Dataplot Vol 2 Vol 1

# CNPK

Name:
CNPK (LET)
Type:
Let Subcommand
Purpose:
Compute the process capability index (CNPK) for a variable.
Description:
The process capability index measure the performance (i.e., the capability) of an industrial process. The CNPK is a variant of the CPK capability indices used for non-normal data and is defined as:

CNPK = MIN(A,B)

where

$$A = \frac{\mbox{USL} - \mbox{MEDIAN}} {p_{0.995} - \mbox{MEDIAN}}$$

$$B = \frac{\mbox{MEDIAN} - \mbox{LSL}} {\mbox{MEDIAN} - p_{0.005}}$$

where USL and LSL are user specified upper and lower specification limits, MEDIAN is the median of the data values, and $$p_{0.995}$$ and $$p_{0.005}$$ are the 99.5 and 0.5 percentiles of the data respectively.

The specification limits define the range within which a product is considered acceptable (values outside this range indicate that a product is defective).

Syntax:
LET <param> = CNPK <y>             <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<param> is a parameter where the computed CNPK is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = CNPK Y1
LET A = CNPK Y1 SUBSET TAG > 2
Note:
The upper and lower specification limits must be specified by the user as follows:

LET LSL = <value>
LET USL = <value>
Note:
Recall that Chebychev's theorem states that at least 75% of the variables data must fall within plus or minus 2 standard deviations of the mean and that at least 88% must fall within plus or minus 3 standard deviations. This is for any distribution. For a normal distribution, these numbers are 95.4% and 99.7% respectively.
Default:
None
Synonyms:
None
Related Commands:
 CONTROL CHART = Generate a control chart. STATISTIC PLOT = Generate a statistic versus subset plot. DEX ... PLOT = Generate a dex plot. CP = Compute the process capability index. CPK = Compute the process capability index. CC = Compute the process capability index. CPM = Compute the process capability index. PERCENT DEFECTIVE = Compute the percentage of defectives in a sample. EXPECTED LOSS = Compute the expected loss of a sample.
Reference:
Kaoru Ishikawa (1982), "Guide to Quality Control," Asian Productivity Organization, (chapter 13).
Applications:
Quality Control
Implementation Date:
2000/1
Program:
LET Y1 = NORMAL RANDOM NUMERS FOR I = 1 1 100
LET LSL = -2
LET USL = 2
LET A1 = CPNK Y1

NIST is an agency of the U.S. Commerce Department.

Date created: 06/05/2001
Last updated: 11/02/2015