670 – Advances in Statistical Process Control
Adjustment for Phase II �� Chart Control Limits Based on Tolerance Intervals
Martin GC Sarmiento
PUC-Rio
Subhabrata Chakraborti
University of Alabama
Eugenio K. Epprecht
PUC-Rio
Since some works in SPC have revealed that a large amount of Phase I data is required to attain an appropriate specified Phase II performance of control charts, some authors have proposed to adjust the control limits in order to achieve the conditional (given the parameter estimates) in-control performance for a given amount of Phase I data. The use of statistical tolerance limits as adjusted control limits is considered in the recent literature on X-bar charts based on the conditional performance perspective, e.g., corrected control limits are obtained for guaranteeing a tolerated conditional false alarm rate (CFAR) or, equivalently, the conditional in-control average run length, with a specified high probability. In this paper, assuming normality, we propose the required adjustments for the two-sided S^2 chart control limits to ensure a specified CFAR, where the adjusted control limits are based on a statistical tolerance interval for sample variances. This ensures that the interval between the adjusted lower and upper limits contain at least a specified proportion of the S^2 distribution with a certain (specified) high confidence.