Quenouille's changeover designs

Abstract

Summary This paper examines the structure of some early examples of serial factorial changeover designs given by Quenouille (1953). Quenouille listed two designs for 3 treatments, 6 periods, 18 subjects and three designs for 5 treatments, 8 periods, 16 subjects. The present paper shows that Quenouille's cyclie method of construction can be extended to designs for any number t of treatments, 2t periods, and t 2 subjects. The enumeration of these designs is shown to be equivalent to the enumeration of Eulerian trails in certain directed graphs.