Page 192 - Contributed Paper Session (CPS) - Volume 6

CPS1870 Longcheen H. et al.
of the profiles are normally distributed which is reasonable for most of
situations. For example, two different approaches to monitor linear profiles
where the error terms are assumed to be normally distributed have been
proposed by Zou, Tsung, and Wang (2007) and Huwang, Wang, Xue, and Zou
(2014), individually. However, in many applications, the error terms of linear
profiles do not follow normal distributions. The non-normality of the error
terms makes the charting schemes, that automatically assume the normality
of the error terms, inappropriate and inefficient for monitoring
linear profiles.
In the non-parametric multivariate SPM, the fact that the performance of
traditional control charts, which perform well for monitoring mean vector
and/or covariance matrix under normal assumption, has been greatly affected
when the process distributions are not normal has been investigated by Qiu
and Hawkins (2001), Qiu (2008), Zhou, Zou, Zhang, and Wang (2009), Zou and
Tsung (2011), and Li, Zou, Wang, and Huwang (2013). Various non-parametric
control charts for monitoring the mean vector and/or the covariance matrix of
non-normal processes have also been developed by these authors at the same
time. However, based on our knowledge, researches on monitoring linear
profiles under the situation that the error distribution is not normal are limited.
A distribution-free robust method which uses a rank-based regression for
monitoring linear profiles under non-normal assumption of error terms has
been proposed by Zi, Zou, and Tsung (2012). Firstly, the so-called Wilcoxon-
type rank-based estimators were used to estimate regression coefficients and
then the multivariate sign EWMA method was applied to these Wilcoxon-type
rank-based estimators to develop their charting scheme. In addition, based on
the multivariate EWMA method to the trimmed least squares estimators of
regression coefficients, control charts for monitoring linear profiles when the
error terms have contaminated normal distributions have been investigated
by Huwang, Wang, and Shen (2014). In this talk, the aforementioned Wilcoxon-
type rank-based estimators of regression coefficients and a transformation of
the error variance estimator will be adopted. Then, the multivariate EWMA
method to the spatial rank of the vector of these Wilcoxon-type rank-based
estimators and the transformed error variance estimator will be applied to
develop the proposed charting scheme. Since the spatial rank extracts more
information from multivariate data than the multivariate sign, it is expected
that the proposed control chart is more effective than the multivariate sign
chart for monitoring linear profiles when the error terms do not follow normal
distributions.
In many applications, to collect a large number of IC profiles from Phase I
study may not be available. As a result, the charting scheme based on the
Phase I data may not have its actual (true) IC ARL (denoted by ARL0) equal to
the nominal ARL0, and this causes the problem that it is difficult to have a fair

181 | I S I W S C 2 0 1 9