The mathematics of motif combination and their use for functional simulation

The concept of Motif Combination was introduced in the French Automotive industry's R&W standard. There has however been no formal mathematical theory for the technique of motif combination. This paper sets out to develop this theory. The main result of the paper is a set of four properties that the motif combination rules must satisfy in order to have certain desirable metrological properties. Motif methods may well provide useful techniques which complement rather than replace the traditional approach based on a mean line. It was found that many functional problems could be simulated very efficiently using motif methods. Examples of functional simulation via motif combination are illustrated in the paper.