4 Normative Decision Analysis in Engineering Design

The basis of making design decisions can be found in decision analysis. Fundamental to decision analysis is the concept of value, which measures what is preferred or desirable about a design [1]. This is the underlying principle behind decision-based design (DBD), which states that engineering design is a decision-making based design exploration task mainly involving three important factors: (1) human values; (2) uncertainty; and (3) risk [1–4]. While DBD has seen substantial growth in recent years, decision analysis itself is an already matured field and has been widely applied to many fields, including engineering. Seminal works relating to system engineering were published by Dr. Howard in the 1960s [5–7]. He has documented a clear overview of the normative decision analysis process and how it can be applied to system engineering. Figure 4.1 presents a schematic representation of his normative decision analysis procedure. This self-explanatory figure captures the essence of the decision-making process and how it relates to human thoughts, feelings and decisions. Paraphrasing Dr. Howard, normative decision analysis does not eliminate judgment, intuition, feelings or opinion. Instead, it provides a mathematical framework to quantify them and express them in a form where logic can operate on them, instead of being buried in a human mind, where we cannot get access to them.

The purpose of decision analysis is to achieve a rational course of action by capturing the structure of a problem relationship and by treating the uncertainty through subjective probability and of attitude towards risk using expected utility theory. The underlying concepts found here are universal, and arguably, they are more relevant today as the computational efforts required to execute design decisions are becoming more feasible due to improved computing capabilities.

Expected utility theory is a normative decision analysis approach with three main components: options, expectations and value, where the decision rule is that the preferred decision is that option with an expectation of the highest value (utility). It is based on the premise that the preference structure can be represented by real-valued functions and can provide a normative analytical method for obtaining the utility value (“desirability”) of a design with the rule of “the larger the better” [8]. Five major steps associated with this technique are [8]:

(1) Identification of significant design attributes and the generation of design alternatives

(2) Verification of relevant attribute independence conditions

(3) Evaluation of single-attribute utility (SAU) functions and trade-off preferences

(4) Aggregation of SAUs into a system multi-attribute utility (MAU) function

(5) Selection of the alternative with the highest MAU value by rank-ordering alternatives

Here, the mechanism to get preference structure is based on the notion of the lottery, referred to as a von Neumann-Morgenstern (vN-M) lottery, and by employing the certainty equivalent, which is the value at which the decision-maker is indifferent to a lottery between the best and the worst [8]. The lottery questions provide the basis for describing the logic between attribute bounds, where analytical function formulations are typically used to complete the preference structure description. Similarly, lottery questions form the basis for eliciting trade-off information among attributes [8].