Fundamentals

While predicting the performance of a system, analysts use models that are deterministic in nature meaning that a simulation produces the same output for a given set of model input parameters. It is a well known fact that these parameters such as material properties, loads are rarely deterministic in nature. Engineers compensate for this loss of accuracy by imposing a factor of safety on their required performances however this may lead to unnecessarily overdesigns.

There are three main reasons why engineers have not been doing stochastic studies. First, there was a lack of stochastic data. Second, efficient tools to study stochastic studies were not available. Third, even with efficient tools, incorporating design variations to the design process is expensive and demanding both in terms of computational resources and post processing capabilities.

As optimization-driven design is gaining ground, inclusion of variations while solving for the design problem is becoming more critical. It is a known fact that optimization tends to push the design requirements to their bounds meaning that at the optimal designs most constraints would be just satisfied with no safety margins. If variations are significant and if a possible failure is expensive, reliability and robustness requirements have to be incorporated into the optimization problem.

In this chapter, we will cover the definitions in reliability and robustness. Then we will discuss methods for reliability and robustness assessment and different types of probabilistic design optimization.