Page 345 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 325

Methodology

Since process capability is not valid unless the process is stable, always analyze
the process using a control chart first. Once statistical control is evidenced, then
process capability may be analyzed.
For normal distributions, the capability indices are calculated as

high spec − low spec
C =
p 6σ x
C = min( Cp Cp )
,
pk l u
C
C = p
pm 2
T
+
1+ (x − )
σ 2
x
where T is the process target, x is the grand average, and σ is process sigma,
x
which is calculated using the moving-range (when subgroup size = 1) or sub-
group sigma (subgroup size > 1) statistic.

Z Z
C = l Cp = u
p u
3 3
Z = x − low spec Z = high spec − x
l σ x u σ x

For nonnormal distributions, the capability indices are calculated as

C = high spec − low spec
p
ordinate − ordinate
.
0
0 99865 0.00135
Z = | Z normal, p | Z = | Z normal , 1 p− |
u
l
where ordinate and ordinate are the z values of the nonnormal
0.99865 0.00135
cumulative distribution curve at the 99.865 and the 0.135 percentage
points, respectively, and Z and Z are the z values of the normal
normal, p normal, 1–p
cumulative distribution curve at the p and the 1 – p percentage points, re-
spectively.