A New R-Ordering Procedure to Rank Multivariate Performances

Performance analysis has become a strategic activity in managing complex systems. The aim of this activity is often benchmarking, that is the comparison among various units on the basis of performance. In statistical terms this corresponds to search for an ordering of units described by a set of p indicators. In this paper we propose a new reduced ordering procedure for multivariate observations based on determining a meaningful direction for the problem in the Euclidean p-dimensional space. Namely, the direction is the one which goes from the “worst” performing units to the “best”, that is the “worst-best” direction. Some proposals for the “worst” and “best” case construction are offered along with the related reduced ordering procedure. Some geometric issues and statistical properties of the proposal are discussed.