Response Surface Models with Mixed Effects
作者:
KhuriAndréI.,
期刊:
Journal of Quality Technology
(Taylor Available online 1996)
卷期:
Volume 28,
issue 2
页码: 177-186
ISSN:0022-4065
年代: 1996
DOI:10.1080/00224065.1996.11979658
出版商: Taylor&Francis
关键词: Maximum Likelihood;Prediction;Random Effects;Variance ComponentsS
数据来源: Taylor
摘要:
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 ofRin 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.
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