Probabilistic Design for Optimization and Robustness for Engineers

5 Modeling variation of complex systems

Before releasing a design, engineers must validate the design against all tolerances. Since a finished product is often a combination of many individual components, this task can be difficult. One approach to validation is to analyze worst-case tolerances. This task can be daunting as the number of combinations dramatically increases as the number of tolerances specified increases. For example, a simple design with 10 tolerances has 1024 possible combinations of high and low tolerance settings. A design with 20 tolerances has over one million combinations of high and low tolerance settings. In addition, as shown in Chapter 3, worst-case tolerance analysis is unrealistic. The likelihood of a part being produced with 20 tolerances all at the edge of the tolerance limit is highly unlikely.

Engineers need a method for modeling the variation of their design as a function of the variation of the inputs. This type of model not only allows validation, but also allows engineers to optimize the design against variation in the inputs and to identify the noncritical components for cost reduction efforts. Models for estimating system variance and expected value for simple systems were presented in Chapter 3. Mathematical complexity for these methods becomes overwhelming for all but the simplest engineering systems. Monte Carlo simulation, presented in Chapter 4, can be used to predict the variance and expected value for even the most complex systems, ...