Uncertainty Analysis of Two Gas Measurement DGA Ratios for Improved Diagnostics Applications

This paper formulates the exact analytical probability density function (PDF) for the ratio of two independent dissolved gas analysis (DGA) measurements that include individual gas measurement errors. It is demonstrated that for small DGA gas measurement errors, the correct two-gas ratio PDF approaches a conventional Gaussian distribution. As the measurement accuracy decreases, the ratio PDF becomes non-Gaussian with the maximum likelihood value of the PDF deviating from the true underlying value. For larger errors, the maximum likelihood estimate of the gas ratio deviates significantly from presumed Gaussian statistics. A method for debiasing measured gas ratio values is presented and a simple application is used to demonstrate the proposed approach.