High precision of about 0. 1 mm is required in the beam position measurement of TRISTAN MR(main ring) which is now under construction. In this respect, position measurement in the TRISTAN AR(accumulation ring) is reviewed. We found that the statistical study of the accumulated measuremnent data gives very useful information on the performance of the monitor system. For example, repeated COD measurements during a beam storage showed not only reproducibility of the position measurement (0. 05 mm) in the beam intens ity range of factor 50 but also pointed out troubles caused by poor contact in coaxial switches. Moreover, it suggested the criterion to abandon erroneous data. Programs for such check has been prepared and has improved the efficiency of COD correction. Improvements have also been made in the calibration and in the mechanical setting of the monitor chambers.