Chapter Contents |
Previous |
Next |
Functions |
where
type | indicates a one-sided or two-sided scheme. Valid values are `ONESIDED' or `O' for a one-sided scheme, and `TWOSIDED' or `T' for a two-sided scheme. |
is the shift to be detected, expressed as a multiple of the process standard deviation . | |
h | is the decision interval (one-sided scheme) or the vertical distance between the origin and the upper arm of the V-mask (two-sided scheme), each time expressed as a positive value in standard units (a multiple of , where n is the subgroup sample size). |
k | is the reference value (one-sided scheme) or the slope of the lower arm of the V-mask (two-sided scheme), each time expressed as a positive value in standard units (a multiple of ,where n is the subgroup sample size). |
headstart | is the headstart value (optional) expressed in standard units (a multiple of ,where n is the subgroup sample size). The default headstart is zero. For details, refer to Lucas and Crosier (1982). |
For a one-sided scheme, the average run length is calculated using the integral equation method (with 24 Gaussian points) described by Goel and Wu (1971) and Lucas and Crosier (1982).
For a two-sided scheme with no headstart, the average
run length (ARL) is calculated using the fact that
For a two-sided scheme with a nonzero headstart, the ARL is calculated by combining average run lengths for one-sided schemes as described in Appendix A.1 of Lucas and Crosier (1982, 204).
For a specified shift , you can use the CUSUMARL function to design a cusum scheme by first calculating average run lengths for a range of values of h and k and then choosing the combination of h and k that yields a desired average run length.
You can also use the CUSUMARL function to interpolate published tables of average run lengths.
data; arl=cusumarl('twosided',2.5,8,0.25); put arl; run; data; arl=cusumarl('onesided',2.5,8,0.25); put arl; run; data; arl=cusumarl('o',2.5,8,0.25,0.1); put arl; run;
Chapter Contents |
Previous |
Next |
Top |
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.