Page 190 - Contributed Paper Session (CPS) - Volume 6

CPS1870 Longcheen H. et al.

A spatial rank-based EWMA chart for monitoring
linear profiles
Longcheen Huwang, Jian-Chi Lin, and Li-Wei Lin
Institute of Statistics National Tsing Hua University Hsinchu, Taiwan

Abstract
Profile monitoring has been recently considered as one of the most promising
areas of research in statistical process monitoring (SPM). It is a technique for
monitoring the stability of a functional relationship between a dependent
variable and one or more independent variables over time. The monitoring of
linear profiles is the most popular one because the relationship between the
dependent variable and the independent variables is easy to describe by
linearity, in addition to its flexibility and simplicity. Furthermore, almost all
existing charting schemes for monitoring linear profiles assume that error
terms are normally distributed. In some applications, however, the normality
assumption of error terms is not justified. This makes the existing charting
schemes not only inappropriate but also less efficient for monitoring linear
profiles. In this article, based on the spatial rank-based regression, we propose
a charting method for monitoring linear profiles where the error terms are not
normally distributed. The charting scheme applies the exponentially weighted
moving average (EWMA) to the spatial rank of the vector of the Wilcoxon-type
rank-based estimators of regression coefficients and a transformed error
variance estimator. Performance properties of the proposed charting scheme
are evaluated and compared with an existing charting method based on
multivariate sign in terms of the in-control (IC) and out-of-control (OC)
average run length (ARL). Finally, a real example is used to demonstrate the
applicability and implementation of the proposed charting scheme.

Keywords
Average run length; Out-of-control; Profile Monitoring; Spatial rank EWMA;
Wilcoxon rank estimators.

1. Introduction
As the progress in sensing and information technologies, automated
quality data collection has been commonly used in many manufacturing
industries. Consequently, SPM based on large amounts of quality data has
become more and more important. Sometimes, the quality of a process can
be best characterized by a relationship between a dependent variable and one
or more independent variables and this relationship is called a profile. SPM for
changes of profile is called profile monitoring. The methods of profile

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