A Study of the Quantile Control Chart

• Activity Number: 37
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Rong Zheng*+ and Subhabrata Chakraborti
• Companies: University of Alabama and University of Alabama
• Keywords: quantile values ; control chart ; asymptotic chi-aquare statistic ; robutness

Abstract

Traditional control charts, such as Shewhart, CUSUM, and EWMA charts, typically monitor the mean and/or the standard deviation, but in many cases, monitoring the shape of the distribution is necessary. Grimshaw and Alt (1997) proposed a quantile control chart to monitor the quantile function of a continuous distribution by monitoring a selected set of quantiles. Their method is based on an asymptotic chi-square statistic. The main goal of this article is to examine the robustness of the quantile control chart under the situations where 1) the underlying distributions are of different shapes, 2) the number of chosen quantiles varies, and 3) the positions of the quantiles vary. By summarizing the simulation results, we provide recommendations for the implementation of the quantile control chart. We also examine an adjustment to the control limit to improve the performance of the quantile control chart.