Change Point Detection with Robust Control Chart

Table 9

Precision of the estimator when used with 𝑋-Bar 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)	0.0943	0.2365	0.4044
𝑃(|𝜏−𝜏|≤1)	0.2295	0.4503	0.6430
𝑃(|𝜏−𝜏|≤2)	0.3184	0.5669	0.7574
𝑃(|𝜏−𝜏|≤3)	0.3873	0.6547	0.8315
𝑃(|𝜏−𝜏|≤4)	0.4595	0.7260	0.8667
𝑃(|𝜏−𝜏|≤5)	0.5234	0.7826	0.8986
𝑃(|𝜏−𝜏|≤6)	0.5672	0.8331	0.9308
𝑃(|𝜏−𝜏|≤7)	0.6074	0.8583	0.9354
𝑃(|𝜏−𝜏|≤8)	0.6413	0.8827	0.9501
𝑃(|𝜏−𝜏|≤9)	0.6655	0.8991	0.9586
𝑃(|𝜏−𝜏|≤10)	0.6928	0.9172	0.9620