Robust balanced measurement designs when errors are serially correlated

This paper considers the situation in which some characteristic is to be measured on each of several specimens. For instance, it may be the concentration of lead or arsenic in water or soil samples and a laboratory may routinely analyze samples from different sources. In the measurement process, there may be some serial correlation among measurement errors, but it is hard to detect or to have a reliable estimation for this existing phenomenon. Therefore, it may be desired to make statistical inference on the true values of unknown specimens without estimating this possible correlation. To help adjust the instrument readings in a process, standards are frequently interspersed among unknown specimens at appropriate intervals. A systematic method of arranging the order of the measurements of unknown specimens and standards is provided. One is able to avoid the difficulty of estimating the possible correlation and still has good estimates of the parameters of interest using the proposed measurement designs. In addition, a simulation study is carried out to evaluate the sensitivity of the measurement designs, showing that they are robust to the existence of various error processes.