Engineering Design Optimization Under Risk

Since engineering designs generally involve a number of elements about which only partial information is available, design optimization should be conducted under conditions of risk. Utility is nonlinear with cost or revenue; consequently, the enterprise's view of risk is considered through utilities assigned to costs or revenues which deviate from the mean. This is termed "risk programming" to distinguish it from previous contributions in this area. General forms of the objective function, yielding expected utility, are derived for utility functions of two types. When the total cost distribution is normal, an exact solution requiring only a knowledge of expected total cost and the cost variance is obtained. For nonnormal cost distributions, an upper bound of the objective function, requiring knowledge only of the same two quantities, is obtained. A model for engineering design, which provides both the expected total cost and cost variance, is developed based upon division of the elements of variability into several categories. With this division, a reasonable computational procedure is possible. The procedure has been incorporated into a modified direct search optimization program capable of solving large-size design problems.