Optimal design allocations for estimating area under curves for studies employing destructive sampling

Optimal allocations of experimental resources for the estimation of integrals is considered for experiments that use destructive sampling. Given a set of sampling times, a minimum mean square error rule is given for the allotment of fixed experimental resources to the independent variable. The results are seen to be functionally dependent upon the pattern of underlying variability assumed in the model and upon the quadrature rule used to estimate the integral. Extensions to other optimality criteria, including a minimum mean absolute deviation criterion, and to cases involving multiple treatment groups, are also noted.