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The Latin Hypercube - Monte Carlo DOE algorithm generates random numbers conforming to several Statistical Distributions.
The Latin Hypercube Sampling (LHS) is a particular Monte Carlo Sampling: more precisely it is a constrained Monte Carlo (i.e. random) sampling scheme. The constraint refers to the way each variable is sampled: the statistical distribution is split in n equally probable intervals, and then a random value is selected within each interval, clearly according to the density function. In this way the points are relatively uniformly distributed over the density function range. On the contrary, with the Monte Carlo scheme, n values are chosen independently, according to the global density function.
Compared to Monte Carlo, LHS maps better the marginal probability distributions (i.e. the statistical distribution of each single variable), especially in case of small number of generated designs.
Given a multivariate statistical distribution, the Monte Carlo technique samples the joint probability distribution (i.e. the statistical distribution of all the variables) generating independently the values of the marginal probability distributions (i.e. the statistical distribution of each single variable). LHS arranges the values of the marginal probability distributions in order to sample the multivariate space in a relatively uniform way. In both cases the variables are considered to be indipendent, i.e. not correlated. Especially in case of small number of generated designs, there could be a small residual correlation between the variables: this can be reduced using two different iterative methods, i.e. the Reduce Correlation and the Maximize Minimum Distance criteria.
Several parameters can be defined for this algorithm:
Sampling Scheme two options exist:
Monte Carlo Monte Carlo sampling technique.
Latin Hypercube Latin Hypercube sampling technique.
Number of Designs a positive integer number between 1 and the maximum number of designs (i.e. 64000).
Reject Out of Bounds Samples check box will let the DOE to automatically keep or reject values that do not respect variables bounds.
Criterion three options exist:
None No iterative method is performed in order to guarantee the indipendence of the variables of the generated designs.
Reduce Correlation The configuration with the minimum variables correlation is chosen.
Maximize Minimum Distance The configuration with the greatest minimum distance is chosen. The distance is defined in the space of multivariate uniform distribution.
Number of Iterations a positive integer number between 1 and the maximum number of iterations (i.e. 9999). This parameter is used if one of the above iterative methods is performed.
Random Generator Seed a positive integer number, used for sequence repeatability. If two Latin Hypercube - Monte Carlo Sequences are created with the same seed, they will generate and return identical sequences of numbers. If the seed value is 0, the sequence is automatically seeded with a clock value.
The Distribution type and parameters for each variable. For a short description of the available distributions and parameters refer to Statistical Distributions.
Note:
To obtain a "correct Distribution" the input variables should be continuous (i.e. bases should be equal to zero).
