A Bayesian statistical method for large-scale MEMS-based sensors calibration: a case study on 100 digital accelerometers

Abstract

Low-cost sensors and in particular micro-electro-mechanical systems (MEMS) devices are widely used in many applications, including consumer electronics, healthcare, automotive, and industrial automation. Their large-scale production (typically in the order of millions per week in a single factory) would require the calibration of a huge number of devices that would be costly and time-consuming. A solution can be found in the use of statistical methods in order to (at least partially) substitute for the typical calibration procedures. In this work, we propose a Bayesian method to statistically calibrate large batches of sensors using probabilistic models and prior knowledge. The method involves experimentally calibrating only a small sample of sensors, then infer the number of reliable sensors in the entire batch and assign an appropriate uncertainty to all the sensors. Therefore, it can be considered as a statistical calibration of the batch. The Bayesian nature of this approach allows reducing the number of experimental calibrations by incorporating the prior knowledge coming from the previous calibration of a ‘benchmark’ batch, which is performed ‘once and for all’ and is representative of the whole production process. The application and validation of the method are performed through the calibration of 100 digital MEMS accelerometers. Validation results showed an acceptable agreement between experimental-based bootstrap and theoretical values, with relative differences within ±7%.