Based on linear models, the inference about the true measurement x$_{f}$ and the optimal designs x (nx1) for the calibration experiments are considered via Baysian statistical decision analysis. The posterior distribution of x$_{f}$ given the observation y$_{f}$ (qxl) and the calibration experiment is obtained with normal priors for x$_{f}$ and for themodel parameters (.alpha., .betha.). This posterior distribution is not in the form of any known distributions, which leads to the use of a numerical integration or an approximation for the calculation of the overall expected loss. The general structure of the expected loss function is characterized in the form of a conjecture. A near-optimal design is obtained through the approximation nof the conditional covariance matrix of the joint distribution of (x$_{f}$ , y$_{f}$ $^{T}$ )$^{T}$ . Numerical results for the univariate case are given to demonstrate the conjecture and to evaluate the approximation.n.