A Multivariate Sign Chart for Monitoring Process Shape Parameters

Abstract

This paper develops a new multivariate nonparametric statistical process control (SPC) control chart for monitoring shape parameters, which is based on integrating a powerful multivariate spatial-sign test and exponentially weighted moving average (EWMA) control scheme to on-line sequential monitoring. It has a strictly distribution-free property over a broad class of population models, which implies the in-control run-length distribution can attain or is always very close to the nominal one when using the same control limit designed for the multivariate normal distribution. This proposed control chart possesses some other positive features: its computation speed is fast with a similar computation effort to the parametric multivariate EWMA (MEWMA) counterpart; it is easy to implement because only the multivariate median and the associated transformation matrix need to be estimated from the historical data before monitoring; it is efficient in detecting small or moderate shifts, when the process distribution is heavy tailed or skewed; it is also able to handle the case when the sample size is one and is effective in downward shifts. Simulation comparisons and a real-data example from a white-wine production process show that it performs quite well in applications.

• Distribution-Free
• Multivariate Covariance Matrix
• Nonparametric Procedure
• Robustness
• Statistical Process Control

Additional information

Notes on contributors

Zhonghua Li

Dr. Li is Assistant Professor in the LPMC and School of Mathematical Sciences. His email is [email protected].

Changliang Zou

Dr. Zou is Associate Professor in the LPMC and School of Mathematical Sciences. His email is [email protected]. Dr. Zou is the corresponding author.

Zhaojun Wang

Dr. Wang is Professor in the LPMC and School of Mathematical Sciences. His email is [email protected].

Longcheen Huwang

Dr. Huwang is Professor in the Institute of Statistics. His email is [email protected].