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