CNPK

CNPK (LET)

Let Subcommand

Compute the process capability index (CNPK) for a variable.

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 = (USL-MEDIAN)/(P(.995)-MEDIAN)
B = (MEDIAN-LSL)/(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(0.0050) 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).

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.

LET A = CNPK Y1
LET A = CNPK Y1 SUBSET TAG > 2

The upper and lower specification limits must be specified by the user as follows:
LET LSL = <value>
LET USL = <value>

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.

None

None

CONTROL CHART	= Generate a control chart.
CP (LET)	= Compute the CP process capability index.
CPK (LET)	= Compute the CPk process capability index.
PERCENT DEFECTIVE (LET)	= Compute the percentage of defectives in a sample.
EXPECTED LOSS (LET)	= Compute the expected loss of a sample.

"Guide to Quality Control", Kaoru Ishikawa, Asian Productivity Organization, 1982 (chapter 13).

Quality Control

2000/1

LET Y1 = NORMAL RANDOM NUMERS FOR I = 1 1 100
LET LSL = -2
LET USL = 2
LET A1 = CPNK Y1