XCHART Statement: CUSUM Procedure

Output Data Sets

OUTLIMITS= Data Set

When you save the parameters for the cusum scheme in an OUTLIMITS= data set, the following variables are included:

Table 6.5: OUTLIMITS= Data Set

Variable	Description
`_ALPHA_`	probability ( $\alpha$ ) of Type 1 error
`_ARLIN_`	average run length for zero shift
`_ARLOUT_`	average run length for shift of $\delta$
`_BETA_`	probability ( $\beta$ ) of Type 2 error
`_DELTA_`	shift ( $\delta$ ) to be detected
`_H_`	decision interval h for one-sided scheme; distance h between origin and upper arm V-mask for two-sided scheme
`_HSTART_`	headstart value
`_INDEX_`	optional identifier for cusum parameters (if the OUTINDEX= option is specified)
`_K_`	reference value k for one-sided scheme; slope of lower V-mask arm for two-sided scheme
`_LIMITN_`	nominal sample size for cusum scheme
`_MEAN_`	estimated process mean ( $\overline{\overline{X}}$ )
`_MU0_`	target mean $\mu _{0}$
`_ORIGIN_`	origin of V-mask
`_SCHEME_`	type of scheme ('ONESIDED' or 'TWOSIDED')
`_SIGMAS_`	$z_{1-\alpha /2}$
`_STDDEV_`	estimated or known standard deviation ( $\hat{\sigma }$ or $\sigma _{0}$ )
`_SUBGRP_`	subgroup-variable specified in XCHART statement
`_TYPE_`	type ('ESTIMATE' or 'STANDARD') of `_STDDEV_`
`_VAR_`	process specified in XCHART statement

Notes:

If the subgroup sample sizes vary, the special missing value V is assigned to the variable _LIMITN_.
If a V-mask is specified with SIGMAS=k, _ALPHA_ is computed as $\alpha =2(1-\Phi (k))$ , where $\Phi (\cdot )$ is the standard normal distribution function.
If a V-mask is specified with ALPHA= $\alpha$ , _SIGMAS_ is computed as $k=\Phi ^{-1}(1-\alpha /2)$ , where $\Phi ^{-1}$ is the inverse standard normal distribution function.
BY variables are saved in the OUTLIMITS= data set.

The OUTLIMITS= data set contains one observation for each process specified in the XCHART statement. For an example, see Saving Cusum Scheme Parameters.

OUTHISTORY= Data Set

When you save subgroup summary statistics in an OUTHISTORY= data set, the following variables are included:

the subgroup-variable
a subgroup mean variable named by process suffixed with X
a subgroup sample size variable named by process suffixed with N
a subgroup standard deviation variable named by process suffixed with S
a cusum variable named by process suffixed with C

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.

Variables containing subgroup summary statistics are created for each process specified in the XCHART statement. For example, consider the following statements:

proc cusum data=Steel limits=Stparm;
   xchart (Width Diameter)*Lot / outhistory=Summary;
run;

The data set Summary would contain nine variables named Lot, WidthX, WidthS, WidthN, WidthC, DiameterX, DiameterS, DiameterN, and DiameterC.

Additionally, if specified, the following variables are included:

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

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

OUTTABLE= Data Set

The OUTTABLE= data set saves subgroup means, subgroup sample sizes, cusums, and cusum limits. The following variables are included:

Variable	Description
`_CUSUM_`	cumulative sum
`_EXLIM_`	decision interval or V-mask arm exceeded
`_H_`	decision interval
`_MASKL_`	lower arm of V-mask
`_MASKU_`	upper arm of V-mask
subgroup	values of the subgroup variable
`_SUBN_`	subgroup sample size
`_SUBX_`	subgroup mean
`_SUBS_`	subgroup standard deviation
`_VAR_`	process specified in XCHART statement

In addition, the following variables are saved if specified:

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

Note that the variables _VAR_ and _EXLIM_ are character variables of length eight. The variable _PHASE_ is a character variable of length 16.