124 FLEXOGRAPHY: PRINCIPLES & PRACTICES
grand average of 1.49. These two values become the
upper and lower control limits of 1.54 and 1.44.
The range is determined for each subgroup of five
readings by subtracting the lowest reading from the
highest reading within the subgroup. As can be seen for
press sheet 1 its range is 1.53 to 1.43, or 0.10. This is
done for all 12 press sheets. The average range is cal-
culated by adding up all the ranges and dividing by 12
and its value is 0.09. The standard deviation of the
average range is calculated and multiplied by 3. This
value is 0.09, which is added to the average range. The
result, 0.18, becomes the upper control limit for the
range as shown in Figure C-1.
In order to understand fully what is happening when
using a control chart it is important to also use a range
chart. When viewing any given subgroup data point on
the control chart one must also review that same point
on the range chart. Add and subtract half the corre-
sponding range number from the control chart number
to determine the variation at that point on the control
chart.
A review of Figure C-1 indicates that the last 4 sheets
were, on average, under the process average line. If
there are 4 consecutive subgroup data points on one
side of the process average, this indicates that there
may be a process shift. Similarly, 4 or more points
heading in the direction of the upper or lower control
limit may indicate a trend in the process away from the
process average. The subgroup average data points
should fall fairly evenly on either side of the process
average.
As can be noted in Figure C-1, the upper and lower
control limits are well within the agreed upon specifica-
tions for the black ink densities. There should never be
a process in which the average data point is not well
within the upper and lower specifications. It is assumed
that whenever a data point is close to the specification
limits there is a tendency for the process to vary enough
to produce out of specification work. One must look at
the specifications in terms of process average, control
limits, range, skewness and kurtosis (Figure C-2).