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268 Part IV: Quality Assurance
A process is considered out of control not only when the points exceed the control
limits, but also when the points show some pattern of nonrandomness. The
Western Electric (1985) Statistical Quality Control Handbook gives a set of decision
rules for determining nonrandom patterns on control charts. In particular, it suggests
that the patterns are nonrandom if either:
1. Two out of three successive points exceeds the 2s warning limits
2. Four out of five successive points fall at a distance of s or beyond
from the center line
3. Eight successive points fall on one side of the center line
4. Seven successive points run either upward or downward
Interpretation of Shewhart X – and R Control Charts
Part IV.B.3
We should investigate any out-of-control points—that is, points on or beyond the
3s control limits—or any patterns of nonrandomness on the R chart before interpreting
the X – chart. As discussed earlier, the reason for doing this is simple. It is
not possible to bring the average under control without first bringing the variability
under control. Normally the X – chart is placed above the R chart and they
are aligned to each other in such a manner that the average and the range for any
sample are plotted on the same vertical line. Examine whether one, both, or neither
chart indicates that the process is out of control for any given sample. If any point
exceeds the control limits in either or both charts, that means that sample did not
come from a stable process. In other words, there are some special or assignable
causes present in the system. More precisely, if the plotted point exceeds the control
limits in the R chart, then it is evident that the variability of the process has
changed. In such cases, before any full-blown investigation is launched, some preliminary
checks should be made. For example,
a. Check that all the calculations are correct or the data is entered in the
computer correctly.
b. Check whether there is any change in workers, machines, or suppliers
of raw material.
If the points exceed the control limits in the X – chart then it means the process mean
has changed. Again, follow the preliminary checks before a full-blown investigation
is launched.
If points exceed the limits in both the X – chart and R chart then that usually
indicates that a sudden shift occurred in the lot from which the samples were
taken. In such cases, after the preliminary checks, there should be a full investigation
concentrating on the period during which that lot was produced. Depending
on the process, the possibility of stopping production until the special causes are
detected should be considered.
In addition to points exceeding the control limits, nonrandom patterns, such
as a run of seven points moving upward or downward, or a run of eight successive
points falling above or below the center line, should be checked.
An upward run or a run above the center line in the R chart indicates: