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The CAPABILITY Procedure

Summary of INSET Keywords

Summary Statistics and Process Capability Indices

Table 5.30 Summary Statistics

Keyword

Description

CSS

corrected sum of squares

CV

coefficient of variation

KURTOSIS

kurtosis

MAX

largest value

MEAN

sample mean

MIN

smallest value

MODE

most frequent value

N

sample size

NEXCL

number of observations excluded by MAXNBIN= or MAXSIGMAS= option

NMISS

number of missing values

NOBS

number of observations

RANGE

range

SKEWNESS

skewness

STD

standard deviation

STDMEAN

standard error of the mean

SUM

sum of the observations

SUMWGT

sum of the weights

USS

uncorrected sum of squares

VAR

variance

Table 5.31 Percentile Statistics

Keyword

Description

P1

1st percentile

P5

5th percentile

P10

10th percentile

Q1

lower quartile (25th percentile)

MEDIAN

median (50th percentile)

Q3

upper quartile (75th percentile)

P90

90th percentile

P95

95th percentile

P99

99th percentile

QRANGE

interquartile range (Q3 - Q1)

Table 5.32 Robust Statistics

Keyword

Description

GINI

Gini’s mean difference

MAD

median absolute difference about the median

QN

, alternative to MAD

SN

, alternative to MAD

STD_GINI

Gini’s standard deviation

STD_MAD

MAD standard deviation

STD_QN

standard deviation

STD_QRANGE

interquartile range standard deviation

STD_SN

standard deviation

Table 5.33 Hypothesis Testing

Keyword

Description

MSIGN

sign statistic

NORMALTEST

test statistic for normality

PNORMAL

probability value for the test of normality

SIGNRANK

signed rank statistic

PROBM

probability of greater absolute value for the sign statistic

PROBN

probability value for the test of normality

PROBS

probability value for the signed rank test

PROBT

probability value for the Student’s test

T

statistics for Student’s test

Table 5.34 Input Data Set

Keyword

Description

DATA=

(label, value) pairs from input data set

Table 5.35 Capability Indices and Confidence Limits

Keyword

Description

CP

capability index

CPLCL

lower confidence limit for

CPUCL

upper confidence limit for

CPK

capability index

CPKLCL

lower confidence limit for

CPKUCL

upper confidence limit for

CPL

capability index CPL

CPM

capability index

CPMLCL

lower confidence limit for

CPMUCL

upper confidence interval for

CPU

capability index CPU

K

capability index

Table 5.36 Specification Limits and Related Information

Keyword

Description

LSL

lower specification limit

USL

upper specification limit

TARGET

target value

PCTGTR

percent of nonmissing observations that exceed the upper specification limit

PCTLSS

percent of nonmissing observations that are less than the lower specification limit

PCTBET

percent of nonmissing observations between the upper and lower specification limits (inclusive)

Statistics Available with Parametric Density Estimates

You can request parametric density estimates with all plot statements in the CAPABILITY procedure (CDFPLOT, COMPHISTOGRAM, HISTOGRAM, PPPLOT, PROBPLOT, and QQPLOT). You can display parameters and statistics associated with these estimates in an inset by specifying a distribution keyword followed by secondary keywords in parentheses. For example, the following statements create a histogram for Strength with a fitted exponential density curve:

proc capability data=Wire;
   histogram Strength / exp;
   inset exp(sigma theta);
run;

The secondary keywords SIGMA and THETA for the EXP distribution keyword request an inset displaying the values of the exponential scale parameter and threshold parameter . You must request the distribution option in the plot statement to display the corresponding distribution statistics in an inset. Specifying a distribution keyword with no secondary keywords produces an inset displaying the full set of parameters for that distribution. See Output 5.15.1 for an example of an inset with statistics from a fitted normal curve.

The following table describes the available distribution keywords. Note that some keywords are not available with all plot statements.

Table 5.37 Density Estimation Primary Keywords

Keyword

Distribution

Plot Statement Availability

BETA

beta

all except COMPHISTOGRAM

EXPONENTIAL

exponential

all except COMPHISTOGRAM

GAMMA

gamma

all except COMPHISTOGRAM

LOGNORMAL

lognormal

all except COMPHISTOGRAM

NORMAL

normal

all plot statements

SB

Johnson

all except COMPHISTOGRAM

SU

Johnson

all except COMPHISTOGRAM

WEIBULL

Weibull

all except COMPHISTOGRAM

WEIBULL2

2-parameter Weibull

PROBPLOT and QQPLOT

Table 5.38 lists the secondary keywords available with each distribution keyword listed in Table 5.37. In many cases, aliases can be used (for example, ALPHA in place of SHAPE1).

Table 5.38 Density Estimation Secondary Keywords

Secondary

   

Keyword

Alias

Description

Secondary Keywords Available with the BETA Keyword

ALPHA

SHAPE1

first shape parameter

BETA

SHAPE2

second shape parameter

SIGMA

SCALE

scale parameter

THETA

THRESHOLD

lower threshold parameter

MEAN

 

mean of the fitted distribution

STD

 

standard deviation of the fitted distribution

Secondary Keywords Available with the EXPONENTIAL Keyword

SIGMA

SCALE

scale parameter

THETA

THRESHOLD

threshold parameter

MEAN

 

mean of the fitted distribution

STD

 

standard deviation of the fitted distribution

Secondary Keywords Available with the GAMMA Keyword

ALPHA

SHAPE

shape parameter

SIGMA

SCALE

scale parameter

THETA

THRESHOLD

threshold parameter

MEAN

 

mean of the fitted distribution

STD

 

standard deviation of the fitted distribution

Secondary Keywords Available with the LOGNORMAL Keyword

SIGMA

SHAPE

shape parameter

THETA

THRESHOLD

threshold parameter

ZETA

SCALE

scale parameter

MEAN

 

mean of the fitted distribution

STD

 

standard deviation of the fitted distribution

Secondary Keywords Available with the NORMAL Keyword

MU

MEAN

mean parameter

SIGMA

STD

scale parameter

Secondary Keywords Available with the SB Keyword

DELTA

SHAPE1

shape parameter

GAMMA

SHAPE2

shape parameter

SIGMA

SCALE

scale parameter

THETA

THRESHOLD

threshold parameter

MEAN

 

mean of the fitted distribution

STD

 

standard deviation of the fitted distribution

Secondary Keywords Available with the SU Keyword

DELTA

SHAPE1

shape parameter

GAMMA

SHAPE2

shape parameter

SIGMA

SCALE

scale parameter

THETA

 

location parameter

MEAN

 

mean of the fitted distribution

STD

 

standard deviation of the fitted distribution

Secondary Keywords Available with the WEIBULL Keyword

C

SHAPE

shape parameter

SIGMA

SCALE

scale parameter

THETA

THRESHOLD

threshold parameter

MEAN

 

mean of the fitted distribution

STD

 

standard deviation of the fitted distribution

Secondary Keywords Available with the WEIBULL2 Keyword

C

SHAPE

shape parameter

SIGMA

SCALE

scale parameter

THETA

THRESHOLD

known lower threshold

MEAN

 

mean of the fitted distribution

STD

 

standard deviation of the fitted distribution

The secondary keywords listed in Table 5.39 can be used with any distribution keyword but only with the HISTOGRAM and COMPHISTOGRAM plot statements.

Table 5.39 Statistics Computed from Any Parametric Density Estimate

Secondary

 

Keyword

Description

CP

capability index

CPK

capability index

CPL

capability index CPL

CPM

capability index

CPU

capability index CPU

ESTPCTLSS

estimated percentage less than the lower specification limit

ESTPCTGTR

estimated percentage greater than the upper specification limit

K

capability index

The secondary keywords listed in Table 5.40 can be used with any distribution keyword but only with the HISTOGRAM plot statement (see Example 5.15).

Table 5.40 Goodness-of-Fit Statistics for Fitted Curves

Secondary

 

Keyword

Description

CHISQ

chi-square statistic

DF

degrees of freedom for the chi-square test

PCHISQ

probability value for the chi-square test

AD

Anderson-Darling EDF test statistic

ADPVAL

Anderson-Darling EDF test -value

CVM

Cramér-von Mises EDF test statistic

CVMPVAL

Cramér-von Mises EDF test -value

KSD

Kolmogorov-Smirnov EDF test statistic

KSDPVAL

Kolmogorov-Smirnov EDF test -value

Table 5.41 lists primary keywords available only with the HISTOGRAM and COMPHISTOGRAM plot statements. These keywords display fill areas on a histogram. If you fit a parametric density on a histogram and request that the area under the curve be filled, these keywords display the percentage of the distribution area that lies below the lower specification limit, between the specification limits, or above the upper specification limit. If you do not fill the area beneath a parametric density estimate, these keywords display the observed proportion of observations (that is, the area in the bars of the histogram).

You should use these options with the FILL, CFILL=, and PFILL= options in the HISTOGRAM and COMPHISTOGRAM statements and with the CLEFT=, CRIGHT=, PLEFT=, and PRIGHT= options in the SPEC statements. See Output 5.16.1 for an example.

Table 5.41 Curve Area Keywords

Keyword

Alias

Description

BETWEENPCT

BETPCT

area between the specification limits

LSLPCT

 

area below the lower specification limit

USLPCT

 

area above the upper specification limit

Statistics Available with Nonparametric Kernel Density Estimates

You can request nonparametric kernel density estimates with the HISTOGRAM and COMPHISTOGRAM plot statements. You can display statistics associated with these estimates by specifying a kernel density keyword followed by secondary keywords in parentheses. For example, the following statements create a histogram for Strength with a fitted kernel density estimate:

proc capability data=Wire;
   histogram Strength / kernel;
   inset kernel(c amise);
run;

The secondary keywords C and AMISE for the KERNEL keyword display the values of the standardized bandwidth and the approximate mean integrated square error.

Note that you can specify up to five kernel density estimates on a single histogram. If you specify multiple kernel density estimates, you can request inset statistics for all of the estimates with the KERNEL keyword, or you can display inset statistics for individual curves with KERNEL keywords, as in the following example:

proc capability data=Wire;
   histogram Strength / kernel(c = 1 2 3);
   inset kernel2(c) kernel3(c);
run;

Three kernel density estimates are displayed on the histogram, but the inset displays the value of only for the second and third estimates.

Table 5.42 lists the kernel density keywords. Table 5.43 lists the available secondary keywords.

Table 5.42 Kernel Density Estimate Primary Keywords

Keyword

Description

KERNEL

displays statistics for all kernel estimates

KERNEL

displays statistics for only the th kernel density estimate

 

Table 5.43 Secondary Keywords Available with the KERNEL Keyword

Secondary Keyword

Description

TYPE

kernel type: normal, quadratic, or triangular

BANDWIDTH

bandwidth for the density estimate

BWIDTH

alias for BANDWIDTH

C

standardized bandwidth for the density estimate:

 

where sample size, bandwidth, and

 

interquartile range

AMISE

approximate mean integrated square error (MISE) for the

 

kernel density

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