00250 y379010282bfa1dc1edfcd76e766f6b

Yander Wiel

Figurę 4. Plots to determine the action limit h yielding a given ARL₀ for

various values of the design parameter in CUSUM and EWMA charts. The left panel shows (h, k) pairs that yield specified ARLs for CUSUM charts. The right panel shows (h, y) pairs that yield specified ARLs for EWMA charts. Gaussian data is assumed.

least 0.5. For 2 standard deviations shifts, values of k between 0.25 and 0.5 give the smallest ARLs. Other values can result in substantially worse performance. A value oik = 0.5 is a reasonable choice. Referring to Figurę 4, h should be set at about 3.5, 4.4, or 5.1 to give ARL₀ near 100, 250, or 500 respectively.

The other columns of Figurę 5 can be used similarly. Usually the rangę of reasonable values for k is fairly obvious. Panels for values of X exceeding 0.5 are not shown because they are virtually identical to those for X =

0.5.

Comparing columns of Figurę 5 is interesting too. One striking feature is that the larger X is, the morę difficult it is to detect shifts of a given size. With X = 0.5, we have virtually no power to detect even 2 standard deviation shifts. This is as we should expect from the discussion of Figurę 3. The most interesting panels in Figurę 5 lie near the top-left to bottom-right diagonal. In these panels the best value of k depends on X. Getting smali

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