A Bayesian approach to gross error detection in chemical process data. Part I: Model development

Tamhane, A.C., Iordache, C. and Mah, R.S.H., 1988. A Bayesian approach to gross error detection in chemical process data. Part I: Model development. Chemometrics and Intelligent Laboratory Systems, 4: 33-45. A new statistical test based on the Bayesian approach for detecting gross errors in chemical process data is presented in this paper. Part I gives the theoretical development of the underlying model and the proposed test, while Part II gives the results of a simulation study for assessing the performance of the test. In Part I we first develop a one-time application of the Bayes test, and then embed it in a sequential setting. For this setting a probabilistic model is proposed for updating the prior probabilities of gross error occurrences in the light of accumulating data. Modifications in the basic model are suggested to take account of unknown magnitudes of gross errors and the aging of measuring instruments. Some practical difficulties in the application of the Bayes test, e.g., adjustments for unknown delay times in detecting gross errors in instruments, adjustments of instrument lifetimes when updating their failure probabilities, and computational complexity of the scheme, are discussed and heuristic methods for their amelioration are suggested.