Evaluating Measurement Uncertainty in Absolute Gravimetry: an Application of the Monte Carlo Method

Absolute gravity measurements are based on the reconstruction of the free-falling motion of a test body in vacuum. In this paper, two large disturbing effects are studied, namely, the non- gravitational accelerations originated by rotation and translation of the flying body. Their contribution to the uncertainty of the free-fall acceleration is evaluated using the method proposed in Supplement 1 to the GUM. The analysis is specifically applied to the IMGC-02 absolute gravimeter, but can be easily extended to other instruments

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

Bayesian analysis of repeated measurements affected by a systematic error and its application to conformity assessment

The Bayesian analysis of a series of correlated indications of an unknown quantity is here presented when they are modelled by a joint Gaussian distribution and their covariance is assumed to be the (known) squared uncertainty associated with a systematic effect common to all the indications. An interesting application of the obtained results to the conformity assessment of a series production is also presented. A criterion is derived so that at least a portion p1 of the series production shows to have a characteristic value below a prescribed limit, with a probability not less than p2