The objective in probabilistic design is to reduce the effects of probabilistic
characteristics of design parameters onto design performance. Generally these effects are
grouped as reliability, robustness, and reliability and robustness.

Reliability

In engineering, reliability is the ability of a system or component to perform its
required functions under stated conditions for a specified period of time. It is
often reported in terms of a probability. During the design process, one of the
requirements can be a minimum level of reliability on a design specification such as
the probability of strength values to be greater than stress values have to be
greater than Po; such as, 95%; meaning that the design has to be at least 95%
reliable with respect to strength requirements.

In Figure 2, two PDF curves are given. The PDF in solid corresponds to a design
with a large area under its curve on the right curve tail violating the g
constraint. In order to increase the reliability of this performance, this area
needs to be reduced; meaning possible number of failures needs to be reduced. This
can be achieved by shifting the mean of performance away from the constraint. The
dotted PDF corresponds to such a design and it can be seen that the area under the
curve in the infeasible area is much smaller than the previous one.

Robustness

A system or design is said to be "robust" if it has minimal change of performance
when subjected to variations in its design; for example, its performance is
consistent within the variations.

Robustness of a product can be improved by shrinking the “variation of
performance”.

Reliability and Robustness

Simultaneously shifting the mean of performance and shrinking the variation of
performance, leads to both reliability and robustness improvement.

Stochastic Assessment

Sampling-based methods generate many random samples and evaluate whether performance
function is violated. They typically use random numbers; the ones that do not use
random numbers are called quasi Monte Carlo methods. Sampling-based methods are also
known as Monte Carlo methods.

In HyperStudy, the following sampling-based methods for
reliability and robustness assessment can be used.

Simple Random

Latin HyperCube

Hammersley

Modified Extensible Lattice Sequence

Simple Random and Latin HyperCube
are based on pseudo-random numbers, whereas Hammersley and
Modified Extensible Lattice Sequence are based on deterministic points.