Summary of INSET Keywords

INSET Statement

Summary of INSET Keywords

Summary Statistics and Process Capability Indices

N	sample size
SUMWGT	sum of the weights
MEAN	sample mean
SUM	sum of the observations
STD	standard deviation
VAR	variance
SKEWNESS	skewness
KURTOSIS	kurtosis
MAX	largest value
MIN	smallest value
NOBS	number of observations
RANGE	range
MODE	most frequent value
NMISS	number of missing values
USS	uncorrected sum of squares
CSS	corrected sum of squares
CV	coefficient of variation
STDMEAN	standard error of the mean
DATA=	arbitrary values from SAS-data-set

Table 5.2: Percentile Statistics

P1	1^st percentile
P5	5^th percentile
P10	10^th percentile
Q1	lower quartile (25^th percentile)
MEDIAN	median (50^th percentile)
Q3	upper quartile (75^th percentile)
P90	90^th percentile
P95	95^th percentile
P99	99^th percentile
QRANGE	interquartile range (Q3 - Q1)

Table 5.3: Test of Normality

NORMALTEST	test statistic for normality
PNORMAL	probability value for the normality test

Table 5.4: Signed Rank Test

SIGNRANK	signed rank statistic
PROBS	probability value for the signed rank test

Table 5.5: Capability Indices and Confidence Limits

CP	capability index C_p
CPLCL	lower confidence limit for C_p
CPUCL	upper confidence limit for C_p
CPK	capability index C_pk
CPKLCL	lower confidence limit for C_pk
CPKUCL	upper confidence limit for C_pk
CPL	capability index CPL
CPM	capability index C_pm
CPMLCL	lower confidence limit for C_pm
CPMUCL	upper confidence interval for C_pm
CPU	capability index CPU
K	capability index K

Table 5.6: Specification Limits and Related Information

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)

Table 5.7: Student's t-Test

T	statistic for Student's t-test
PROBT	probability value for Student's t-test

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 $\sigma$ and threshold parameter $\theta$ . 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 5.1.1 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 5.8: 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 S_B	all except COMPHISTOGRAM
SU	Johnson S_U	all except COMPHISTOGRAM
WEIBULL	Weibull	all except COMPHISTOGRAM
WEIBULL2	2-parameter Weibull	PROBPLOT and QQPLOT

Table 5.9 through Table 5.17 list the secondary keywords available with each distribution keyword listed in Table 5.8. In many cases, aliases can be used (for example, ALPHA in place of SHAPE1).

Table 5.9: Secondary Keywords Available with the BETA Keyword

Secondary Keyword	Alias	Description
ALPHA	SHAPE1	first shape parameter $\alpha$
BETA	SHAPE2	second shape parameter $\beta$
SIGMA	SCALE	scale parameter $\sigma$
THETA	THRESHOLD	lower threshold parameter $\theta$

Table 5.10: Secondary Keywords Available with the EXP Keyword

Secondary Keyword	Alias	Description
SIGMA	SCALE	scale parameter $\sigma$
THETA	THRESHOLD	threshold parameter $\theta$

Table 5.11: Secondary Keywords Available with the GAMMA Keyword

Secondary Keyword	Alias	Description
ALPHA	SHAPE	shape parameter $\alpha$
SIGMA	SCALE	scale parameter $\sigma$
THETA	THRESHOLD	threshold parameter $\theta$

Table 5.12: Secondary Keywords Available with the LOGNORMAL Keyword

Secondary Keyword	Alias	Description
SIGMA	SHAPE	shape parameter $\sigma$
THETA	THRESHOLD	threshold parameter $\theta$
ZETA	SCALE	scale parameter $\zeta$

Table 5.13: Secondary Keywords Available with the NORMAL Keyword

Secondary Keyword	Alias	Description
MU	MEAN	mean parameter $\mu$
SIGMA	STD	scale parameter $\sigma$

Table 5.14: Secondary Keywords Available with the SB Keyword

Secondary Keyword	Alias	Description
DELTA		shape parameter $\delta$
GAMMA		shape parameter $\gamma$
SIGMA	SHAPE	scale parameter $\sigma$
THETA	THRESHOLD	threshold parameter $\theta$

Table 5.15: Secondary Keywords Available with the SU Keyword

Secondary Keyword	Alias	Description
DELTA		shape parameter $\delta$
GAMMA		shape parameter $\gamma$
SIGMA	SHAPE	scale parameter $\sigma$
THETA		location parameter $\theta$

Table 5.16: Secondary Keywords Available with the WEIBULL Keyword

Secondary Keyword	Alias	Description
C	SHAPE	shape parameter c
SIGMA	SCALE	scale parameter $\sigma$
THETA	THRESHOLD	threshold parameter $\theta$

Table 5.17: Secondary Keywords Available with the WEIBULL2 Keyword

Secondary Keyword	Alias	Description
C	SHAPE	shape parameter c
SIGMA	SCALE	scale parameter $\sigma$
THETA	THRESHOLD	known lower threshold $\theta_0$

The secondary keywords listed in Table 5.18 can be used with any distribution keyword but only with the HISTOGRAM and COMPHISTOGRAM plot statements.

Table 5.18: Statistics Computed from Any Parametric Density Estimate

Secondary Keyword	Description
CP	capability index C_p
CPK	capability index C_pk
CPL	capability index CPL
CPM	capability index C_pm
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 K

The secondary keywords listed in Table 5.19 can be used with any distribution keyword but only with the HISTOGRAM plot statement (see Example 5.1).

Table 5.19: 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 p-value
CVM	Cram $\acute{e}$ r-von Mises EDF test statistic
CVMPVAL	Cram $\acute{e}$ r-von Mises EDF test p-value
KSD	Kolmogorov-Smirnov EDF test statistic
KSDPVAL	Kolmogorov-Smirnov EDF test p-value

Table 5.20 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 5.2.1 for an example.

Table 5.20: 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 c 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 KERNELn 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 c only for the second and third estimates.

Table 5.21 lists the kernel density keywords. Table 5.22 lists the available secondary keywords.

Table 5.21: Kernel Density Estimate Primary Keywords

Keyword	Description
KERNEL	displays statistics for all kernel estimates
KERNELn	displays statistics for only the n^th kernel density estimate
	n = 1, 2, 3, 4, or 5

Table 5.22: Secondary Keywords Available with the KERNEL Keyword

Secondary Keyword	Description
TYPE	kernel type: normal, quadratic, or triangular
BANDWIDTH	bandwidth $\lambda$ for the density estimate
BWIDTH	alias for BANDWIDTH
C	standardized bandwidth c for the density estimate:
	$c=\frac{\lambda}Q n^{\frac{1}5}$ where n= sample size, $\lambda=$ bandwidth, and
	Q= interquartile range
AMISE	approximate mean integrated square error (MISE) for the
	kernel density

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