CPL

CPL (LET)

Let Subcommand

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

The process capability index measure the performance (i.e., the capability) of an industrial process and is defined as follows:
\[ CP = \frac{USL -LSL}{6s} \]

where \( s \) is the sample standard deviation and where USL and LSL are user specified upper and lower specification limits. The specification limits define the range within which a product is considered acceptable (values outside this range indicate that a product is defective). Values less than 1 indicate that there are still some defectives. A value of 6Ss yields a range of plus or minus 3 standard deviations. For example, if the specification limits are symmetric about the mean and the calculated CP is exactly 1, this means that the specification limits fall at plus and minus 3 standard deviations from the mea (and almost all the data will fall within these limits). Values greater than 1 indicate the specification limits are even greater than 3 standard deviations from the mean while values less than 1 indicate specification limits are less than 3 standard deviations from the mean.

The CPL statistic is used when only the lower specification limit is of interest. That is,

\[ CPL = \frac{\bar{x} - LSL} {3s} \]

where \( \bar{x} \) is the sample mean.

LET <par> = CPL <y1>             <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <par> is a parameter where the computed CPL is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

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

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.

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

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

None

None

CAPABILITY ANALYSIS	=	Compute a capability analysis.
CP	=	Compute the process capability index.
CPU	=	Compute the process capability index.
CPK	=	Compute the process capability index.
CNPK	=	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.

Kotz and Johnson (1993), "Process Capability Indices," Chapman & Hall (chapter 2).

Quality Control

2001/04

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