Dataplot Vol 2 Vol 1

# CNPMK

Name:
CNPMK (LET)
Type:
Let Subcommand
Purpose:
Compute the Cnpmk process capability index for a variable.
Description:
This statistic computes the sample Cnpmk process capability index of an industrial process and is defined as follows:

$$C_{npmk} = \frac{\min(ENGUSL - \tilde{x},\tilde{x}- ENGLSL)} {3 \sqrt{((P(0.99865) - P(0.00135)/6)^2 + (\tilde{x} - TARGET)^2}}$$

with $$P(x)$$, TARGET, ENGLSL, ENGUSL and MEDIAN denoting the percentile function, the target engineering limit, the lower engineering specification limit, the upper engineering specification limit and the sample median, respectively. This statistic is a non-parametric alternative to the normal-based Cpmk statistic and has coverage comparable to Cpmk for $$\pm 3 \sigma$$. An alternative definition has 99% coverage and uses P(0.995) and P(0.005) in the above formula. This capability index combines both precision and unbiasedness.

The Cnpmk statistic can have values from 0 to infinity with values between 0.5 and 1 being typical.

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

LET TARGET = <value>
LET LSL = <value>
LET USL = <value>
Note:
To use the alternative definition, enter the command

SET CNPK DEFINITION AIRFORCE

To reset the default, enter

SET CNPK DEFINITION PEARN
Note:
Dataplot statistics can be used in a number of commands. For details, enter

Default:
None
Synonyms:
None
Related Commands:
 CAPABILITY ANALYSIS = Perform a capability analysis. CP = Compute a Cp process capability index. CPK = Compute a Cpk process capability index. CNPK = Compute a Cnpk process capability index. CPM = Compute a Cpm process capability index. CPMK = Compute a Cpmk process capability index. CC = Compute a Cc process capability index. CPL = Compute a Cpl process capability index. CPU = Compute a Cpu process capability index. CNP = Compute a Cnp process capability index. CNPM = Compute a Cnpm process capability index. PERCENT DEFECTIVE = Compute the percentage of defectives in a sample. EXPECTED LOSS = Compute the expected loss of a sample.
Reference:
Chen and Ding (2001), "A New Process Capability Index for Non-Normal Distributions," International Journal of Quality & Reliability Management, Vol. 18, No. 7, pp. 762-770.

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

Applications:
Quality Control
Implementation Date:
2015/04
Program:

SKIP 25
READ FURNACE.DAT X1 X2 X3 Y
LET TARGET = 550
LET LSL = 460
LET USL = 660
LET A = CNPM Y
MULTIPLOT CORNER COORDINATES 5 5 95 95
MULTIPLOT 2 2
MULTIPLOT SCALE FACTOR 2
TITLE AUTOMATIC
CNPM PLOT Y X1
CNPM PLOT Y X2
CNPM PLOT Y X3
END OF MULTIPLOT

Date created: 07/31/2023
Last updated: 07/31/2023