# Uncertainty in Design

Many factors can be a source for variations in design parameters changing the nature of a design problem from deterministic to probabilistic.

These factors can be due to various types of uncertainty.

Physical uncertainty:
• Boundary and initial conditions
• Material properties
• Geometry
Numerical simulation uncertainty:
• Conceptual modeling
• Mathematical modeling
Manufacturing:
• Sheet metal thickness
• Welds
• Random design (controlled) variables
• Direction
• Magnitude
• Random noise (uncontrolled) variables
Material data:
• Elastic properties
• Failure
• Random noise or input variables

Uncertainties can affect input variables, also called controlled parameters, such as thickness or stiffness. They can also affect design parameters, also called uncontrolled or noise parameters, such as temperature or humidity. The resulting variations in these parameters are usually modeled by one of the many probability distribution functions based on their nature. In HyperStudy, normal, uniform, weibull, triangular, and exponential distributions are available.

Corresponding to the variations in controlled or uncontrolled parameters, the design performance will also have variations. In Figure 1 probabilistic characteristics of both the parameter types and output response are shown with a typical probability density function, PDF, curve. PDF curve is a plot of variable values and corresponding probabilities. PDF describes the range of values that a probabilistic variable can attain along with the occurrence probability of each value.