Analysis of Replicated Order-of-Addition Experiments

The objective of the order-of-addition (OofA) problem is to find the optimal (addition) order. Existing literature concentrated on the responses of different orders with homoscedasticity. Study was made here for the cases of heteroscedasticity, where the dispersion effects for replicated OofA experiments should be considered. This paper proposes some approaches to speculate optimal orders for the replicated OofA experiment. Based on the pair-wise-order (PWO) model, the obtained orders from the proposed methodologies not only achieve the goal of OofA experiment, but also minimize the standard deviation within the OofA framework. Theoretical support is given under the specific setups. Simulation studies are used to illustrate these methodologies. It is shown that the proposed methods perform well for replicated OofA experiments.