Bayesian credible intervals for monitoring liquid blending rates

We consider the problem of constructing confidence intervals (CIs) for the blending coefficient of different liquid, such as the blended underground storage tank (UST) leak data for compliance. For this problem, confidence intervals based on Fieller's Method have been proposed. This method utilizes a blending coefficient estimator which is a ratio of two correlated normal random variables. However, this method assumes normally distributed random errors in the UST leak model and therefore may be inappropriate for the UST leak data which typically have heavy-tailed empirical distributions. In this paper we develop a Bayesian approach assuming non-normal random errors with the Power Exponential Distribution (PED). A real-data example using Cary blended site data is given to illustrate both the Fieller's CIs and the Bayesian credible intervals. Monte Carlo simulations are conducted to compare the coverage probability and average width of CIs for both methods. For data with heavy-tailed distributions, the simulations show that both Fieller's and Bayesian intervals perform adequately in terms of coverage. However, Bayesian intervals perform better in terms of yielding CIs with shorter expected width.