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Biometrika 1978 65(3):541-551; doi:10.1093/biomet/65.3.541
© 1978 by Biometrika Trust
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Design criteria for detecting model inadequacy

E. R. JONES1 and T. J. MITCHELL2

1Chevron Research Company Richmond, California
2Union Carbide Corporation, Nuclear Division, Computer Sciences Division Oak Ridge, Tennessee

Two criteria are proposed for choosing response surface designs for detecting inadequacy of the assumed model. They are both members of classes of criteria proposed by Atkinson & Fedorov (1975a), and are based on maximizing in some sense the expectation of the residual sum of squares over the region in the parameter space where the departure of the true surface from the assumed model is deemed unacceptable. Characterizations of these criteria are obtained and used to construct optimal designs for first-order versus second-order polynomial models. In the simple one-dimensional case, a simulation comparison of these designs with minimum bias designs and D-optimal designs for the higher-order model is made under a procedure in which the outcome of the lack of fit test determines the model to be used.

Key Words: D-optimality • Lack of fit • Model inadequacy • Optimal experimental design


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