Design of Experiments for Estimating Inverse Quadratic Polynomial Responses

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Abstract
The precision of the parameter estimates from nonlinear response curves depends on the number of positioning of the levels of the stimulus variable and the parameter values. For the four-parameter inverse quadratic polynomial we show that the optimal designs have four geometrically spaced levels. The efficiencies of equally and geometrically spaced designs with more than four levels are compared and it is shown that it is important to extend the range of experimentation as far as possible and that designs with six levels over a wide range with a geometric spacing factor of 2 are robust to a wide range of parameter values.