Introduction
The MACONTROL procedure creates
moving average control charts, which are tools
for deciding
whether a process is in a state of statistical control and for
detecting shifts in a process average. The procedure
creates the following two types of charts:
- uniformly weighted moving average charts (commonly
referred to as moving average charts). Each point on a
moving average chart represents the average of the w most
recent subgroup means, including the present subgroup mean.
The next moving average is
computed by dropping the oldest of the previous w subgroup
means and including the newest subgroup mean.
The constant w, often referred to as the span of
the moving average, is a parameter of the moving average chart.
There is an inverse relationship between w and the
magnitude of the shift to be detected; larger values of
w are used to guard against smaller shifts.
- exponentially weighted moving average (EWMA) charts, also
referred to as geometric moving average (GMA) charts. Each
point on an EWMA chart represents the weighted average of all the
previous subgroup means, including the mean of the present subgroup
sample. The weights decrease exponentially going backward in time.
The weight r 
assigned to the present
subgroup sample mean is a parameter of the EWMA chart. Small values
of r are used to guard against small shifts.
If r=1, the EWMA chart reduces to a Shewhart
chart.
In the MACONTROL procedure, the EWMACHART statement produces EWMA charts, and
the MACHART statement produces uniformly weighted moving average
charts.
In contrast to the Shewhart chart where each point is based on
information from a single
subgroup sample, each point on a moving average chart combines
information from the current sample and past samples.
Consequently, the moving average chart is more sensitive to small
shifts in the process average. On the other hand, it is more
difficult to interpret patterns of points on a moving average chart,
since consecutive moving averages can be highly correlated, as
pointed out by Nelson (1983).
You can use the MACONTROL procedure to
-
read raw data (actual measurements) or summarized data
(subgroup means and standard deviations) to create charts
-
specify control limits as probability limits or in
terms of a multiple of the standard error of the moving average
-
adjust the control limits to compensate
for unequal subgroup sample sizes
-
accept numeric- or character-valued subgroup variables
-
display subgroups with date and time formats
-
estimate the process standard deviation
using a variety of
methods or specify a standard (known) value for -
analyze multiple process variables in the same chart statement
-
provide multiple chart statements. If used with a BY statement,
the procedure generates charts separately for BY groups of observations.
- tabulate the information displayed in the control chart
-
save
moving averages, control limits, and control limit parameters in
output data sets
-
superimpose plotted points with stars (polygons) whose vertices
indicate the values of multivariate data related to the process
-
display a trend chart below the moving average chart that plots a
systematic or fitted trend in the data
-
produce charts on line printers or on graphics devices. Charts
produced on line printers can use special formatting characters that
improve the appearance of the chart. Charts produced on graphics
devices can be annotated, saved, and replayed.
