Page 194 - The Handbook for Quality Management a Complete Guide to Operational Excellence

180 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 181

subgroup counts will be between the control limits, and they will
fluctuate randomly about the centerline.

np = subgroup defective count

sum of subgroup defective counts
u
np =
number of subgroups
1
LCL = np − 3 np − p)
n
(
UCL = np + 3 np − p)
1
(
Note that
np
p =
n

The data in Table 9.8 were obtained by opening randomly selected crates
from each shipment and counting the number of bruised peaches. There
are 250 peaches per crate (constant n is required for np charts).
Using the above data the centerline and control limits are found as
follows:

sum of subgroup defective counts 838
np = = = 27 93.
number of subgroups 30
f
 27 93
.
.
LCL = np − 3 np − (1 p ) = 27.993 3 27 93− . ×   1− 250   = 12 99
.
+
.
.
.
UCL = np + 3 np 1− ( 1 ) = 27 93 3 27 93 ×   1− 27 93  = 42 88
p
 250 
The control limits and the subgroup defective counts are shown in
Fig. 9.13.
Control Charts for Average Occurrences-per-Unit (u Charts)
u charts are statistical tools used to evaluate the average number of
occurrences-per-unit produced by a process. u charts can be applied to any
variable where the appropriate performance measure is a count of how
often a particular event occurs. u charts answer the question “Has a spe-
cial cause of variation caused the central tendency of this process to pro-
duce an abnormally large or small number of occurrences over the time
period observed?” Note that, unlike p or np charts, u charts do not neces-
sarily involve counting physical items. Rather, they involve counting

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