Probabilistic Design for Optimization and Robustness for Engineers

3 Introduction to variation in engineering design

Engineers spend years studying physical models that are used to predict system behavior from input parameters. For example, an engineer may estimate the deflection in a beam based on the beam length, width, height, and modulus of elasticity. Typically, engineers are not taught to model the stochastic behavior of systems. Variability in design inputs is addressed through extreme techniques such as worst-case analysis and safety factors. This text presents the methods engineers may use to expand physical models to predict the variation in systems as a function of the variation of the input parameters. This prevents over designing and allows true system optimization including cost and performance of all functions.

3.1 Variation in engineering design

Variation is a part of the world we live in. The voltage measured at each of the outlets in your home will not be identical. The weight of each lug nut retaining the wheels on your car will vary. This variation makes life difficult for engineers. Engineers and process designers must understand and compensate for variation. The product engineers design may behave unexpectedly because the nominal values specified on drawings are difficult to achieve.

A parameter diagram (P-diagram), shown in Figure 3.1, is an ideal document for identifying sources of variation. A P-diagram shows the inputs, outputs, error states, control factors, and noise factors for a system. The design engineer has ...