How to elicit a cost function? Lessons of hope and disappointment from a diced bacon case-study

Résumé

Statistical decision theory provides an attractive framework to help choose decisions under uncertainty. Unfortunately, it does not seem to be often implemented for specific applications. In this paper, we rely on this theory to determine the optimal sampling plan for a plant producing diced bacon. Sampling plans are widely used in the food industry to assess the quality of products. After presenting the most common sampling plan in use, we developa Bayesian reanalysis to interpret the common practice for sampling by attribute. Then, we turn to a more elaborate problem and propose a way to get the best plan by minimizing the expected cost a food plant could face. Although the cost function was designed to be easily understandable by manufacturers, we encountered difficulties in determining the correct costs through discussion with an expert. After correction, our alternative approach gives applicable results. We finally discuss what we learnt from this practical experience and give our thoughts on how cost elicitation could be improved and extended by discussing with more manufacturers.