Research Interests
Peihua Qiu's Research on Statistical Process Control
Statistical process control (SPC) is for monitoring sequential
processes (e.g., production lines, internet traffics, medical
systems, social or economic status) to make sure that they work
stably. In the literature, most SPC procedures assume that the
process measurements are normally distributed, which is often
invalid, especially when the process measurements are multivariate.
One important contribution made by my co-authors and me is that
i) we demonstrated that conventional SPC procedures could give
misleading results when the normality assumption was violated
in mutivariate cases, and ii) we proposed rank-based multivariate
SPC procedures which were appropriate to use in most applications
(Qiu and Hawkins 2001, 2003). Qiu (2008) proposed a general
framework to handle the multivariate SPC problem without the
normality assumption, by first categorizing the observed data
and then using categorical data analysis methodologies (e.g.,
log-linear modeling). Recently, Qiu and Li (2011a,b) compared the
methods based on ranks and the methods based on categorization of
the observed data in 1-D cases, and concluded that the latter
methods would be more efficient in many different cases. Qiu and
Zhang (2015) demonstrated that the transformation approach may
not be a good solution to solve the nonparametric SPC problem. In a
different but related direction, Zou and Qiu (2009) proposed an
efficient SPC procedure, after adapting the popular model selection
procedure LASSO to the SPC problem.
Another major contribution made by my co-authors and me is that we
proposed a general framework for constructing SPC control charts
(Hawkins, Qiu and Kang 2003, Hawkins, Qiu and Zamba 2008), which is
based on change-point estimation and which has been widely used in
the SPC literature. Besides, Chatterjee and Qiu (2009) proposed a novel
CUSUM chart, using a sequence of control limits and a bootstrap
algorithm.
A recent contribution made by my co-authors and me is about profile
monitoring. Most people in this area assume that profiles are linear
or parametric, which is invalid in many applications. To overcome this
limitation, we proposed flexible profile monitoring charts for cases
when the profiles were nonparametric and the data within profiles were
correlated with arbitrary design (Zou, Qiu and Hawkins 2009, Qiu and
Zou 2010, Qiu, Zou and Wang 2010, Paynabar, Qiu and Zou 2016).
All the research described above has been summarized in my book
Qiu (2014, Chapman&Hall/CRC).
Peihua Qiu's Home Page