MonitoringStrategiesfor Chatter Detection In a Drilling ProcessAmor Ben Salah MessaoudDoctoral Thesissubmitted in partial fulfillmentthe requirements for the Degree of“Doktor der Naturwissenschaften”in the Department of StatisticsUniversity of DortmundDortmund, November 2006Pru¨fungskommission:Prof. Dr. Joachim Kunert (Vorsitzender) Universita¨t DortmundProf. Dr. Claus Weihs (Gutachter) Universita¨t DortmundProf. Dr. Franz Hering (Gutachter) Universita¨t DortmundProf. Dr. Mohamed Limam (Gutachter) University of TunisDr. Uwe Ligges (Beisitzer) Universita¨t DortmundTag der mu¨ndlichen Pru¨fung: 21. Dezember 2006cCopyright 2006 by Amor MessaoudAll rights reservedDEDICATIONTo the memory of my fatherandto my mother for her unconditional love, sacrificesand supportThis page intentionally left blankContentsAcknowledgements v1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Introduction to Statistical Process Control (SPC) . . . . . . . . . . . . . . 21.3 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4I ANonparametric ControlChartforMultivariateData 72 TheRankBasedMultivariateEWMAControlChart 92.1 Data Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 The Proposed rMEWMA Control Chart . . . . . . . . . . . . . . . . . . . 122.3 Asymptotic Average Run Length of the In-Control Process . . . . . . . . 132.4 Illustrative Example .