Again you need to provide an interface to transfer input data to this program and get output data (the loads) back to ANSYS. If there is more than just one single load value generated by the program then you should also check for potential correlations.

1.4.1.4. Distribution Functions

Beta Distribution

The Beta distribution is very useful for random variables that are bounded at both sides. If linear operations are performed on random variables that are all subjected to a uniform distribution then the results can usually be described by a Beta distribution. An example is if you are dealing with tolerances and assemblies, where the components are assembled and the individual tolerances of the components follow a uniform distribution. In this case the overall tolerances of the assembly are a function of adding or subtracting the geometrical extension of the individual components (a linear operation). Hence, the overall tolerances of the assembly can be described by a Beta distribution. Also, as previously mentioned, the Beta distribution can be useful for describing the scatter of individual geometrical extensions of components as well. The uniform distribution is a special case of the Beta distribution.

Exponential Distribution

The exponential distribution is useful in cases where there is a physical reason that the probability density function is strictly decreasing as the random input variable value increases. The distribution is mostly used to describe time-related effects; for example, it describes the time between independent events occurring at a constant rate. It is therefore very popular in the area of systems reliability and lifetime-related systems reliability, and it can be used for the life distribution of non-redundant systems. Typically, it is used if the lifetime is not subjected to wear-out and the failure rate is constant with time. Wear-out is usually a dominant life-limiting factor for mechanical components, which would preclude the use of the exponential distribution for mechanical parts. However in cases where preventive maintenance exchanges parts before wear-out can occur, then the exponential distribution is still useful to describe the distribution of the time until exchanging the part is necessary.

Gamma Distribution

The Gamma distribution is again a more time-related distribution function. For example it describes

the distribution of the time required for exactly k events to occur under the assumption that the events take place at a constant rate. It is also used to describe the time to failure for a system with standby components.

Gaussian (Normal) Distribution

The Gaussian or normal distribution is a very fundamental and commonly used distribution for statistical matters. It is typically used to describe the scatter of the measurement data of many physical phenomena. Strictly speaking, every random variable follows a normal distribution if it is generated by a linear combination of a very large number of other random effects, regardless which distribution these random effects originally follow. The Gaussian distribution is also valid if the random variable is a linear combination of two or more other effects if those effects also follow a Gaussian distribution.

Lognormal Distribution

The lognormal distribution is a basic and commonly used distribution. It is typically used to describe the scatter of the measurement data of physical phenomena, where the logarithm of the data would follow a normal distribution. The lognormal distribution is very suitable for phenomena that arise from the multiplication of a large number of error effects. It is also correct to use the lognormal distribution