Change Point Detection with Robust Control Chart

Table 12

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 (slash distribution).

	Magnitude of shift, 𝛿
	𝛿=1.0	𝛿=2.0	𝛿=3.0
𝑃(𝜏=𝜏)	0.0341	0.0531	0.0829
𝑃(|𝜏−𝜏|≤1)	0.1057	0.1444	0.1798
𝑃(|𝜏−𝜏|≤2)	0.1541	0.2064	0.2547
𝑃(|𝜏−𝜏|≤3)	0.1862	0.2542	0.3053
𝑃(|𝜏−𝜏|≤4)	0.2225	0.2937	0.3547
𝑃(|𝜏−𝜏|≤5)	0.2547	0.3356	0.3892
𝑃(|𝜏−𝜏|≤6)	0.2899	0.3659	0.4222
𝑃(|𝜏−𝜏|≤7)	0.3038	0.3891	0.4482
𝑃(|𝜏−𝜏|≤8)	0.3307	0.4165	0.4690
𝑃(|𝜏−𝜏|≤9)	0.3554	0.4358	0.4849
𝑃(|𝜏−𝜏|≤10)	0.3787	0.4618	0.5094