Experimental Design for Sensitivity Testing: The Weibull Model

Abstract

Attribute responses are often elicited by the simultaneous action of two or more variables. Experimental design and parameter estimation schemes, analogous to the familiar univariate plans, are developed here for the bivariate case. Using general exponential distributions of the form P(U = I) = exp (−γ). where γ is a suitably defined function, the elements of the information matrix are derived explicitly. Minimizing the determinant of this matrix. which is equivalent to minimizing the generalized variance. leads to optimal experimental designs. Explicit derivations are presented for univariate and bivariate exponential and Weibull distributions. The conditions are detined under which sequential optimal designs based on these results can be used.