ABSTRACT
Design of a car, aircraft, or cell phone is a decision inwhich a designer selects the configuration that is likely to produce the most desirable outcome (e.g., highest profit). There are many sources of uncertainty in design, including variability in material properties and geometry, human errors and operating conditions. Figure 3.1 explains the role of uncertainty in design and shows three important tasks
for managing it: a) modeling uncertainty in the variables that drive the performance of a design or the profit from a risky venture, b) estimation of the resulting uncertainty in the performance, and c) selection of the best design. In this last step, the designer should account for his/her attitude toward risk. This chapter presents probabilistic tools for the first two tasks for managing uncer-
tainty; model sources of uncertainty and estimate the resulting uncertainty in the performance of a system (Figure 3.1). Probability is viewed as the long-term relative frequency of an event. Objective probability deals with averages of mass phenomena such as arrival of
customers in a bank, stamping of parts in a factory, telephone calls in a call center, and failure of a system. Certain averages converge to a constant value (long-term average) with the number of observations. For example, the average time to failure of a pump approaches a constant with the number of pumps tested. Probability and statistics process knowledge about these averages. The term statistics
refers to methods for estimating long-term averages from observations. For example, statistical methods estimate the average frequency of failure of a fuel pump from records. Probabilistic methods calculate long-term averages of some events from those of other events. For example, using probabilistic methods, we can find the probability that no more than three out of 100 pumps will fail over a certain period, given the probability of failure of a single pump. This chapter explains the fundamental concepts of probability theory in three
sections. First, the definition and properties of objective probability are presented. Probability distributions, which are tools for modeling uncertainty in experiments with numerical outcomes (such as the demand for a new product, the stress in a rod or the time to failure of a pump), are studied. The second section reviews the properties of common probability distributions.
Experimental and analytical studies have shown that some distributions describe well
some uncertain quantities. This section provides guidelines for selecting a distribution for a probabilistic analysis or a design problem. The last section studies the fundamental problem of calculating the probability dis-
tribution of a function of random variables and presents tools for solving this problem. These tools enable a decisionmaker to quantify uncertainty in the payoff of a risky venture or the uncertainty in the performance of a design. This information is important for selecting the best course of action among alternatives. This chapter also demonstrates through examples that probabilistic analysis can
help people avoid bad decisions by enabling them to estimate the probabilities of the consequences of their actions. A bad decision is one that a person would avoid if an expert had shown him that it was likely to produce undesirable consequences.
