Bayesian credible intervals for monitoring liquid blending rates

Abstract

We consider the problem of constructing confidence interval s (CIs) for the blending coefficient of different liquid, suc h as the blended underground storage tank (UST) leak data for compliance. For this problem, confidence intervals based on F ieller's Method have been proposed. This method utilizes a blending coefficient estimator which is a ratio of two correlated norma l 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 develo p 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 C Is 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 an d Bayesian intervals perform adequately in terms of coverage. However, Bayesian intervals perform better in terms of yielding CIs with shorter expected width.