Page 200 - The Handbook for Quality Management a Complete Guide to Operational Excellence

186 P r o c e s s C o n t r o l Q u a n t i f y i n g P r o c e s s Va r i a t i o n 187

Control Limit Equations for c Charts Like all control charts, c charts consist
of three guidelines: centerline, a lower control limit, and an upper
control limit. The centerline is the average number of occurrences-
per-unit and the two control limits are set at plus and minus three
standard deviations. If the process is in statistical control then virtu-
ally all subgroup occurrences-per-unit should be between the control
limits and they should fluctuate randomly about the centerline.

sum of subgroup occurrences
c =
number of subgroups
r
c
LCL = − 3 c
c
UCL = + 3 c

The data in Table 9.10 were obtained by opening randomly selected
crates from each shipment and counting the number of bruises. There
are 250 peaches per crate. Our unit size will be taken as one full crate;
that is, we will be counting crates rather than the peaches themselves.
Every subgroup consists of one crate. If the subgroup size varied, a u
chart would be used.
Using the above data the centerline and control limits are found as
follows:
sum of subgroup occurrences 1006
c = = = 33 53.
r
number of subgroups 30
.
LCL = − 3c c =33 53 3 33 53. − . = 16.158
+
UCL = − 3 8c = 33 .53 3 33 .53 = 50 .902
c
The control limits and the occurrence counts are shown in Fig. 9.15.
One way of helping determine whether or not a particular set of data
is suitable for a c chart or an np chart is to examine the equation used to
compute the centerline for the control chart. If the unit of measure is the
same in both the numerator and the denominator, then a p chart is indi-
cated; otherwise, a c chart is indicated. For example, if

bruises
Centerline =
number of crates

then the numerator is in terms of bruises while the denominator is in
terms of crates, indicating a c chart.
The unit size is arbitrary but, once determined, it cannot be changed
without recomputing all subgroup occurrences-per-unit and control limits.

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