Latin Hypercube

 

Standard factorial designs (Tornado, Plackett-Burman, Box-Behnken, Central Composite Face etc.) limit each of the uncertainty variables to having a small number of distinct values, typically three levels of low, middle and high values (or -1,0,+1). Latin Hypercube designs use a different value for each variable in each generated experimental run (or in our case in each generated simulation deck). The sampling procedure is based on dividing the range of each uncertainty variables into N intervals of equal probability (where we are generating N samples). So in effect Latin Hypercube is a constrained Monte-Carlo sampling.

For each variable a value is generated randomly from each of the N equal probability intervals.The N generated values for each variable are then randomly combined without replacement to generate the N experimental runs or simulation decks.

In Rezen when the Latin Hypercube algorithm is selected, each uncertainty variable is defined by a probability distribution and its associated parameters, e.g. uniform distribution (with min and max), normal distribution with mean and standard deviation, truncated normal distribution (mean, standard deviation, lower cutoff, upper cutoff) etc.

Because the generated variable values are combined randomly there is an implicit assumption that there are no or at least minor interactions between variables, e.g. a higher value of one variable can be combined realistically with a lower value of another.