Phase I Control Chart Based on a Kernel Estimator of the Quantile Function

• Activity Number: 235
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Quality and Productivity
• Author(s): Gary R. Mercado*+ and Michael D. Conerly and Marcus Perry
• Companies: University of Alabama and University of Alabama and University of Alabama
• Keywords: kernel estimation ; bandwidth ; root mean square error ; average run length ; Shewhart control chart

Abstract

To measure the statistical performance of a control chart in Phase I applications, the in-control average run length (ARL) is the most frequently used parameter. For start up situations, control limits must be computed without knowledge of the underlying distribution of the quality characteristic, in many cases. Assumptions of an underlying normal distribution are not always fulfilled and can increase the probability of false alarms which can lead to unnecessary process adjustments. In this talk, a control chart based on a kernel estimator of the quantile function is suggested. Monte Carlo simulation and the mean absolute index (MAI) were used to evaluate the in-control ARL performance of this chart relative to that of the Shewhart individuals control chart. Results indicate that the proposed chart is robust with respect to the in-control ARL and results in an alternative method of designing control charts for individual units.