Guidelines for placing additional sensors to improve variation diagnosis in assembly processes

Dimensional variation reduction is critical to assuring high quality in assembly and manufacturing processes. The extent to which data from a multiple-sensor system aids the diagnosis of variation sources depends on the effective placement of the sensors. The diagnostic objective that we consider is to estimate the variance components for potential variation sources. Using a linear structured model to represent the effects of the variation sources on the measurement data, this paper studies the problem of how to add additional sensor(s) to ensure diagnosability and/or improve estimation accuracy. Most prior work on sensor placement focused on automated numerical search algorithms that optimize rather unintuitive mathematical measures of diagnosability and accuracy. Our objective is to translate the measures into expressions that provide better conceptual guidance into how to most appropriately locate additional sensors to improve accuracy and diagnosability. The expressions may be used in conjunction with qualitative judgment and expert knowledge as the basis for locating additional sensors. Alternatively, they can be used in conjunction with existing numerical search routines by providing initial guesses for the sensor location and/or substantially narrowing the space of feasible sensor locations that must be searched during the numerical optimization. The proposed method is illustrated with examples from automotive panel assembly.