Multivariate control charts for calibration of hydrophones using the Mahalanobis statistic

Statistical analysis of data to ensure the validity of calibrations can be challenged when the measurement model describes a process and result that spans a high-dimensional parameter space. Calibration of hydrophones presents one such case whereby the sensitivity to acoustic pressure is calculated using measured values for several different quantities and the result is needed at many excitation frequencies distributed over a large bandwidth. We addressed this challenge by developing a multivariate statistical analysis procedure that supports efficient and effective process control for hydrophone calibrations. We first characterize the in-control condition by the mean and covariance of measurements expressed in a p-dimensional parameter space using a curated training data set. We then test subsequent measurements against a control limit using Hotelling's T (2)-test to compare the current measurement process to the training data. We report a case study for secondary calibration of hydrophones spanning a frequency range of 1 kHz-200 kHz where we detected an emergent defect in the laboratory's calibrated reference hydrophone by inspection of data presented in multivariate control charts. Process control data collected during calibration services exceeded the control limits in intermediate and high-frequency bands by factors of 5.1 and 11.2, respectively. The process remained in control for the low-frequency band. These observations were consistent with misalignment of the reference hydrophone's sensitive element, which we confirmed upon disassembly, inspection and repair of the instrument.