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PROC CAPABILITY and General Statements |
The interpretation of Cp 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 Cp values as
Exact lower and upper confidence limits for Cp (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:
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
If you specify only the upper limit in the SPEC statement or the SPEC= data set, then Cpk is computed as CPU, and if you specify only the lower limit in the SPEC statement or the SPEC= data set, then Cpk is computed as CPL.
Bissell (1990) derived approximate two-sided 95% confidence limits for Cpk 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 Cpm as
If you specify only a single specification limit SL
in the SPEC statement or the SPEC= data set, then Cpm is
estimated as
Boyles (1991) proposed a slightly modified point estimate for Cpm computed as
Boyles also suggested approximate two-sided 100% confidence limits for Cpm, 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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