A linear mixed-effects calibration in qualifying experiments

In many applications, controls are used to monitor the process or experiment and to assess whether the process is in control or the experiment is valid. In this case, the traditional fixed-effects calibration is usually not adequate, but a mixed-effects model is appropriate. In this article, a linear mixed-effects calibration model is considered to qualify an experiment. Two estimating methods for the controls based on maximum likelihood and restricted maximum likelihood are proposed. The bias and mean squared error performances are studied by simulation. Five different methods to construct confidence intervals for the controls are compared. A dataset is used to demonstrate the advantages of the mixed-effects model.