A Bayesian Approach Employing Generalized Dirichlet Priors in Predicting Microchip Yields

用貝式統計分析來做晶片生產的預測

10.29977/JCIIE.200505.0003

翁慈宗(Tzu-Tsung Wong)

Bayesian analysis ； conjugate ； correlation ； generalized Dirichlet distribution

工業工程學刊

22卷3期（2005 / 05 / 01）

210 - 217

英文

在Jewell和Chou所討論的微電子晶片生產模式中，晶片需按照大小來分成四類，由於有些晶片類別產生的機率存在著正相關的關係，因此不適合假設各個晶片類別產生機率的連結分佈為Dirichlet分佈，Jewell和Chou便提出求近似解的方法，他們的方法很難用來計算變數二階以上的動率，而且用來預測生產量的計算較複雜，因此本研究假設各個晶片類別產生機率的連結分佈為generalized Dirichlet分佈，然後用貝氏統計的方式來預測各類晶片的生產量。由於在generalized Dirichlet分佈中，允許各變數間為正相關，而且對於相同期望值的變數，允許它們有不同的變異數，因此對本問題而言，generalized Dirichlet分佈是一個合適的多變量機率分佈。本研究所採用的貝氏統計分析方式，對於預測生產量的計算，比求近似解的方法簡單，可計算變數二階以上的動率，而且在使用的時機上較不受限制。

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.

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