Change Point Detection with Robust Control Chart

Table 6

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 (normal distribution).

	Magnitude of shift, 𝛿
	𝛿=1.0	𝛿=2.0	𝛿=3.0
𝑃(𝜏=𝜏)	0.2660	0.6049	0.8168
𝑃(|𝜏−𝜏|≤1)	0.4790	0.8323	0.9393
𝑃(|𝜏−𝜏|≤2)	0.6230	0.9139	0.9734
𝑃(|𝜏−𝜏|≤3)	0.7080	0.9537	0.9834
𝑃(|𝜏−𝜏|≤4)	0.7610	0.9720	0.9843
𝑃(|𝜏−𝜏|≤5)	0.7990	0.9783	0.9893
𝑃(|𝜏−𝜏|≤6)	0.8260	0.9811	0.9900
𝑃(|𝜏−𝜏|≤7)	0.8580	0.9831	0.9909
𝑃(|𝜏−𝜏|≤8)	0.8790	0.9848	0.9909
𝑃(|𝜏−𝜏|≤9)	0.9100	0.9877	0.9915
𝑃(|𝜏−𝜏|≤10)	0.9220	0.9899	0.9915