Response Surface Models with Mixed Effects


Khuri, Andre I.   (1996, ASQC)   University of Florida, Gainesville, FL

Journal of Quality Technology    Vol. 28    No. 2
QICID: 11448    April 1996    pp. 177-186
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Article Abstract

The purpose of this article is to demonstrate how to conduct a response surface investigation concerning a linear model that contains, in addition to fixed polynomial effects, a random effect representing an extraneous source of variation. The model also contains interactions involving the random effect. Estimates of the polynomial effects are obtained in a two-stage procedure. The variance components of the random effects are first estimated by applying the method of restricted maximum likelihood. The resulting values are then used to compute generalized least-squares estimates of the polynomial effects. This procedure leads to an expression for predicting the response within a certain region of interest. R Optima of the predicted response are determined over portions of R in which the prediction variance falls within specified bounds. Finally, a procedure is described for establishing operating conditions that result in a predicted response close to some target value. A numerical example is given for illustrative purposes.


Maximum likelihood estimate (MLE),Random effects,Prediction

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