A bayesian approach employing generalized dirichlet priors in predicting microchip yields

In the production model studied by Jewell and Chou, since some of the sorting probabilities for different categories of microelectronic chips tend to be positively correlated, a Dirichlet distribution is an inappropriate prior for that model. Jewell and Chou therefore propose an approximation approach to predict coproduct yields. Since a generalized Dirichlet distribution allows variables to be positively correlated, a Bayesian method by assuming generalized Dirichlet priors is presented to calculate the probabilities of future yields in this paper. We consider not only the mean values, but also either the variances or the covariances of the sorting probabilities to construct generalized Dirichlet priors. The numerical results indicate that the generalized Dirichlet distribution should be a reasonable prior, and the computation in forecasting coproduct output is relatively straightforward with respect to the approximation approach.