Probabilistic Design for Optimization and Robustness for Engineers

8 Modeling system cost and multiple outputs

Chapter 7 presented methods for optimizing variation in design outputs. This chapter extends the optimization to consider additional factors such as component cost and manufacturing cost. This is an alternative to using the desirability index explained in Chapter 6. The methods presented in Chapter 7 are also extended to systems with multiple outputs, and offer techniques for large systems having hundreds or even thousands of inputs.

8.1 Optimizing for total system cost

Achieving a design that is insensitive to input variation is of no use if the design is too expensive to take to market. Consider the circuit example discussed in earlier chapters. If an attempt is made to minimize the sensitivity of power to voltage and resistance, the result will be a very large nominal voltage and resistance. The physics of the system yield lower power sensitivity as resistance increases.

Minimizing output sensitivity is considered a good design practice, but this objective is not independent. Insensitivity reduces scrap and re-work, which have associated costs. These costs must be balanced against the cost of the design. There is no value in reducing the scrap and re-work costs by 50% if the design costs are increased by more than 50%.

Example 8.1¹

The power in a circuit is

(8.1)

where V is the voltage and R is the resistance.

Given the following ...