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.
KeywordsPredictive Distribution Predictive Density Yield Fraction Positive Covariance Prior Covariance
Unable to display preview. Download preview PDF.
- Chou, S.-K. (1988) Control and Planning of Co-Product Production, D.Eng. Dissertation, Industrial Engineering and Operations Research, University of California at Berkeley.Google Scholar
- Jewell, W.S. (1974) Model variations in credibility theory, in Credibility: Theory and Applications, Proceedings of Actuarial Research Conference on Credibility, Berkeley, September 1974, (P. Kahn, ed.). Academic Press, New York.Google Scholar
- Jewell, W.S., Chou, S.-K. (1988) Predicting multinomial bin splits with arbitrary yield information, ESRC 88–24, Engineering System Research Center, University of California at Berkeley.Google Scholar
- Jewell, W.S. (1989). A general framework for credibility prediction of first and second moments. ESRC 88–12, Engineering Systems Research Center, University of California, Berkeley. Insurance: Mathematics and Economics, 8, 127–136.Google Scholar