Minimal number of runs for an orthognal array

In this example we calculate the minimum number of runs required for an orthogonal array. For more details, see Schoen et al.

import itertools
import numpy as np


def minimum_number_of_runs(factor_levels, strength):
    """Calculate the minimum number of runs for an orthogonal array

    The minimum number of runs is based on the strength conditions. IWhether a design actually exists
    Args:
        factor_levels: Factor levels of the design
        strength: Strength of the array
    Returns:
        Minimum number of runs

    """
    runs = [np.prod(tt) for tt in itertools.combinations(factor_levels, strength)]
    N = np.lcm.reduce(runs)
    return N

We run the method on several examples.

strength = 3
factor_levels = [2, 3, 3, 4, 5]
N = minimum_number_of_runs(factor_levels, strength)

print(f"for a design of strength {strength} and factor levels {factor_levels} we require (a multiple of) {N} runs")

for a design of strength 3 and factor levels [2, 3, 3, 4, 5] we require (a multiple of) 360 runs

strength = 2
factor_levels = [3, 2, 2, 2, 2]
N = minimum_number_of_runs(factor_levels, strength)

print(f"for a design of strength {strength} and factor levels {factor_levels} we require (a multiple of) {N} runs")

for a design of strength 2 and factor levels [3, 2, 2, 2, 2] we require (a multiple of) 12 runs