Testing multiple dispersion effects from unreplicated order-of-addition experiments

Optimal addition orders of several components can be determined systematically to address order-of-addition problems when active location and dispersion effects are both taken into account. Based on the concept of fiducial generalised pivotal quantities, a new testing procedure is proposed in this paper to identify active dispersion effects from unreplicated order-of-addition experiments. Because the proposed method is free of all nuisance parameters indexed by the requirement set, it is capable of testing multiple dispersion effects. Simulation results show that the proposed method can maintain the empirical sizes close to the nominal level. A paint viscosity study is used to show that the proposed method can be practical. In addition, testable requirement sets are characterised when an order-of-addition orthogonal array is used to design an experiment.