A New Approach to Rank Several Multivariate Normal Populations with Application to Life Cycle Assessment

The need to establish the relative superiority of each treatment when compared to all the others, i.e., ordering the underlying populations according to some pre-specified criteria, often occurs in many applied research studies and technical/business problems. When populations are multivariate in nature, the problem may become quite difficult to deal with especially in case of small sample sizes or unreplicated designs. The purpose of this work is to propose a new approach for the problem of ranking several multivariate normal populations. It will be theoretically argued and numerically proved that our method controls the risk of false ranking classification under the hypothesis of population homogeneity while under the nonhomogeneity alternatives we expect that the true rank can be estimated with satisfactory accuracy, especially for the “best” populations. Our simulation study proved also that the method is robust in the case of moderate deviations from multivariate normality. Finally, an application to a real case study in the field of life cycle assessment is proposed to highlight the practical relevance of the proposed methodology.