Mixture distribution modelling of the sensitivities of a digital 3-axis MEMS accelerometers large batch

Huge quantities of low-cost analogue or digital MEMS sensors, in the order of millions per week, are produced by manufacturers. Their use is broad, from consumer electronic devices to Industry 4.0, Internet of Things and Smart Cities. In many cases, such sensors have to be calibrated by accredited laboratories to provide traceable measurements. However, at present, such a massive number of sensors cannot be calibrated and large-scale calibration systems and procedures are still missing. A first step to implementing these methods can be based on the distribution of the sensitivities of the large batches produced. Such distribution is also useful for sensor network end-users who need a single sensitivity, with the associated uncertainty, to be attributed to the whole network. Recently, a large batch of 100 digital 3-axis MEMS accelerometers was calibrated with a primary calibration system developed at INRiM and suitable for 3-axis accelerometers. Distributions of their sensitivities as a function of axis and frequency were analyzed and their non-normal behaviour was shown. However, in the preliminary phase of the study, the calibration uncertainties were not considered in these distributions. Therefore, in this paper, a mixture distribution modelling, based on Monte Carlo simulations and aimed at including the calibration uncertainties in the sensitivity distributions, is implemented and the resulting distributions are compared to the previous ones in histogram form. These distributions are also fitted with Johnson's unbounded and bimodal functions to get continuous distributions. This paper represents a further step towards the development of large-scale statistical calibration methods.