THE SYSTEMATIC-ERROR DETECTION AS A CLASSIFICATION PROBLEM

A classification approach to the detection of a systematic displacemen t Delta is described based on a single measurement mu = Delta + delta, where delta is a random error. Delta is supposed to be constant withi n a group of n measurements but may vary from one group to another. No rmal distributions N(Delta; 0, sigma(Delta)(2)) and N(delta; 0, sigma( delta)(2)) are assumed for Delta and delta, respectively. Two classes A and B are defined that correspond to the presence and absence of a s ignificant Delta. A classification rule: Delta is an element of A, if \mu\ less than or equal to beta, otherwise Delta is an element of B, i s used, where beta is an optimal threshold in the sense of minimal ave rage loss due to the classification errors. Also, an evaluation of the magnitude of the required correction is suggested based on the maximu m likelihood estimation of d. Experiments have been carried out to eva luate the efficacy of the approach, For this, 5000 groups of 25 measur ements each were simulated at different values of delta(Delta) and sig ma(delta). Comparison was carried out with the rule suggested by Eel e t al. (1993) in terms of (a) goodness, defined as a difference in perc ent between successful corrections and unsuccessful corrections, (b) m agnitude of the residual systematic displacement Delta(r), and (c) ave rage number of corrections. The obtained results have shown that the n ew approach outperforms Eel's rule for the tested parameters by about 30% in goodness and about 10% in Delta(r) at sigma(Delta) = sigma(delt a) = 2.0, but at the expense of a factor of 1.1 more corrections and m easurement of all displacements. Eel et al. measure about 10% of the d isplacements. The approach may be used in different areas like radiati on therapy, manufacture or process control.