A Linear Rank Nonparametric CUSUM Control Chart for Detecting Mean Shifts

• Activity Number: 169
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Gary Mercado*+ and Subha Chakraborti
• Companies: Utah Valley University and University of Alabama
• Keywords: Distribution free ; Linear Rank Statistic ; CUSUM ; Robustness ; Statistical Process Control

Abstract

In this talk, we introduce a new distribution-free control chart based on a suitable linear rank statistic to detect possible shifts of a monitored process. The choice of a suitable rank test should depend on the underlying density function of a process output, i.e. it may be symmetric or asymmetric and it may have short, medium, or long tails. In most cases, practitioners have no clear idea of the distribution of the data. Thus, an adaptive test should be applied since it takes into account the given data set. In a first stage, the unknown distribution function is classified with respect to some measures like tailweight, skewness, or leptokurtosis. Then, an appropriate linear rank test for that classified type of distribution is selected. A numerical study carried out reveals that the proposed control chart is more attractive to the practitioner since it has a know and stable in-control performance and has a better out-of-control performance than the traditional CUSUM Control Chart.