Predicting Coproduct Yields in Microchip Fabrication
Microelectronic chips are produced in larger units called wafers. Because of process variation, the hundreds of chips from each wafer differ slightly in electronic and physical characteristics, and are thus considered to be different products. The automatic sorting of these wafers, called ‘bin splitting’, leads to variable joint output in the different product categories. Prediction of future coproduct output is of obvious importance in production planning to meet future demand.
The natural model for bin splitting is a multinomial process, but the sorting probabilities are usually not known with certainty, as the engineers regularly ‘tweak’ the process to try and improve yields in certain categories. Furthermore, actual production data shows that some of these sorting probabilities tend to have positive covariance between different lots, which eliminates the Dirichlet as an appropriate prior. There are no other standard analytic priors from which to calculate predictive distributions. Instead, this study develops approximate linearized joint forecasts of mean yields that require only (arbitrary) prior means and covariances. Predictive approximations can also be developed for coproduct yield (co)variance.
KeywordsCovariance Sorting Peaked Under Sampling
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