Page 191 - Contributed Paper Session (CPS) - Volume 6

CPS1870 Longcheen H. et al.
monitoring, in general, can be divided into parametric and non-parametric
approaches. In the parametric approach, the dependent and independent
variables are assumed to satisfy a known, either linear or non-linear, model
and then the charting statistics are developed based on the estimated model
parameters from the profile data to monitor whether the functional
relationship has changed or not. On the other hand, in the non-parametric
approach, the relationship between the dependent and independent variables
is not assumed to be known. Some nonparametric methodologies are
employed to estimate such a relationship and thus the charting statistics are
constructed using the estimated relationship to monitor the stability of the
unknown functional relationship.
For monitoring simple linear profiles, there are many studies in the
literature. See, for example, Kang and Albin (2000), Kim, Mahmoud, and
Woodall (2003), Mahmoud and Woodall (2004), Zou, Zhang, and Wang (2006),
Gupta, Montgomery, and Woodall (2006), Mahmoud, Parker, Woodall, and
Hawkins (2007), Zou, Zhou, Wang, and Tsung (2007), among several others.
Multiple linear profile monitoring has been studied by Zou, Tsung, and Wang
(2007), Mahmoud (2008), Eyvazian, Noorossana, Saghaei, and Amiri (2011),
Zou, Ning, and Tsung (2012), Huwang, Wang, Xue, and Zou (2014), Amiri, Zou,
and Doroudyan (2014), Kazemzadeh, Amiri, and Kouhestani (2016), Zhang,
Shang, Gao, and Wang (2017), and Ghashghaei and Amiri
(2017). Although monitoring linear profiles is an important task, in many
practical applications profiles cannot be adequately represented by linear
models. Non-linear profile monitoring has been investigated by Walker and
Wright (2002), Woodall, Spitzner, Montgomery, and Gupta (2004), Williams,
Woodall, and Birch (2007), Colosimo and Pacella (2007), Williams, Birch,
Woodall, and Ferry (2007), Yu, Zou, and Wang (2012), Maleki, Amiri, and
Taheriyoun (2017), Maleki, Amiri, Taheriyoun, and Castagliola (2017), Esmaeeli,
Sadegheih, Amiri, and Doroudyan (2017), Maleki, Castagliola, Amiri, and Khoo
(2018), Fotuhi, Amiri, and Maleki (2018), Menafoglio, Grasso, Secchi, and
Colosimo (2018), and Khosravi and Amiri (2018). There are many works in the
literature that aim to monitor generalized linear model-based regression
profiles. See, for example, Yeh, Huwang, and Li (2009), Shang, Tsung, and Zou
(2011), Koosha and Amiri (2013), Shadman, Mahlooji, Yeh, and Zou, (2015),
Amiri, Koosha, Azhdari, and Wang (2015), Amiri, Yeh, and Asgari (2016), Qi,
Wang, Zi, and Li (2016), and Izadbakhsh, Noorossana, and Niaki (2018).
Recently, monitoring profiles based on non-parametric regression models has
been developed by Zou, Tsung, and Wang (2008), Qiu, and Zou (2010), Qiu,
Zou, and Wang (2010).
In this talk, we focus on monitoring profiles which can be represented by
linear models. Our study will concentrate on the on-line phase II monitoring.
Traditionally, studies on monitoring linear profiles assume that the error terms

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