An Affine Invariant Spatial Ranked-Sign MEWMA Control Chart

• Activity Number: 239
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Jamil Zeinab*+ and Jamil Zeinab
• Companies: University of Northern Colorado and University of Northern Colorado
• Keywords: Affine-invariant ; Spatial ; Ranked-sign

Abstract

Nonparametric control charts are useful in statistical process control when there is limited knowledge about the underlying process output distribution, specifically when the process measurement is multivariate. We propose a new multivariate EWMA-type scheme for monitoring location parameters. The scheme is based on adapting a multivariate spatial signed-rank test. The test is affine-invariant and the weighted version of this test is used to formulate the charting statistic by incorporating the exponentially weighted moving average (EWMA) scheme. The test's in-control (IC) run length distribution will be examined and the IC control limits will be established for different multivariate distributions, both symmetrical and skewed. The average run length (ARL) performance of the proposed scheme will be computed using Monte Carlo Simulation for select parameters: smoothing, shift, and number of p-variate quality characteristics. The ARL performance will be compared to the performance of the Hotelling T2 and the multivariate exponentially moving average (MEWMA) control charts for observation vectors sampled the multivariate normal, multivariate t, and multivariate gamma distributions.