PROC CAPABILITY: Summary of INSET Keywords

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	$\text{[math]}$ , alternative to MAD
SN	$\text{[math]}$ , alternative to MAD
STD_GINI	Gini’s standard deviation
STD_MAD	MAD standard deviation
STD_QN	$\text{[math]}$ standard deviation
STD_QRANGE	interquartile range standard deviation
STD_SN	$\text{[math]}$ 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 $\text{[math]}$ test
T	statistics for Student’s $\text{[math]}$ 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 $\text{[math]}$
CPLCL	lower confidence limit for $\text{[math]}$
CPUCL	upper confidence limit for $\text{[math]}$
CPK	capability index $\text{[math]}$
CPKLCL	lower confidence limit for $\text{[math]}$
CPKUCL	upper confidence limit for $\text{[math]}$
CPL	capability index CPL
CPM	capability index $\text{[math]}$
CPMLCL	lower confidence limit for $\text{[math]}$
CPMUCL	upper confidence interval for $\text{[math]}$
CPU	capability index CPU
K	capability index $\text{[math]}$

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 $\text{[math]}$ and threshold parameter $\text{[math]}$ . 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 $\text{[math]}$	all except COMPHISTOGRAM
SU	Johnson $\text{[math]}$	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 $\text{[math]}$
BETA	SHAPE2	second shape parameter $\text{[math]}$
SIGMA	SCALE	scale parameter $\text{[math]}$
THETA	THRESHOLD	lower threshold parameter $\text{[math]}$
MEAN		mean of the fitted distribution
STD		standard deviation of the fitted distribution
Secondary Keywords Available with the EXPONENTIAL Keyword
SIGMA	SCALE	scale parameter $\text{[math]}$
THETA	THRESHOLD	threshold parameter $\text{[math]}$
MEAN		mean of the fitted distribution
STD		standard deviation of the fitted distribution
Secondary Keywords Available with the GAMMA Keyword
ALPHA	SHAPE	shape parameter $\text{[math]}$
SIGMA	SCALE	scale parameter $\text{[math]}$
THETA	THRESHOLD	threshold parameter $\text{[math]}$
MEAN		mean of the fitted distribution
STD		standard deviation of the fitted distribution
Secondary Keywords Available with the LOGNORMAL Keyword
SIGMA	SHAPE	shape parameter $\text{[math]}$
THETA	THRESHOLD	threshold parameter $\text{[math]}$
ZETA	SCALE	scale parameter $\text{[math]}$
MEAN		mean of the fitted distribution
STD		standard deviation of the fitted distribution
Secondary Keywords Available with the NORMAL Keyword
MU	MEAN	mean parameter $\text{[math]}$
SIGMA	STD	scale parameter $\text{[math]}$
Secondary Keywords Available with the SB Keyword
DELTA	SHAPE1	shape parameter $\text{[math]}$
GAMMA	SHAPE2	shape parameter $\text{[math]}$
SIGMA	SCALE	scale parameter $\text{[math]}$
THETA	THRESHOLD	threshold parameter $\text{[math]}$
MEAN		mean of the fitted distribution
STD		standard deviation of the fitted distribution
Secondary Keywords Available with the SU Keyword
DELTA	SHAPE1	shape parameter $\text{[math]}$
GAMMA	SHAPE2	shape parameter $\text{[math]}$
SIGMA	SCALE	scale parameter $\text{[math]}$
THETA		location parameter $\text{[math]}$
MEAN		mean of the fitted distribution
STD		standard deviation of the fitted distribution
Secondary Keywords Available with the WEIBULL Keyword
C	SHAPE	shape parameter $\text{[math]}$
SIGMA	SCALE	scale parameter $\text{[math]}$
THETA	THRESHOLD	threshold parameter $\text{[math]}$
MEAN		mean of the fitted distribution
STD		standard deviation of the fitted distribution
Secondary Keywords Available with the WEIBULL2 Keyword
C	SHAPE	shape parameter $\text{[math]}$
SIGMA	SCALE	scale parameter $\text{[math]}$
THETA	THRESHOLD	known lower threshold $\text{[math]}$
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
Keyword	Description
Secondary
CP	capability index $\text{[math]}$
CPK	capability index $\text{[math]}$
CPL	capability index CPL
CPM	capability index $\text{[math]}$
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 $\text{[math]}$

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
Keyword	Description
Secondary
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 $\text{[math]}$ -value
CVM	Cramér-von Mises EDF test statistic
CVMPVAL	Cramér-von Mises EDF test $\text{[math]}$ -value
KSD	Kolmogorov-Smirnov EDF test statistic
KSDPVAL	Kolmogorov-Smirnov EDF test $\text{[math]}$ -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 $\text{[math]}$ 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 $\text{[math]}$ 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 $\text{[math]}$ 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 $\text{[math]}$	displays statistics for only the $\text{[math]}$ th kernel density estimate
	$\text{[math]}$

Table 5.43 Secondary Keywords Available with the KERNEL Keyword
Secondary Keyword	Description
TYPE	kernel type: normal, quadratic, or triangular
BANDWIDTH	bandwidth $\text{[math]}$ for the density estimate
BWIDTH	alias for BANDWIDTH
C	standardized bandwidth $\text{[math]}$ for the density estimate:
	$\text{[math]}$ where $\text{[math]}$ sample size, $\text{[math]}$ bandwidth, and
	$\text{[math]}$ interquartile range
AMISE	approximate mean integrated square error (MISE) for the
	kernel density

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