Change Point Detection with Robust Control Chart

Table 11

Precision of the estimator when used with proposed MM chart for different magnitudes of process change (magnitude of shift, 𝛿) based on 10,000 trials. Subgroup size 𝑛=5, change point 𝜏=100 (contaminated distribution, 𝛽=0.10, 𝐶=9).

	Magnitude of shift, 𝛿
	𝛿=1.0	𝛿=2.0	𝛿=3.0
𝑃(𝜏=𝜏)	0.1241	0.2525	0.3788
𝑃(|𝜏−𝜏|≤1)	0.3107	0.4753	0.5946
𝑃(|𝜏−𝜏|≤2)	0.4218	0.5861	0.6901
𝑃(|𝜏−𝜏|≤3)	0.5115	0.6690	0.7437
𝑃(|𝜏−𝜏|≤4)	0.5732	0.7138	0.7631
𝑃(|𝜏−𝜏|≤5)	0.6241	0.7476	0.7812
𝑃(|𝜏−𝜏|≤6)	0.6720	0.7834	0.7995
𝑃(|𝜏−𝜏|≤7)	0.7024	0.7961	0.8045
𝑃(|𝜏−𝜏|≤8)	0.7316	0.8120	0.8169
𝑃(|𝜏−𝜏|≤9)	0.7506	0.8234	0.8215
𝑃(|𝜏−𝜏|≤10)	0.7684	0.8350	0.8244