CNPMK

CNPMK (LET)

Let Subcommand

Compute the Cnpmk process capability index for a variable.

This statistic computes the sample C_npmk 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 C_pmk statistic and has coverage comparable to C_pmk 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 C_npmk 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).

LET <par> = CNPMK <y>             <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
            <par> is a parameter where the computed C_npmk is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

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

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

To use the alternative definition, enter the command
SET CNPK DEFINITION AIRFORCE

To reset the default, enter

SET CNPK DEFINITION PEARN

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

None

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.

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).

Quality Control

2015/04

 
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