The optimum design of industrial experiments

Two important problems in industry are the control of an "ongoing process", and the improvement (which will hopefully lead to the optimization) of a process. The two chapters of this dissertation attack problems in these two areas. To improve an ongoing process often it is desired to examine the relationship between variables in a process, say between a y variable where y represents a "response" variable and x₁, x₂, ..., x[subscript n], where the x 's represent "input" or "control" variables. In Chapter I we develop optimum composite designs for fitting a quadratic response surface under the standard regression assumptions, and solve some related design of experiments problems. The optimization criterion we use is the minimization of the generalized variance (the |x'x| criterion). In an ongoing process where readings of process variables and outputs are taken to aid in the control of a process, the so-called "V" mask proposed by Barnard [1959] has been a useful control scheme. In Chapter II we investigate the properties of a modified "V" mask control scheme which enables the quicker detection of large shifts of the mean from the desired operating levels