Robert F. Hart, Ph.D.
Marilyn K. Hart, Ph.D.
The control chart for individual values (called
an I or X chart) and for moving ranges (Moving
Range or MR chart) is useful when individual
readings are taken from discrete processes,
from continuous processes when an occasional
measurement is taken, from managerial processes
such as monthly sales, etc. Under some circumstances,
consecutive observations may be taken only for
a small number of consecutive pieces, followed
by an interruption in either the manufacturing
process or the data acquisition process. This
could result, for a very short example, in short
runs of data, such as where "?" designates
an interruption in the process. (In fact, this
is how Statit handles the interruption.) This
condition could exist because of:
| 1. |
only short runs of a particular
part number, |
| 2. |
tool adjustments made at irregular
intervals after only a few pieces, or |
| 3. |
data was gathered in this
way because those were the pieces the operator
considered to be of interest. |
| Measurement |
Piece_Number |
|
4
|
1
|
|
1
|
2
|
|
7
|
3
|
|
?
|
-
|
|
30
|
4
|
|
26
|
5
|
|
25
|
6
|
|
19
|
7
|
|
?
|
-
|
|
3
|
8
|
|
?
|
-
|
|
1
|
9
|
|
5
|
10
|
It is essential to note the discontinuous nature
of the data by not using the moving range over
the interruptions for the calculation of the
control limits for either the Individual chart
or the MR chart. Otherwise, if there was a large
change over the interruption, a large would
occur resulting in wide control limits on both
charts that would mask the change in the process.1
In this example, the MR values would be:
| X |
4 |
1 |
7 |
? |
30 |
26 |
25 |
19 |
? |
3 |
? |
1 |
5 |
| MR |
|
3 |
6 |
|
|
4 |
1 |
6 |
|
|
|
|
4 |
and
.
The 3-sigma control limits would then be
 |
= 12.1 + (2.66)(4) = 22.7
|
 |
= 12.1 - (2.66)(4) = 1.5 |
 |
= (3.27)(4) = 13.1 |
 |
|
This results in the chart in Figure 1. Note
that the points are connected within a run but
not connected between runs (over the interruptions).
The MR chart is optional, but is required.2
Figure 1. Interrupted X and Moving Range Chart
on Short Run Data, Same Part Number
If the interruptions were not considered in
the calculation of the control limits, the resulting
charts would be the ones shown in Figure 2.
Note that the calculation of the Moving Range
value over the interruption caused the limits
to be so wide that the process no longer has
points outside the control limits.
Figure 2. Individual and Moving Range Chart
Without Recognizing Interruptions
It will be noted that we have found very few
software packages that calculate the control
limits correctly for the interrupted Individual
and Moving Range chart. Consequently, this has
become one of our tests to evaluate the correctness
of software.
References:
| 1. |
Hart, Marilyn, and Robert Hart. Quantitative
Methods for Quality and Productivity Improvement.
Milwaukee, WI: ASQC Quality Press, 1989. |
| 2. |
Nelson, Lloyd S. "Control Charts
for Individual Measurements," Journal
of Quality Technology, vol. 14(3), pp.172-173,
July 1982. |
For more information, contact Drs. Robert and
Marilyn Hart at robthart@aol.com.
