35 / 2023-03-29 17:06:31

Efficiency evaluations of statistical decision probabilities with multiple alternative hypotheses for quality control

Quality control; Data snooping; Multiple alternative hypotheses; Multivariate normal distribution

Efficiency evaluations of statistical decision probabilities with multiple alternative hypotheses are a prerequisite for data quality control in positioning, navigation, and many other applications. Commonly, one uses a time-consuming simulation technique to obtain the statistical decision probabilities or builds lower and/or upper bounds to control the probability, which may be unconvincing when the bounds are loose. We aim to provide a computationally efficient way to calculate the multivariate statistical decision probabilities when performing data snooping in quality control. However, accurate evaluation of those probabilities is complicated considering the complexity of the critical region where the integration intervals contain a variable corresponding to the one with the largest absolute value. Hence, to improve the calculation of statistical decision probabilities, a simplified algorithm for computing the probabilities under the critical region is proposed based on a series of transformation strategies. We implement the proposed algorithm in a simulated numerical experiment and a GPS single-point positioning experiment. The results show that the probabilities computed with the proposed algorithm approximate the results of the simulation technique, but the proposed algorithm is computationally more efficient.