Basic Analysis and Graphing - SAS

86 Performing Univariate Analysis Chapter 2
Statistical Details for the Distribution Platform
C pk
=
P 0.5
– LSL USL – P
min ------------------------------------
0.5
,------------------------------------
P 0.5
– P 0.00135
P 0.99865
– P 0.5
1
--( USL + LSL) – P
2
0.5
K = 2 × ------------------------------------------------------
USL – LSL
min
T – LSL
------------------------------------
USL – T
,------------------------------------
P 0.5
– P 0.00135
P 0.99865
– P 0.5
C pm
= -------------------------------------------------------------------------------------------
μ – T
1 + ------------
σ
2
If the data are normally distributed, these formulas reduce to the formulas for standard capability indices.
See Table 2.19.
Set Spec Limits for K Sigma
Type a K value and select one-sided or two-sided for your capability analysis. Tail probabilities
corresponding to K standard deviations are computed from the Normal distribution. The probabilities are
converted to quantiles for the specific distribution that you have fitted. The resulting quantiles are used for
specification limits in the capability analysis. This option is similar to the Quantiles option, but you provide
K instead of probabilities. K corresponds to the number of standard deviations that the specification limits
are away from the mean.
For example, for a Normal distribution, where K=3, the 3 standard deviations below and above the mean
correspond to the 0.00135 th quantile and 0.99865 th quantile, respectively. The lower specification limit is
set at the 0.00135 th quantile, and the upper specification limit is set at the 0.99865 th quantile of the fitted
distribution. A capability analysis is returned based on those specification limits.