A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

Table 2

In-control ARLs (in groups of size 10) of the Two-sided Shew-XB and the Shew-KS charts for a process with a gamma (shape 𝛼, scale 𝛽, location 𝜃) Distribution. Training Sample Size 𝑚=39 and Test Sample Size 𝑛=10.

			Shew-XB	Shew-KS
Shape; 𝛼	Scale; 𝛽=𝛼^−1/2	Location; 𝜃=−√𝛼	𝑘=2.75	𝐶𝐿=0.541
1	1	−1	1099.2	165
2	0.7071	−1.4142	2125.4	167.3
3	0.5774	−1.7321	1764.9	164.3
4	0.5000	−2.0000	320.5	176.7
5	0.4472	−2.2361	289.1	173.1
9	0.3333	−3.0000	227	166.6
10	0.3162	−3.1623	181.6	181.0
12	0.2887	−3.4641	235.7	171.6
16	0.2500	−4.0000	189.9	160.5
20	0.2236	−4.4721	168.5	179.5
Normal	1.0	0.0	170	170

Note: for the Shew-XB chart, 2.75 is the “k” value in the control limits 𝑋₀±𝑘𝑆₀/√𝑛.