A sequential Bayesian cumulative conformance control chart for high yield processes

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Toubia, Gracia J.
Liao, Haitao
Twomey, Janet M.

For mass production, the traditional approach of drawing the confidence limits was satisfactory when many bad units were being produced; however, the same approach becomes ineffective for high yield processes, when the defective rates have small magnitudes, such as parts per million. In particular, the traditional p-control charts used to control nonconformance rates present many problems when p, the rate of nonconformance, is small. One problem is an increase in the probability of false alarm, and another is the increase in sample size, sometimes making the extremely large size of the sample prohibitive. The biggest problem with the pcontrol chart is discussed by Brown, Cai and DasGupta (2001), where the theory of the normal approximation to the binomial distribution is debunked and the need for rewriting the chapter on binomial distribution in statistics textbooks is suggested. Many rejoinders to this work also agree on this important discussion.

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Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Industrial and Manufacturing Engineering