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.