of the difficulty of defining situations with equally likely and mutually exclusive outcomes.

A second definition of probability is based on the concept of relative frequency. If an experiment is performed N times, and if...