Effects of correlation on fraction non-conforming statistical process control procedures

High-yield production processes that involve a low fraction non-conforming are becoming more common, and the limitations of the standard control charting procedures for such processes are well known. This paper examines the control procedures based on the conforming unit run lengths applied to near-zero-defect processes in the presence of serial correlation. Using a correlation binomial model, a few control schemes are investigated and control limits are derived. The results reduce to the traditional case when the measurements are independent. However, it is shown that the false alarm rate cannot be reduced to below the amount of serial correlation present in the process.