Optimal allocation of measurements in a linear calibration process

A problem of allocation of measurements for a linear calibration process is considered in this article. It is assumed that a total of N measurements are made some of which may be measurements on two distinct standards, while the remaining measurements are on m different unknown specimens. We discuss allocation of the N measurements for the two standards and m unknown specimens based on A-optimality criterion, which is applied to asymptotic variances of maximum likelihood estimators for the true values of unknown specimens. It can be shown that the optimal allocation depends on the true values of unknown specimens. Hence, the user may resort to locally or Bayesian A-optimal measurement designs. Some practical solution is presented. Furthermore, the impact of prior on the allocation is also discussed.