Page 219 - The Handbook for Quality Management a Complete Guide to Operational Excellence

206 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 207

assure that 0.1 percent or less defective will be produced. A value of +4
is generally desired to allow some room for process drift.
Z The Z index measures the process location relative to its standard
L
L
deviation and the lower requirement. If the distribution is normal, the
value of Z can be used to determine the percentage above the upper
L
requirement by using the table in Appendix 2. In general, the bigger Z
L
is, the better. A value of at least +3 is required to ensure that 0.1 percent
or less defective will be produced. A value of +4 is generally desired to
allow some room for process drift.
Z MIN The value of Z MIN is simply the smaller of the Z or the Z values.
L
U
It is used in computing C .
PK
C The value of C is simply Z MIN divided by 3. Since the smallest
PK
PK
value represents the nearest specification, the value of C tells you if
PK
the process is truly capable of meeting requirements. A C of at least
PK
+1 is required, and +1.33 is preferred. Note that C is closely related to
PK
C , and that the difference between C and C represents the potential
P
PK
P
gain to be had from centering the process.
C A C of at least 1 is required, and 1.33 is preferred. C is closely
PM
PM
PM
related to C . The difference represents the potential gain to be obtained
P
by moving the process mean closer to the target. Unlike C , the target
PK
need not be the center of the specification range.
For example, assume that a process is in statistical control based on
an X and R chart with subgroups of 5. The grand average (or centerline
of the X chart) is calculated as 0.99832, and the average range (or center-
line of the R chart) is calculated as 0.02205. From the table of d values
2
(Appendix 1), we find d is 2.326 for subgroups of 5. Thus, using the equa-
2
tion above for calculating the process standard deviation using the Range
chart method:
. 0 02205
ˆ σ = = . 0 00948
. 2 326
If the process requirements are a lower specification of 0.980 and an
upper specification of 1.020 (i.e., 1:000 ± 0:020), the Z values are calculated as:
0
upper specification − X . 1 020 − .99832
Z = = = 2 3
.
U ˆ σ . 0 000948
−
X − lower specification 0 99832 − 0 980.
.
Z = = = 1 9
.
.
L ˆ σ 0 00948
−
engineering tolerance . 1 020 0 .9800
C P = 6 ˆ σ = 6 × . 0 00948 = . 0 703
ˆ

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