Error-in-variables model (EVM) methods require information about input and output measurement variances when estimating model parameters. In EVM, using replicate experiments for estimating output measurement variances is complicated, because true values of inputs may be different when multiple attempts are made to repeat an experiment. To address this issue, we categorize attempted replicate experiments as: i) true replicates (TRs) when uncertain inputs are the same in replicated runs and ii) pseudo-replicates (PRs) when measured inputs are the same, but unknown true values of inputs are different. We propose methodologies to obtain output measurement variance estimates and associated parameter estimates for both situations. We also propose bootstrap methods for obtaining joint-confidence information for the resulting parameter estimates. A copolymerization case study is used to illustrate the proposed techniques. We show that different assumptions noticeably affect the uncertainties in the resulting reactivity-ratio estimates.
Sequential model-based design of experiments (MBDOE) is used to select operating conditions for new experiments in a batch-reactor that produces bio-based poly(trimethylene) ether glycol (PO3G). These Bayesian A-optimal experiments are designed to obtain improved estimates of the 70 fundamental-model parameter estimates, while accounting for the model structure and for data from eight previous industrial batch-reactor runs. Settings are selected for three decision variables: reactor temperature, initial catalyst level, and initial water concentration. If only one new experiment is conducted, it should be run at high temperature, with relatively high concentrations of catalyst and initial water. When two new runs are conducted, one should use an intermediate catalyst concentration. The effectiveness of the proposed MBDOE approach is tested using Monte-Carlo simulations, revealing that the selected experiments are superior compared to new experiments selected randomly from corners of the permissible design space.
Sequential model-based design of experiments (MBDoE) uses information from previous experiments to select run conditions for new experiments. Computation of the objective functions for popular MBDoE can be impossible due to a non-invertible Fisher Information Matrix (FIM). Previously, we evaluated a leave-out (LO) approach that design experiments by removing problematic model parameters from the design process. However, the LO approach can be computationally expensive due to its iterative nature and some model parameters are ignored. In this study, we propose a simple Bayesian approach that makes the FIM invertible by accounting for prior parameter information. We compare the proposed Bayesian approach to the LO approach for designing sequential A-optimal experiments. Results from a pharmaceutical case study show that the Bayesian approach is superior, on average, to the LO approach for design of experiments. However, for subsequent parameter estimation, a subset-selection-based LO approach gives better parameter values than the Bayesian approach.