A Distribution-Free CUSUM Control Chart for Joint Monitoring of Location and Scale

• 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): Amitava Mukherjee*+
• Companies: Indian Institute of Management
• Keywords: Ansari-Bradley Statistic ; Average Run Length ; CUSUM Lepage Chart ; Nonparametric ; Statistical process control ; Wilcoxon Rank sum Statistic

Abstract

In the present work, we have introduced a single distribution-free CUSUM chart based on Lepage statistics, referred to as CUSUM-Lepage (CL) chart. Like Shewhart-type chart, its nonparametric nature ensures that all in control (denoted IC) properties of the proposed chart remain invariant and known for all continuous distributions. Control limits are tabulated for implementation in practice. The IC and out of control (denoted OOC) performance properties of the chart are investigated through simulation studies in terms of the average, the standard deviation, the median and some percentiles of the run length distribution. Detailed comparison with Shewhart-type chart is presented. We also examine the influence of the reference sample size. The proposed chart is illustrated through a real data. Summary and conclusions are also presented.