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

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

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

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).

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.
STATISTIC PLOT	= Generate a statistic versus subset plot.
DEX ... PLOT	= Generate a dex <statistic> 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.

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