An Introduction to the Basics of Reliability and Risk Analysis: Series in Quality, Reliability and Engineering Statistics, Vol. 13

The subject of risk has become very popular in the last few years and is much talked about at all levels of industry. We shall first give a definition of risk in qualitative terms and then translate it in quantitative terms [5] in the following Section.
A first, intuitive observation comes from the fact that there is risk if there exists a potential source of damage, or hazard. When a hazard exists, e.g. posed by a system which in certain conditions may cause undesired consequences, safeguards are typically devised to prevent the occurrence of such hazardous conditions and its associated undesired consequences. However, the presence of a hazard does not suffice itself to define a condition of risk. Indeed, inherent in the latter there is the uncertainty that the hazard translates from potential to actual damage. Thus, the notion of risk involves some kind of loss or damage that might be received and the uncertainty of its transformation in an actual loss or damage:
This qualitative analysis is reflected in the various Dictionary-definitions of risk, such as 'possibility of loss or injury and the degree of probability of such loss'.
Let x and p denote a given damage and the probability of receiving such damage, respectively. From a quantitative point of view, it is common to define a measure of the...