Change Point Detection with Robust Control Chart

Table 8

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 (normal distribution).

	Magnitude of shift, 𝛿
	𝛿=1.0	𝛿=2.0	𝛿=3.0
𝑃(𝜏=𝜏)	0.2590	0.5961	0.8163
𝑃(|𝜏−𝜏|≤1)	0.4800	0.8288	0.9415
𝑃(|𝜏−𝜏|≤2)	0.6240	0.9125	0.9777
𝑃(|𝜏−𝜏|≤3)	0.7090	0.9535	0.9878
𝑃(|𝜏−𝜏|≤4)	0.7600	0.9714	0.9878
𝑃(|𝜏−𝜏|≤5)	0.7980	0.9783	0.9928
𝑃(|𝜏−𝜏|≤6)	0.8240	0.9811	0.9935
𝑃(|𝜏−𝜏|≤7)	0.8610	0.9822	0.9935
𝑃(|𝜏−𝜏|≤8)	0.8830	0.9839	0.9935
𝑃(|𝜏−𝜏|≤9)	0.8960	0.9868	0.9935
𝑃(|𝜏−𝜏|≤10)	0.9130	0.9877	0.9935