BOXCHART Statement: SHEWHART Procedure

Output Data Sets

OUTLIMITS= Data Set

The OUTLIMITS= data set saves control limits and control limit parameters. The following variables can be saved:

Table 18.7: OUTLIMITS= Data Set

Variable	Description
`_ALPHA_`	Probability ( $\alpha$ ) of exceeding limits
`_CP_`	Capability index $C_{p}$
`_CPK_`	Capability index $C_{pk}$
`_CPL_`	Capability index $CPL$
`_CPM_`	Capability index $C_{pm}$
`_CPU_`	Capability index $CPU$
`_INDEX_`	Optional identifier for the control limits specified with the OUTINDEX= option
`_LCLM_`	Lower control limit for subgroup median
`_LCLR_`	Lower control limit for subgroup range
`_LCLS_`	Lower control limit for subgroup standard deviation
`_LCLX_`	Lower control limit for subgroup mean
`_LIMITN_`	Nominal sample size associated with the control limits
`_LSL_`	Lower specification limit
`_MEAN_`	Process mean (value of central line on box chart)
`_R_`	Value of central line on R chart
`_S_`	Value of central line on s chart
`_SIGMAS_`	Multiple (k) of standard error of $\bar{X}_{i}$ or $M_{i}$
`_STDDEV_`	Process standard deviation ( $\hat{\sigma }$ or $\sigma _{0}$ )
`_SUBGRP_`	Subgroup-variable specified in the BOXCHART statement
`_TARGET_`	Target value
`_TYPE_`	Type (estimate or standard value) of `_MEAN_` and `_STDDEV_`
`_UCLM_`	Upper control limit for subgroup median
`_UCLR_`	Upper control limit for subgroup range
`_UCLS_`	Upper control limit for subgroup standard deviation
`_UCLX_`	Upper control limit for subgroup mean
`_USL_`	Upper specification limit
`_VAR_`	Process specified in the BOXCHART statement

Notes:

The variables _LCLM_ and _UCLM_ are included if you specify CONTROLSTAT= MEDIAN; otherwise, the variables _LCLX_ and _UCLX_ are included.
The variables _LCLR_, _R_, and _UCLR_ are included if you specify the RANGES option; otherwise, the variables _LCLS_, _S_, and _UCLS_ are included. These variables are not used to create box charts, but they enable the OUTLIMITS= data set to be used as a LIMITS= data set with the XRCHART, XSCHART, MRCHART, SCHART, and RCHART statements.
If the control limits vary with subgroup sample size, the special missing value V is assigned to the variables _LIMITN_, _LCLX_, _UCLX_, _LCLM_, _UCLM_, _LCLR_, _R_, _UCLR_, _LCLS_, _S_, and _UCLS_.
If the limits are defined in terms of a multiple k of the standard error of $\bar{X_{i}}$ , the value of _ALPHA_ is computed as $\alpha =2(1-\Phi (k))$ , where $\Phi (\cdot )$ is the standard normal distribution function. If the limits are defined in terms of a multiple k of the standard error of $M_{i}$ , the value of _ALPHA_ is computed as $\alpha =2(1-F_{med}(k,n))$ , where $F_{med}(\cdot ,n)$ is the cumulative distribution function of the median of a random sample of n standard normally distributed observations, and n is the value of _LIMITN_. If _LIMITN_ has the special missing value V, this value is assigned to _ALPHA_.
If the limits for means are probability limits, the value of _SIGMAS_ is computed as $k=\Phi ^{-1}(1-\alpha /2)$ , where $\Phi ^{-1}$ is the inverse standard normal distribution function. If the limits for medians are probability limits, the value of _SIGMAS_ is computed as $k=F_{med}^{-1}(1-\alpha /2,n)$ , where $F_{med}^{-1}(\cdot ,n)$ is the inverse distribution function of the median of a random sample of n standard normally distributed observations, and n is the value _LIMITN_. If _LIMITN_ has the special missing value V, this value is assigned to _SIGMAS_.
The variables _CP_, _CPK_, _CPL_, _CPU_, _LSL_, and _USL_ are included only if you provide specification limits with the LSL= and USL= options. The variables _CPM_ and _TARGET_ are included if, in addition, you provide a target value with the TARGET= option. See Capability Indices for computational details.
Optional BY variables are saved in the OUTLIMITS= data set.

The OUTLIMITS= data set contains one observation for each process specified in the BOXCHART statement. For an example, see Saving Control Limits.

OUTBOX= Data Set

The OUTBOX= data set saves subgroup summary statistics, control limits, and outlier values. The following variables can be saved:

the subgroup-variable
the variable _VAR_, containing the process variable name
the variable _TYPE_, identifying features of box-and-whisker plots
the variable _VALUE_, containing values of box-and-whisker plot features
the variable _ID_, containing labels for outliers
the variable _HTML_, containing links associated with box-and-whisker plot features

_ID_ is included in the OUTBOX= data set only if one of the keywords SCHEMATICID or SCHEMATICIDFAR is specified with the BOXSTYLE= option. _HTML_ is present only if one or more of the HTML= , OUTHIGHHTML= , OUTLOWHTML= , or POINTSHTML= options are specified.

Each observation in an OUTBOX= data set records the value of a single feature of one subgroup’s box-and-whisker plot, such as its mean. The _TYPE_ variable identifies the feature whose value is recorded in _VALUE_. Table 18.8 lists valid _TYPE_ variable values:

Table 18.8: Valid _TYPE_

Value	Description
N	Subgroup size
SIGMAS	Multiple (k) of standard error of $\bar{X}_{i}$ or $M_{i}$
ALPHA	Probability ( $\alpha$ ) of exceeding limits
LIMITN	Nominal sample size associated with control limits
LCLM	Lower control limit for subgroup median
LCLX	Lower control limit for subgroup mean
UCLM	Upper control limit for subgroup median
UCLX	Upper control limit for subgroup mean
PROCMED	Process median
PROCMEAN	Process mean
EXLIM	Control limit exceeded on box chart
TREND	Trend variable value
MIN	Minimum subgroup value
Q1	Subgroup first quartile
MEDIAN	Subgroup median
MEAN	Subgroup mean
Q3	Subgroup third quartile
MAX	Subgroup maximum value
LOW	Low outlier value
HIGH	High outlier value
LOWHISKR	Low whisker value, if different from MIN
HIWHISKR	High whisker value, if different from MAX
FARLOW	Low far outlier value
FARHIGH	High far outlier value

Additionally, the following variables, if specified, are included:

block-variables
symbol-variable
BY variables
ID variables

OUTHISTORY= Data Set

The OUTHISTORY= data set saves subgroup summary statistics. The following variables can be saved:

the subgroup-variable
a subgroup minimum variable named by the prefix process suffixed with L
a subgroup first-quartile variable named by the prefix process suffixed with 1
a subgroup mean variable named by the prefix process suffixed with X
a subgroup median variable named by the prefix process suffixed with M
a subgroup third-quartile variable named by the prefix process suffixed with 3
a subgroup maximum variable named by the prefix process suffixed with H
a subgroup sample size variable named by the prefix process suffixed with N
a subgroup range variable named by the prefix process suffixed with R or a subgroup standard deviation variable named by process suffixed with S

A subgroup range variable is included if you specify the RANGES option; otherwise, a subgroup standard deviation variable is included.

Given a process name that contains 32 characters, the procedure first shortens the name to its first 16 characters and its last 15 characters, and then it adds the suffix.

Subgroup summary variables are created for each process specified in the BOXCHART statement. For example, consider the following statements:

proc shewhart data=steel;
   boxchart (Width Diameter)*Lot / outhistory=Summary;
run;

The data set Summary contains variables named Lot, WidthL, Width1, WidthM, WidthX, Width3, WidthH, WidthS, WidthN, DiameterL, Diameter1, DiameterM, DiameterX, Diameter3, DiameterH, DiameterS, and DiameterN.

The variables WidthS and DiameterS are included because the RANGES option is not specified. If you specified the RANGES option, the data set Summary would contain the variables WidthR and DiameterR rather than WidthS and DiameterS.

Additionally, the following variables, if specified, are included:

BY variables
block-variables
symbol-variable
ID variables
_PHASE_ (if the OUTPHASE= option is specified)

For an example of an OUTHISTORY= data set, see Saving Summary Statistics.

OUTTABLE= Data Set

The OUTTABLE= data set saves subgroup summary statistics, control limits, and related information. Table 18.9 list the variables that can be saved.

Table 18.9: OUTTABLE= Data Set Variables

Variable	Description
`_ALPHA_`	Probability ( $\alpha$ ) of exceeding control limits
`_EXLIM_`	Control limit exceeded on box chart
`_LCLM_`	Lower control limit for median
`_LCLX_`	Lower control limit for mean
`_LIMITN_`	Nominal sample size associated with the control limits
`_MEAN_`	Process mean
`_SIGMAS_`	Multiple (k) of the standard error associated with control limits
Subgroup	Values of the subgroup variable
`_SUBMAX_`	Subgroup maximum
`_SUBMED_`	Subgroup median
`_SUBMIN_`	Subgroup minimum
`_SUBN_`	Subgroup sample size
`_SUBQ1_`	Subgroup first quartile (25th percentile)
`_SUBQ3_`	Subgroup third quartile (75th percentile)
`_SUBX_`	Subgroup mean
`_TESTS_`	Tests for special causes signaled on box chart
`_UCLM_`	Upper control limit for median
`_UCLX_`	Upper control limit for mean
`_VAR_`	Process specified in the BOXCHART statement

The variables _LCLM_ and _UCLM_ are included if you specify CONTROLSTAT= MEDIAN; otherwise, the variables _LCLX_ and _UCLX_ are included. In addition, the following variables, if specified, are included:

BY variables
block-variables
symbol-variable
ID variables
_PHASE_ (if the READPHASES= option is specified)
_TREND_ (if the TRENDVAR= option is specified)

Notes:

Either the variable _ALPHA_ or the variable _SIGMAS_ is saved depending on how the control limits are defined (with the ALPHA= or SIGMAS= options, respectively, or with the corresponding variables in a LIMITS= data set).
The variable _TESTS_ is saved if you specify the TESTS= option. The kth character of a value of _TESTS_ is k if Test k is positive at that subgroup. For example, if you request all eight tests and Tests 2 and 8 are positive for a given subgroup, the value of _TESTS_ has a 2 for the second character, an 8 for the eighth character, and blanks for the other six characters.
The variables _EXLIM_ and _TESTS_ are character variables of length 8. The variable _PHASE_ is a character variable of length 48. The variable _VAR_ is a character variable whose length is no greater than 32. All other variables are numeric.

For an example, see Saving Control Limits.