Reliability and Robustness

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.


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.

Figure 1. Example: Reliability
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.

Figure 2. Improving Reliability of a Performance


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”.

Figure 3. Improving Robustness of a Performance

Reliability and Robustness

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

Figure 4. Improving Reliability and Robustness Simultaneously

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.

Figure 5. Position of the Sampling in the Stochastic Analysis

Figure 6. Illustration of the Sampling