Ms Helena Billington
Two stage sampling with application to the wine industry
The wine industry is important to many countries, including Australia. Cork taint is a significant problem for this industry. The majority of cork taint is caused by the chemical 2,4,6-trichloroanisole (TCA). TCA manifests as an unpleasant odour or taste and causes billions of dollars of loss each year. If a winery receives complaints about a batch of wine, they will conduct a survey to try to quantify the rate of taint in the batch. This analysis may provide evidence that substandard corks are the likely cause of the taint. If the winery brings legal action against the cork supplier, a loss assessor will usually seek to quantify, separately, the proportion of tainted bottles in the batch. The current method is to select a sample, and then retain some of the bottles and send the rest of the sample to a independent chemical laboratory to test for TCA traces. In present practice, the total sample size, and the number of bottles retained are usually not determined on statistical grounds. This thesis addresses this problem and ?nds a solution that minimizes the expected number of bottles needing to be tested overall. The method described uses Bayesian methods to incorporate the data collected by the winery, and basic marginalization and minimization techniques. The method described uses information available about overall rates of taint to ?nd a suitable prior for the proportion of tainted bottles in a randomly selected batch of wine. This also utilizes the Bayesian idea of conjugacy to allow ease of calculations. The method for determining the optimal size sample to test initially is highly dependent on the winery data, and slightly in?uenced by the choice of prior. A mathematical exploration of the use of Stirling's approximation for the Gamma function enables an approximate solution to be found directly.