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354 Statistical Process Control for Autocorrelated Processes
based on time series models 1−8 and those which are model-free. 6,19−28 For the former,
three general approaches have been proposed: those which monitor residuals, 1−18,16,17
15
those based on direct observations, 9−14,18 and those based on new statistics. A brief
account of these approaches is presented in this chapter.
2
Wardell et al. and Lu and Reynolds 3,4 proposed the use of exponentially weighted
moving average (EWMA) control charts for monitoring residuals. Apley and Shi 5
proposed a generalized likelihood ratio test (GLRT) approach in detecting the mean
6
shift in autocorrelation processes. Apley and Tsung proposed a triggered cumulative
score (cuscore) chart, which has similar character to GLRT but is easier to implement.
7
Castagliola and Tsung studied the impact of non-normality on residual control charts.
They proposed a modified Shewhart control chart for residuals -- the special cause
8
chart (SCC) -- which is more robust to non-normal situations. Testik considered the
uncertainty in the time series model due to estimated parameters and proposed wider
EWMA control limits for monitoring the residuals of the first-order autoregressive
AR(1) process.
Taking a different approach involving direct monitoring of process outputs in-
9
stead of the residuals, Montgomery and Mastrangelo proposed the moving center-
line EWMA (MCEWMA) chart, which approximates the time series model with the
EWMA model. Mastrangelo and Brown 10 provided a further study of the properties
11
of the MCEWMA chart. Alwan developed a general strategy to study the effects of
autocorrelation using the Shewhart control chart. Timmer et al. 12 compared different
13
CUSUM control charts for AR(1) processes. Lu and Reynolds study the performance
of CUSUM control charts for both residuals and observations, and concluded that they
are almost equally effective. The authors claimed that the performance of CUSUM and
EWMA charts in detecting mean shift is comparable. Atienza, et al. 14 also proposed
a CUSUM scheme for autocorrelated observations. They also 15 proposed a new test
statistic for detecting the additive outlier (AO), innovational outlier (IO), and level
shift (LS).
The time series model based approach is easy to understand and effective in some
situations. However, it requires identification of an appropriate time series model
from a set of initial in-control data. In practice, it may not be easy to establish and may
appear to be too complicated to practicing engineers. Hence, the model-free approach
has recently attracted much attention. The most popular model-free approach is to
form a multivariate statistic from the autocorrelated univariate process, and then
monitor it with the corresponding multivariate control chart.
6
Krieger et al. 19 used a multivariate CUSUM scheme. Apley and Tsung adapted
2
the T control chart for monitoring univariate autocorrelated process. Atienza et al. 20
2
21
proposed a Multivariate boxplot-T control chart. Dyer et al. adapted the use of the
multivariate EWMA control chart for autocorrelated processes.
Another model-free approach is to use a batch means control chart, proposed by
22
29
Runger and Willemain, referenced by Montgomery, and discussed in detail by Sun
and Xu. 23 The main advantage of this approach lies in its simplicity. In an attempt
to ‘break’ dependency, it simply divides sequential observations into a number of
batches, and then monitors the means of these batches on a standard individuals
control chart.
Other works on SPC of autocorrelated processes includes Balkin and Lin 24 who
studied the use of sensitizing rules for the Shewhart control chart on autocorrelated