A five-class variance swapping rule for simulation experiments: A correlated-blocks design

Abstract

A simulation experiment is frequently performed to estimate a metamodel, which is a functional relationship between the mean response of the simulation model and a set of simulation inputs. Variance Swapping Rules (VSRs), which assign pseudo-random number streams in simulation experiments, are often used to increase the precision of the functional relationship. This paper proposes a five-class VSR, which classifies all variances of the effects estimators into five classes for linear metamodels of 2 ^k factorial designs. The five-class VSR induces correlations among all blocks for which all design points have a special correlation structure. This five-class correlated-blocks VSR is a generalization of all existing VSRs, which are viewed as one, two, or three-class VSRs in terms of the variances of the effects estimators. The five-class rule provides a better VSR than the existing VSRs in that it allows one to make a finer distinction among all effects for which the variances are not allowed to be swapped in three-class VSRs.

Keywords::

• Simulation
• metamodel
• variance swapping rules
• 2 ^k factorial designs* correlated blocks

Acknowledgement

This research is supported by the National Science Council of the Republic of China under grant NSC-93-2213-E-007-060.

Notes

*This CB rule is equivalent to the MB rule.

**This CB rule is equivalent to the AR rule.

*Effects are A, B, C, D, AC, AD, BC, BD, ABC, ABD, ACD, BCD.

**This CB rule is equivalent to the MB rule.

***This CB rule is equivalent to the AR rule.

*Effects are A, B, C, D, ABC, ABD, ACD, BCD.

**This CB rule is equivalent to the MB rule.

***This CB rule is equivalent to the AR rule.