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264 Part IV: Quality Assurance
CL = x
LCL = x = 3sˆ
x
sˆ
= x 3
n
R
= x 3
d n
2
= x
A R
2
(19.7)
(19.8)
where the values of A 2 and d 2 for various sample sizes are given
in Appendix E.
Note: Instead of calculating three-sigma limits (common in
the United States), we can also calculate the probability limits
(common in Europe) at the desired level of significance a simply
by replacing 3 with z a/2 in equations (19.6) and (19.8). Thus, the
control limits will be
Part IV.B.3
UCL = x+
z
= x+
z
LCL = x
z
= x
z
a / 2
a / 2
a / 2
a / 2
sˆ
n
R
d
2
sˆ
n
n
R
.
d n
Step 4. Calculate the control limits for the R control chart:
UCL = R + 3sˆ
2
= R+
3d R 3
d
d
3
= +
1 3
d
R
= DR
4
R
2
2
(19.9)
(19.10)
(19.11)
CL = R
(19.12)