Optimal coordinate sensor placements for estimating mean and variance components of variation sources

In-process optical coordinate measuring machines offer the potential to diagnose the sources of the variations that are responsible for product quality defects. Such a sensor system can thus help manufacturers to improve product quality and reduce process downtime. The effective use of sensor data in the diagnosis of the sources of variations depends on the optimal design of the sensor system, which is often also called the problem of sensor placement. This paper addresses coordinate sensor placement for the diagnosis of dimensional variation sources in assembly processes. Sensitivity indices for the detection of the process mean and variance components are defined as the design criteria and are derived in terms of process layout and sensor deployment information. Exchange algorithms, originally developed for optimal experimental design, are revised and then used to maximize the detection sensitivity. A sort-and-cut procedure is proposed, which is able to significantly improve the algorithm efficiency of the current exchange routine. The resulting optimal sensor layout and its implications are illustrated in the specific context of a panel assembly process.