A Multivariate Sign EWMA Control Chart

Changliang Zou · Fugee Tsung

190 citations0/0 files storedTechnometrics

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

Nonparametric control charts are useful in statistical process control (SPC) when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate SPC methodology for monitoring location parameters. It is based on adapting a powerful multivariate sign test to online sequential monitoring. The weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme, which results in a nonparametric counterpart of the classical multivariate EWMA (MEWMA). It is affine-invariant and has a strictly distribution-free property over a broad class of population models. That is, the in-control (IC) run length distribution can attain (or is always very close to) the nominal one when using the same control limit designed for a multivariate normal distribution. Moreover, when the process distribution comes from the elliptical direction class, the IC average run length can be calculated via a one-dimensional Markov chain model. This control chart possesses some other favorable features: it is fast to compute with a similar computational effort to the MEWMA chart; it is easy to implement because only the multivariate median and the associated transformation matrix need to be specified (estimated) from the historical data before monitoring; it is also very efficient in detecting process shifts, particularly small or moderate shifts when the process distribution is heavy tailed or skewed. Two real-data examples from manufacturing show that it performs quite well in applications. This article has supplementary material online.

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References

1992Introduction to Statistical Quality Control 1990Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements 1992A Multivariate Exponentially Weighted Moving Average Control Chart 1972An Approach to the Probability Distribution of Cusum Run Length 1998Cumulative Sum Charts and Charting for Quality Improvement 1988Multivariate Generalizations of Cumulative Sum Quality-Control Schemes 1999Research Issues and Ideas in Statistical Process Control 2006Effects of Parameter Estimation on Control Chart Properties: A Literature Review

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2019Nonparametric (distribution-free) control charts: An updated overview and some results 2018Some perspectives on nonparametric statistical process control 2012A spatial rank‐based multivariate EWMA control chart 2014An Efficient Online Monitoring Method for High-Dimensional Data Streams 2015A Distribution-Free Multivariate Control Chart 2012

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