Classification on Quality Control Using Unsupervised Learning

• Main Authors: Shui-Ching Chang, 張水清
• Other Authors: Tze-Fen Li
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/68468282859873215266

博士 === 國立中興大學 === 應用數學系 === 93 === A set of unlabelled items is used to establish a decision rule to classify defective items. In this study, we suppose that the lifetime of an item has an exponential distribution and a Weibull distribution. The Bayes decision rule needs to know the prior probability (defective percentage) and two mean lifetimes in exponential distribution and needs four parameters in Weibull distribution. In the set of unidentified samples, the defective percentage and parameters are unknown. Hence, before we can use the Bayes decision rule, we have to estimate these unknown parameters. In this study, a set of unlabelled samples is used to establish a decision rule which leads to a stochastic approximation procedure to estimate these unknown parameters. The Bayes decision rule with these estimated parameters is called an empirical Bayes (EB) decision rule. When the size of unlabelled items increases, the estimates computed by the procedure converge to the true parameters and hence gradually adapt our EB decision rule to be a better and more accurate classifier until it becomes the Bayes decision rule. The results of a Monte Carlo simulation study are presented to demonstrate the convergence of the correct classification rates made by the EB decision rule to the highest correct classification rates given by the Bayes decision rule, and the speed of estimates converge to true parameters in the general Weibull distribution case is fast except (a,b)=(1,1), which is the exponential distribution. Hence the estimates for the Weibull distribution are more stable and accurate except (a,b)=(1,1), which is the exponential distribution.