X-bar R, X-bar S and Individual charts are
often the focus of control chart discussions.
In fact, they are frequently presented as the
only options for statistical process control
charting. There are actually other alternatives.
This discussion will look at the benefits of
EWMA, exponentially weighted moving average,
and moving average or uniformly weighted moving
average, UWMA, charts. This article will discuss
the data requirements and the advantages of
the Moving Average EWMA and UWMA charts.
X-Bar and Individual charts are valuable for
detecting relatively large shifts in the process
mean. The definition of additional rules, for
example the Western Electric rules, are attempts
to increase the sensitivity of these charts.
EWMA and Moving Average charts can detect relatively
small shifts in the process mean faster than
X-bar charts with the same sample size.
Moving Average and EWMA charts vary in the
calculation of the plotted average values. A
Moving Average or UWMA chart weights the values
uniformly over time. An EWMA chart allows the
user to determine the amount of weight given
to prior data. The EWMA statistic gives progressively
less weight to data that are further removed
in time. This weighting factor is commonly represented
by the symbol lambda. Lambda varies from 0 to
1. The smaller values of lambda give greater
influence to historical data. For example, lambda
= .4 means that 60% of the weight will be given
to past information and 40% to current information.
A lambda = 1 is equivalent to an X-bar chart.
One advantage of Moving Average charts is the
lack of sensitivity to normality assumptions.
If the dataset subgroup size = 1, an appropriate
alternative is the Individual X chart. For this
chart, it is necessary to estimate the distribution
of the process in order to define the control
limits. In contrast, the data points on an EWMA
or Moving Average chart are averaged values.
The estimate of the process distribution becomes
less important since the data points are averages
or moving averages. The Central Limit Theorem
can be invoked to describe the distribution
of the averages as normally distributed.
Another advantage of Moving Average charts
is that they smooth the affects of known, uncontrollable
noise in data. This is important where fluctuations
exist, yet the fluctuations are not completely
indicative of process instability.
Before opting to construct Moving Range charts,
it is necessary to inspect the Range chart for
the data. If any of the Range chart values are
out of control, it is necessary to remove them
from the data set.
The following Range chart illustrates at least
one data point that must be removed.
