Non-linear design problem in a chemical kinetic model with non-constant error variance

For a locally optimum non-linear design problem for a chemical kinetic model, we investigate the influence of the dispersion structure of the random observation errors on the design and its efficiency. We find that there are two kinds of design determined by the model parameters and the error variance function: “interior” designs, and “boundary” designs that depend also on the design range. We give an exact criterion for determining which kind of design will arise and we illustrate the qualitative difference between the two kinds of design in terms of the design locus and the equivalence theorem. We tabulate quantitative details of the designs for a range of parameter values.