## EWMAARL Function

computes the average run length for an exponentially weighted moving
average.

*Syntax*

**EWMAARL**where

| is the shift to be detected, expressed as a multiple
of the process standard deviation (),
where . |

*r* | is the weight factor for the current subgroup
mean in the EWMA, where . If *r*=1, the
EWMAARL function returns the average run length for a
Shewhart chart for means. Refer to Wadsworth and others
(1986). If , , and ,the algorithm used is unstable. However,
note that the EWMA behaves like a cusum when
, and in this case the CUSUMARL
function is applicable. |

*k* | is the multiple of used to define the
control limits, where . Typically
*k*=3. |

*Description*

The EWMAARL function computes the average run length for an
exponentially weighted moving average (EWMA) scheme using the method
of Crowder (1987a,b). The notation used in the preceding list
is consistent with that used in the MACONTROL procedure.
For a specified shift , you can use the EWMAARL function
to design an exponentially weighted moving average scheme by first
calculating average run lengths for a range of values of *r* and
*k* and then choosing the combination of *r* and *k* that yields a
desired average run length.

*Examples*

The following statements specify a shift of 1, a weight factor
of 0.25, and 3 control limits. The EWMAARL function
returns an average run length of 11.154267016.

data;
arl=ewmaarl(1.00,0.25,3.0);
put arl;
run;

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.