Design and Analysis of Experiments with Continuous On-O® Factors

Response surface methodology (RSM) is a well known technique in industrial statistics to identify optimal process and product settings. Most of the work in RSM were motivated by applications soon after World War II. Box and Wilson (1951) and Box (1957) set o® a wave of research in design, analysis and assessment of RSM. Hill and Hunter (1966) gave a detail review of work done during the 1950's and 1960's. Recent books, such as Box and Draper (1987), Khuri and Cornell (1987), and Myers and Montgomery (1995) cover the development of RSM in the past 45 years. Despite all these activities, little has been done on design and response optimization with continuous on-o® factors. Consider an experiment to determine the optimal placement of chines on an aircraft nacelle to increase maximum lift. A chine is an air de°ector that resembles the dorsal ̄n of a shark protruding from its body surface. A nacelle is the outer casting of an aircraft engine. Placing a chine on a nacelle is intended to provide a good mixing of vortices to create proper lift at a certain angle of attack. A chine can be placed in a location on either side of a nacelle. Suppose that the location within this region is represented by a horizontal (h) and a vertical (v) coordinates. Optimal placement implies that a chine must be present. Hence, an additional variable is needed to represent the presence and absence of a chine. The measure of lift is determined by the entire aircraft, so placing chines is merely an enhancement, and placing no chine is a possible combination in the experiment. Suppose that an experiment has M location to consider whenever a chine is placed on one side of a nacelle. Each nacelle has two sides. Then there areM ¤M+2¤M+1 = (M+1) possible