The CAPABILITY Procedure

Summary of INSET Keywords

Summary Statistics and Process Capability Indices

Table 38: Summary Statistics

Keyword Description
CSS Corrected sum of squares
CV Coefficient of variation
GEOMEAN Geometric mean
HARMEAN Harmonic 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 39: 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 40 lists keywords for distribution-free confidence limits for percentiles requested with the CIPCTLDF option.

Table 40: 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 41 lists keywords for percentile confidence limits computed assuming normality requested with the CIPCTLNORMAL option.

Table 41: Keywords for 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 42: Robust Statistics

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


Table 43: 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 44: Input Data Set

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


Table 45: Capability Indices and Confidence Limits

Keyword Description
CP Capability index upper C Subscript p
CPLCL Lower confidence limit for upper C Subscript p
CPUCL Upper confidence limit for upper C Subscript p
CPK Capability index upper C Subscript p k
CPKLCL Lower confidence limit for upper C Subscript p k
CPKUCL Upper confidence limit for upper C Subscript p k
CPL Capability index upper C upper P upper L
CPM Capability index upper C Subscript p m
CPMLCL Lower confidence limit for upper C Subscript p m
CPMUCL Upper confidence interval for upper C Subscript p m
CPU Capability index upper C upper P upper U
K Capability index K


Table 46: 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 6.15.1 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 47: 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 upper S Subscript upper B HISTOGRAM
SU Johnson upper S Subscript upper U HISTOGRAM
WEIBULL Weibull All but COMPHISTOGRAM
WEIBULL2 2-parameter Weibull PROBPLOT, QQPLOT


Table 48 lists the secondary keywords available with each distribution keyword listed in Table 47. In many cases, aliases can be used (for example, ALPHA in place of SHAPE1).

Table 48: 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 lamda
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 49 can be used with any distribution keyword but only with the HISTOGRAM and COMPHISTOGRAM plot statements.

Table 49: Statistics Computed from Any Parametric Density Estimate

Secondary
Keyword Description
CP Capability index upper C Subscript p
CPK Capability index upper C Subscript p k
CPL Capability index upper C upper P upper L
CPM Capability index upper C Subscript p m
CPU Capability index upper C upper P upper U
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 50 can be used with any distribution keyword but only with the HISTOGRAM plot statement (see Example 6.15).

Table 50: 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 51 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 6.16.1 for an example.

Table 51: 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 52 lists the kernel density keywords. Table 53 lists the available secondary keywords.

Table 52: 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 equals 1 comma 2 comma 3 comma 4 comma or 5


Table 53: Secondary Keywords Available with the KERNEL Keyword

Secondary Keyword Description
TYPE Kernel type: normal, quadratic, or triangular
BANDWIDTH Bandwidth lamda for the density estimate
BWIDTH Alias for BANDWIDTH
C Standardized bandwidth c for the density estimate:
c equals StartFraction lamda Over upper Q EndFraction n Superscript one fifth where n = sample size, lamda equals bandwidth, and
Q = interquartile range
AMISE Approximate mean integrated square error (MISE) for the kernel density


Last updated: April 11, 2025