Page 353 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 333

initial stages of product or process design,or in the measure stage we may have
processes that lack statistical control.
The statistic P can be used when there are both and upper and lower speci-
p
fications for the sample. P can be used when only one or the other or both
pk
specifications are provided.

Measure Stage
• To provide a process baseline estimate for an uncontrolled process

Methodology

For normal distributions, the performance indices are calculated as

P = high spec − low spec
p 6σ
x
,
P = min( Pp Pp )
pk l u
p
p = p
pm (x − ) 2
T
+
1+
σ 2
x
where T is the process target, x is the grand average, and σ is the sample sigma.
x
Z Z
P = l P = u
pl pu
3 3
Z = x − low spec Z = high spec − x
l σ x u σ x

For nonnormal distributions, the performance indices are calculated as

high spec − low spec
p =
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 cu-
0.99865 0.00135
mulative distribution curve at the 99.865 and 0.135 percentage points, respec-
tively, and Z and Z are the z values of the normal cumulative
normal, p normal, 1–p
distribution curve at the p and 1 – p percentage points, respectively.