An example of CUSUM status chart for μ1 = 5 mm and σ = 3 mm in the LR direction. A change in the systematic offset was detected on 18th day where C − exceeds the decision interval H. The solid circles denote the offsets after being corrected with a shift magnitude of 3.6 mm calculated using Eq. (5). The corrected offsets were observed to be closer to the target value of zero than the original offsets.
An example of false positive CUSUM status chart for μ1 = 5 mm and σ = 3 mm in the SI direction. A change in the systematic offset due to an unusual spike in the localization data on the sixth day where the CUSUM value exceeds the decision interval H. The chart self-corrects by indicating another systematic shift of equal magnitude on the seventh day.
Percentage reduction in the frequency of localization offset exceeding action levels (Δ) range from 1 to 8 mm. For the optimal values of Δ = 5 mm and μ1 = 5 mm, the frequency of localization offsets exceeding Δ was reduced by approximately half with the incorporation of CUSUM method.
Frequency of localization offsets exceeding 5 mm action level, with and without the incorporation of the CUSUM chart method, for the 18 cases with persistent shifts for μ1 = 5 mm. In majority of the cases, the use of the CUSUM chart reduced the frequency of interventions. For example, the number of interventions required for two cases was reduced from 5 interventions to 1 and from 4 interventions to 1.
Values of decision interval (h) for a range of σ and μ1 derived using Hawkin’s formulation (Ref. 23).
Percentage of charts with systematic shifts, false positives and magnitudes of shift for μ1 = 3, 5, and 7 mm.
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