INSET Statement: CAPABILITY Procedure

Summary of INSET Keywords

Summary Statistics and Process Capability Indices

Table 5.32: Summary Statistics

Keyword	Description
CSS	Corrected sum of squares
CV	Coefficient of variation
GEOMEAN	Geometric mean
KURTOSIS \| KURT	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 \| SKEW	Skewness
STD \| STDDEV	Standard deviation
STDMEAN \| STDERR	Standard error of the mean
SUM	Sum of the observations
SUMWGT	Sum of the weights
USS	Uncorrected sum of squares
VAR	Variance

Table 5.33: Percentile Statistics

Keyword	Description
P1	1st percentile
P5	5th percentile
P10	10th percentile
Q1 \| P25	Lower quartile (25th percentile)
MEDIAN \| Q2 \| P50	Median (50th percentile)
Q3 \| P75	Upper quartile (75th percentile)
P90	90th percentile
P95	95th percentile
P99	99th percentile
QRANGE	Interquartile range (Q3 - Q1)

Table 5.34 lists keywords for distribution-free confidence limits for percentiles requested with the CIPCTLDF option.

Table 5.34: Keywords for Distribution-Free Confidence Limits for Percentiles

Keyword	Description
P1_LCL_DF	1st percentile lower confidence limit
P1_UCL_DF	1st percentile upper confidence limit
P5_LCL_DF	5th percentile lower confidence limit
P5_UCL_DF	5th percentile upper confidence limit
P10_LCL_DF	10th percentile lower confidence limit
P10_UCL_DF	10th percentile upper confidence limit
Q1_LCL_DF \| P25_LCL_DF	Lower quartile (25th percentile) lower confidence limit
Q1_UCL_DF \| P25_UCL_DF	Lower quartile (25th percentile) upper confidence limit
MEDIAN_LCL_DF \| Q2_LCL_DF \| P50_LCL_DF	Median (50th percentile) lower confidence limit
MEDIAN_UCL_DF \| Q2_UCL_DF \| P50_UCL_DF	Median (50th percentile) upper confidence limit
Q3_LCL_DF \| P75_LCL_DF	Upper quartile (75th percentile) lower confidence limit
Q3_UCL_DF \| P75_UCL_DF	Upper quartile (75th percentile) upper confidence limit
P90_LCL_DF	90th percentile lower confidence limit
P90_UCL_DF	90th percentile upper confidence limit
P95_LCL_DF	95th percentile lower confidence limit
P95_UCL_DF	95th percentile upper confidence limit
P99_LCL_DF	99th percentile lower confidence limit
P99_UCL_DF	99th percentile upper confidence limit

Table 5.35 lists keywords for percentile confidence limits computed assuming normality requested with the CIPCTLNORMAL option.

Table 5.35: Keywords Percentile Confidence Limits Assuming Normality

Keyword	Description
P1_LCL	1st percentile lower confidence limit
P1_UCL	1st percentile upper confidence limit
P5_LCL	5th percentile lower confidence limit
P5_UCL	5th percentile upper confidence limit
P10_LCL	10th percentile lower confidence limit
P10_UCL	10th percentile upper confidence limit
Q1_LCL \| P25_LCL	Lower quartile (25th percentile) lower confidence limit
Q1_UCL \| P25_UCL	Lower quartile (25th percentile) upper confidence limit
MEDIAN_LCL \| Q2_LCL \| P50_LCL	Median (50th percentile) lower confidence limit
MEDIAN_UCL \| Q2_UCL \| P50_UCL	Median (50th percentile) upper confidence limit
Q3_LCL \| P75_LCL	Upper quartile (75th percentile) lower confidence limit
Q3_UCL \| P75_UCL	Upper quartile (75th percentile) upper confidence limit
P90_LCL	90th percentile lower confidence limit
P90_UCL	90th percentile upper confidence limit
P95_LCL	95th percentile lower confidence limit
P95_UCL	95th percentile upper confidence limit
P99_LCL	99th percentile lower confidence limit
P99_UCL	99th percentile upper confidence limit

Table 5.36: Robust Statistics

Keyword	Description
GINI	Gini’s mean difference
MAD	Median absolute difference about the median
QN	$Q_ n$ , alternative to MAD
SN	$S_ n$ , alternative to MAD
STD_GINI	Gini’s standard deviation
STD_MAD	MAD standard deviation
STD_QN	$Q_ n$ standard deviation
STD_QRANGE	Interquartile range standard deviation
STD_SN	$S_ n$ standard deviation

Table 5.37: 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 t test
T	Statistics for Student’s t test

Table 5.38: Input Data Set

Keyword	Description
DATA=	(label, value) pairs from input data set

Table 5.39: Capability Indices and Confidence Limits

Keyword	Description
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 5.40: 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 $\sigma$ 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 5.15.1 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 5.41: Density Estimation Primary Keywords

Keyword	Distribution	Plot Statement Availability
BETA	beta	all but COMPHISTOGRAM
EXPONENTIAL	exponential	all but COMPHISTOGRAM
GAMMA	gamma	all but COMPHISTOGRAM
GUMBEL	Gumbel	all but COMPHISTOGRAM
IGAUSS	inverse Gaussian	CDFPLOT, HISTOGRAM, PPPLOT
LOGNORMAL	lognormal	all but COMPHISTOGRAM
NORMAL	normal	all
PARETO	generalized Pareto	all but COMPHISTOGRAM
POWER	power function	all but COMPHISTOGRAM
RAYLEIGH	Rayleigh	all but COMPHISTOGRAM
SB	Johnson $S_ B$	HISTOGRAM
SU	Johnson $S_ U$	HISTOGRAM
WEIBULL	Weibull	all but COMPHISTOGRAM
WEIBULL2	2-parameter Weibull	PROBPLOT, QQPLOT

Table 5.42 lists the secondary keywords available with each distribution keyword listed in Table 5.41. In many cases, aliases can be used (for example, ALPHA in place of SHAPE1).

Table 5.42: Density Estimation Secondary Keywords

Secondary
Keyword	Alias	Description
Secondary Keywords Available with the BETA Keyword
ALPHA	SHAPE1	First shape parameter $\alpha$
BETA	SHAPE2	Second shape parameter $\beta$
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Lower threshold parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the EXPONENTIAL Keyword
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Threshold parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the GAMMA Keyword
ALPHA	SHAPE	Shape parameter $\alpha$
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Threshold parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the GUMBEL Keyword
MU		Location parameter $\mu$
SIGMA	SCALE	Scale parameter $\sigma$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the IGAUSS Keyword
MU		Mean parameter $\mu$
LAMBDA		Shape parameter $\lambda$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the LOGNORMAL Keyword
SIGMA	SHAPE	Shape parameter $\sigma$
THETA	THRESHOLD	Threshold parameter $\theta$
ZETA	SCALE	Scale parameter $\zeta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the NORMAL Keyword
MU	MEAN	Mean parameter $\mu$
SIGMA	STD	Scale parameter $\sigma$
Secondary Keywords Available with the PARETO Keyword
ALPHA		Shape parameter $\alpha$
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Threshold parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the POWER Keyword
ALPHA		Shape parameter $\alpha$
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Threshold parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the RAYLEIGH Keyword
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Threshold parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the SB Keyword
DELTA	SHAPE1	Shape parameter $\delta$
GAMMA	SHAPE2	Shape parameter $\gamma$
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Threshold parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the SU Keyword
DELTA	SHAPE1	Shape parameter $\delta$
GAMMA	SHAPE2	Shape parameter $\gamma$
SIGMA	SCALE	Scale parameter $\sigma$
THETA		Location parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the WEIBULL Keyword
C	SHAPE	Shape parameter c
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Threshold parameter $\theta$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution
Secondary Keywords Available with the WEIBULL2 Keyword
C	SHAPE	Shape parameter c
SIGMA	SCALE	Scale parameter $\sigma$
THETA	THRESHOLD	Known lower threshold $\theta _0$
MEAN		Mean of the fitted distribution
STD		Standard deviation of the fitted distribution

The secondary keywords listed in Table 5.43 can be used with any distribution keyword but only with the HISTOGRAM and COMPHISTOGRAM plot statements.

Table 5.43: 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 5.44 can be used with any distribution keyword but only with the HISTOGRAM plot statement (see Example 5.15).

Table 5.44: 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	Cramér-von Mises EDF test statistic
CVMPVAL	Cramér-von Mises EDF test p-value
KSD	Kolmogorov-Smirnov EDF test statistic
KSDPVAL	Kolmogorov-Smirnov EDF test p-value

Table 5.45 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 5.45: 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 more than one kernel density estimate 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 up to five 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 5.46 lists the kernel density keywords. Table 5.47 lists the available secondary keywords.

Table 5.46: Kernel Density Estimate Primary Keywords

Keyword	Description
KERNEL	displays statistics for all kernel estimates
KERNELn	displays statistics for only the nth kernel density estimate
	$n = 1, 2, 3, 4, \mbox{or } 5$

Table 5.47: 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