ABSTRACT
In Section 4.1, we have explained that Shewhart charts are not effective for detecting
small and persistent shifts because they evaluate the process performance based on
observed data at a single time point alone. To overcome this limitation, the CUSUM
charts described in the previous chapter try to make use of all observed data available
at the current time point, including those observed at the current time point and all
historical data that are observed before the current time point, to evaluate the process
performance. One major feature of the CUSUM charts is their re-starting mechanism,
which is that their charting statistics reset to the initial state every time when evidence
of a shift in the observed data is smaller than a threshold. As it has been described in
Subsection 4.2.4, they have certain optimality properties under some regularity con-
ditions. However, they are relatively complicated to construct and use. Is there a more
convenient way to construct control charts that have similar performance? Roberts
(1959) provided an answer to this question by proposing the so-called exponentially
weighted moving average (EWMA) control chart. This chart is constructed based on
a weighted average of all observed data available at the current time point. Thus, it
is easy to perceive. In the literature, there has been an extensive discussion about
its design, implementation, and properties. See, for instance, Capizzi and Masarotto
(2003), Crowder (1987a,b, 1989), Gan (1995), Han and Tsung (2004), Knoth (2007),
Lucas and Saccucci (1990), and Reynolds and Stoumbos (2005, 2006), among many
others. From all these discussions, it can be seen that the EWMA charts have similar
performance to the CUSUM charts.