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 6.6: 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:

  1. If the subgroup sample sizes vary, the special missing value V is assigned to the variable _LIMITN_.

  2. 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.

  3. 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.

  4. 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. Table 6.7 lists the variables that are included.

Table 6.7: OUTTABLE= Data Set Variables

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.