Change Point Detection with Robust Control Chart

Table 7

Precision of the estimator when used with median chart for different magnitudes of process change (magnitude of shift, 𝛿) based on 10,000 trials. Subgroup size 𝑛=5, change point 𝜏=100 (normal distribution).

	Magnitude of shift, 𝛿
	𝛿=1.0	𝛿=2.0	𝛿=3.0
𝑃(𝜏=𝜏)	0.2520	0.5959	0.8164
𝑃(|𝜏−𝜏|≤1)	0.4720	0.8346	0.9412
𝑃(|𝜏−𝜏|≤2)	0.6120	0.9166	0.9769
𝑃(|𝜏−𝜏|≤3)	0.6960	0.9557	0.9870
𝑃(|𝜏−𝜏|≤4)	0.7510	0.9722	0.9882
𝑃(|𝜏−𝜏|≤5)	0.7910	0.9794	0.9923
𝑃(|𝜏−𝜏|≤6)	0.8200	0.9822	0.9930
𝑃(|𝜏−𝜏|≤7)	0.8560	0.9833	0.9930
𝑃(|𝜏−𝜏|≤8)	0.8760	0.9850	0.9930
𝑃(|𝜏−𝜏|≤9)	0.8880	0.9879	0.9930
𝑃(|𝜏−𝜏|≤10)	0.9060	0.9888	0.9930