A Markovian model to study products shelf-lives

We consider an experiment where a panel of assessors are asked to assess the quality of a product at different intervals of time. The assessment of the panellists consists in rating the products on a categorical scale ranging from ‘fresh’ to ‘very decayed’. We wish to investigate the dynamic of degradation. We propose a Markovian modelisation for the decay of the products in the course of time. Markov chains models are based on the estimation of a transition matrix which states the probability that the assessment of a product changes from one category to another.The advantage of using transition matrices lies in the fact that they give a simple representation of the dynamic of degradation. Moreover, these transition matrices may be used in conjunction with correspondence analysis in order to investigate the evolution of the decay of the products (different conservation modes, different composition, …). The efficiency of the general approach is demonstrated on the basis of real data sets.