A Sequential Bayesian Cumulative Conformance Count Approach to Deterioration Detection in High Yield Processes Gracia Toubia-Stucky, a Haitao Liao b * † and Janet Twomey c Cumulative conformance count (CCC) control chart is a powerful alternative to the traditional p-control chart, particularly in monitoring high yield processes with extremely low proportions of nonconformance. However, a prevalent limitation of the CCC control chart is its inability to detect small process deterioration. A sequential Bayesian CCC approach capable of detect- ing small process deterioration is proposed in this paper. The new approach outperforms the traditional CCC chart in that it does not require a large sample of initial observations of the process, which may be difficult, if not impossible to obtain in practice. Moreover, the approach is self-starting, and thus may be used in short production runs. A Bayesian updating procedure is developed, which allows for the determination of initial control limits based on only three initial observations or some prior knowledge about the proportion of nonconformance of the process. Values of proportions of nonconformance, ranging from 0.1 to 0.00001, are tested to demonstrate the deterioration detection capability of the new approach in con- junction with the proposed deterioration detection rules. Copyright © 2011 John Wiley & Sons, Ltd. Keywords: high yield process; cumulative conformance count chart; sequential Bayesian 1. Introduction R are events usually contain important information and may lead to significant, adverse consequences. As a result, it is essential to monitor such events to quickly respond to a shift, particularly an increase in their frequency of occurrence. Demand for the strong capability of rare event monitoring partly stems from stringent quality requirements for highly technological products ranging from surveillance systems used in the area of healthcare 1,2 to production of microelectronics. In modern manufacturing pro- cesses, the commitment to high quality is leading to significant decrease in product defective rates. The defective rate of a so-called high yield process is in such a small magnitude as parts per million (ppm). One example of high yield processes is the thermo-sonic wire bonding, 3 where the defective rate is about 116ppm. Another example is the fabrication of integrated circuits as stated by Pesotchinsky. 4 Traditional process control approaches perform well when defective rates are high, but they are ineffective in handling such high yield processes. The p-control chart is a traditional approach to monitoring the proportion of nonconformance based on the binomial distribution, and the control limits (CLs) are easy to calculate. 5 Based on the central limit theorem, it appears that the larger the sample size, the better the normal approximation. In addition, it has been widely accepted that the actual coverage of the confidence interval of this method is close to the nominal level except when the sample size is small’, and/or the proportion of nonconformance p is close to zero or one. 6–10 However, an important finding by Brown et al. 11 debunks the normal approximation behind the p-control chart and shows some unpredictable and problematic behaviors of the binomial distribution. Many statisticians suggest readdressing this issue in statistics books. There are other obvious obstacles facing the implementation of the p-control chart in high yield environments, primarily because of its inability to detect process shift and because of the increase in the rate of false alarms. Other problems with the p-control chart are negative lower control limits (LCL) and the significant increase in sample size under such circumstances. 12 a Department of Mathematics, College of Coastal Georgia, Brunswick, GA 31520, USA b Department of Nuclear Engineering/Department of Industrial and Information Engineering, University of Tennessee, Knoxville, TN 37996, USA c Department of Industrial and Manufacturing Engineering, Wichita State University, Wichita, KS 67226, USA *Correspondence to: Haitao Liao, Nuclear Engineering & Industrial and Information Engineering, University of Tennessee, Knoxville, TN 37996, USA. † E-mail: hliao4@utk.edu Copyright © 2011 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2012, 28 203–214 Research Article (wileyonlinelibrary.com) DOI: 10.1002/qre.1236 Published online 16 August 2011 in Wiley Online Library 203