On Nonparametric Phase-II Joint Monitoring of Location and Scale Based on a Single Chart

• Activity Number: 599
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Amitava Mukherjee*+
• Companies: Indian Institute of Technology, Madras
• Keywords: Average Run Length ; Cucconi Statistic ; Joint Monitoring ; Lepage Statistic ; Nonparametric ; Robust

Abstract

New developments on single control chart for joint monitoring of unknown process location and scale parameters are considered. While the assumption of normality is required for the validity of most of the charts available in the literature, we propose and study some distribution-free charts based on certain statistics. We also propose a follow-up diagnostic procedure useful to discover the type of shift the process may have undergone when the chart signals an out-of-control process. Control limits for the proposed chart are tabulated for implementation in practice for some typical nominal in control (IC) average run length (ARL) values. Large sample approximations to the control limits are also considered. Performance of the proposed charts are examined in a simulation study on the basis of the mean (average), the standard deviation, the median and some percentiles of the run length distribution. The effect of estimation of parameters is studied by examining the influence of the size of the reference (phase I) sample on the IC performance of the proposed charts. An illustration is given in the light of environmental monitoring. Summary and conclusions are offered.