Decisions in risk and reliability: An explanatory perspective

The paper discusses issues that surround decisions in risk and reliability, with a major emphasis on quantitative methods. We start with a brief history of quantitative methods in risk and reliability from the 17th century onwards. Then, we look at the principal concepts and methods in decision theory. Finally, we give several examples of their application to a wide variety of risk and reliability problems: software testing, preventive maintenance, portfolio selection, adversarial testing, and the defend-attack problem. These illustrate how the general framework of game and decision theory plays a relevant part in risk and reliability.