Engineers are decision makers, and decision making is what distinguishes engineers from scientists. The decisions that engineers make are often of very high consequence, to the engineer himself or herself, to the engineer’s employer, and to society at large. The decisions that an engineer makes often affect his or her job security, income and opportunity for advancement, they impact the profitability or performance of the engineer’s employer, and they often impact the environment and our safety. Thus it makes sense that engineers study the mathematics of decision making in order to become better decision makers.
Three hundred years ago, Nicolas Bernoulli posed a problem known as the St. Petersburg paradox. The solution given by Daniel Bernoulli in 1738 marks the beginning of modern normative decision theory. The theory was embellished by Lewis Carroll in the adventures of Alice, and extended to decision making under uncertainty by John von Neumann and Oskar Morgenstern in the 1940s. This rigorous mathematic prescribes how a person should make decisions. It applies to all those aspects of engineering design and systems engineering that involve choice from among a set of alternatives.
Unfortunately, decision theory has not been included in most engineering curricula. In part, this is because it has not been presented in a way that is accessible by and pertinent to engineers and, as a result, we have suffered considerable loss. The purpose of this book is to make the theory accessible and to illustrate its application in many aspects of engineering decision making for product and system design.
The book begins with careful derivation of the mathematics of engineering decision making, beginning with the derivation of the number sets and arithmetical operations. It then provides a unique insight into the mathematics of optimization and prediction. From there, it derives the notion of expected utility and shows that there is one and only one way to correctly compare engineering alternatives. Next, the book addresses issues of aggregation, which are ubiquitous in engineering design processes, and illustrates serious pitfalls of typical aggregation processes. Finally, it introduces game theory in a way that provides deep insights into perplexing everyday situations.
The latter half of the book applies the theory to design and systems issues including determination of system reliability, optimization of system operation and maintenance, cost estimation and demand estimation. Throughout, the goal is to maintain a rational or fully self-consistent framework for design and systems engineering. The final chapter outlines the limits to rationality in these activities and offers suggestions for minimizing damage that might be caused by poor decision making in large programs.