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PROC CAPABILITY and General Statements |

where

The interpretation of *C*_{p} can depend on the
application, on past experience, and on local
practice. However, broad guidelines for
interpretation have been proposed by several
authors. Ekvall and Juran (1974) classify *C*_{p} values as

- "not adequate" if
*C*_{p}< 1 - "adequate" if , but
requiring close control as
*C*_{p}approaches 1 - "more than adequate" if
*C*_{p}> 1.33

- 1.33 for existing processes
- 1.50 for new processes or for existing processes when the variable is critical (for example, related to safety or strength)
- 1.67 for new processes when the variable is critical

Exact lower and upper confidence limits for *C*_{p}
(denoted by LCL and UCL) are computed using
percentiles of the chi-square distribution,
as indicated by the following equations:

Here, denotes the lower percentile of the chi-square distribution with degrees of freedom. Refer to Chou et al. (1990) and Kushler and Hurley (1992).

You can specify with the ALPHA= option in the
PROC CAPABILITY statement
or with the
CIINDICES( ALPHA=*value* )
in the
PROC CAPABILITY statement.
The default *value* is 0.05.
You can save these limits in the OUT=
data set by specifying the keywords CPLCL and CPUCL
in the OUTPUT statement.
In addition, you can display these limits on plots produced
by the CAPABILITY procedure by specifying the
keywords in the INSET statement.

Montgomery (1996) refers to *CPL* as the
"process capability ratio" in the case of
one-sided lower specifications and recommends minimum
values as follows:

- 1.25 for existing processes
- 1.45 for new processes or for existing processes when the variable is critical
- 1.60 for new processes when the variable is critical

Exact lower and upper confidence limits for *CPL*
are computed using a
generalization of the method
of Chou et al. (1990),
who point out that
the lower confidence limit for
*CPL* (denoted by CPLLCL )satisfies the equation

Montgomery (1996) refers to *CPU* as the
"process capability ratio" in the case of
one-sided upper specifications and recommends minimum
values that are the same as those specified previously
for *CPL*.

Exact lower and upper confidence limits for *CPU*
are computed using a
generalization of the method
of Chou et al. (1990),
who point out that
the lower confidence limit for
*CPU* (denoted by CPULCL )satisfies the equation

where

If you specify only the upper limit in the SPEC statement
or the SPEC= data set, then *C*_{pk} is computed as *CPU*,
and if you specify only the lower limit in the SPEC
statement or the SPEC= data set, then *C*_{pk} is computed
as *CPL*.

Bissell (1990) derived approximate
two-sided 95% confidence limits for
*C*_{pk} by assuming that the distribution of
is normal.
Using Bissell's approach, 100%
lower and upper confidence limits ycan be computed as

where denotes the cumulative standard normal distribution function. Kushler and Hurley (1992) concluded that Bissell's method gives reasonably accurate results.

You can specify with the ALPHA= option in the PROC CAPABILITY statement. The default value is 0.05. These limits can be saved in an output data set by specifying the keywords CPKLCL and CPKUCL in the OUTPUT statement. In addition, you can display these limits on plots produced by the CAPABILITY procedure by specifying these same keywords in the INSET statement.

The CAPABILITY procedure computes an
estimator of *C*_{pm} as

If you specify only a single specification limit *SL*
in the SPEC statement or the SPEC= data set, then *C*_{pm} is
estimated as

Boyles (1991) proposed a
slightly modified point estimate for *C*_{pm} computed
as

Boyles also suggested approximate
two-sided 100% confidence limits for
*C*_{pm}, which are computed as

Here denotes the lower percentile of the chi-square distribution with degrees of freedom, where equals

You can specify with the ALPHA= option in the PROC CAPABILITY statement. The default value is 0.05. These confidence limits can be saved in an output data set by specifying the keywords CPMLCL and CPMUCL in the OUTPUT statement. In addition, you can display these limits on plots produced by the CAPABILITY procedure by specifying these keywords in the INSET statement.

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