Detection of Thermometer Clustering in the Calibration of Large Batches of Industrial Thermometers for the LHC by Automated Data Processing

The complete procedure to calibrate thermometers is a complex process, especially when several thousand semiconductor-type thermometers are used and must be individually calibrated, as in the case of the instrumentation of the new Large Hadron Collider (LHC) machine at CERN. Indeed, the similarity of the characteristics of semiconducting thermometers is more limited than that of wire-wound thermometers. The span of the characteristics spread can appear as a homogeneous set, or can show clusters (groups) of characteristics. In the latter case, one of the reasons for clustering may be the fabrication process by batches of numerous devices on the same wafer. Consequently, the detection of the groups can be useful, from the supplier point of view, to give information relevant to improving the fabrication uniformity. From the user point of view, it is useful for making a guess of the possible thermometer stability with time, when this is a must, as in the LHC case. In fact, thermometers showing characteristics outlying or in small clusters should be considered to be potentially anomalous. In addition, the identification of anomalous groups allows the detection of artifacts due to the experimental process. For a large number of thermometers, this analysis requires the use of automated procedures and, consequently, automated decisions that avoid false effects. The paper describes the mathematical methodology adopted for the identification of the clusters, based on the mixed-effect modeling of the thermometer characteristics.