ENBIS-18 in Nancy

2 – 25 September 2018; Ecoles des Mines, Nancy (France) Abstract submission: 20 December 2017 – 4 June 2018

The Steady-State Behavior of Multivariate Exponentially Weighted Moving Average Control Charts

4 September 2018, 12:00 – 12:20

Abstract

Submitted by
Sven Knoth
Authors
Sven Knoth (Helmut Schmidt University, University of the Federal Armed Forces Hamburg)
Abstract
Multivariate Exponentially Weighted Moving Average (MEWMA) charts are popular, handy and effective procedures to detect distributional changes in a stream of multivariate data. For doing appropriate performance analysis, dealing with the steady-state behavior of the MEWMA statistic is essential. Going beyond early papers like Prabu and Runger (1997), we derive quite accurate approximations of the respective steady-state densities of the MEWMA statistic. It turns out that these densities could be rewritten as the product of two functions depending on one argument only, which allows feasible calculation. Using the new methods it was found that for large dimensions, the steady-state behavior becomes different to what one might expect from the univariate monitoring field. Based on the integral equation driven methods, steady-state and worst-case average run lengths are calculated with higher accuracy than before.

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