Table 3 The \(k_1, k_2\) values of the proposed Auxiliary HWMA-SR repetitive control chart to attain nominal \(ARL_0 = 370, 500\).

\(n=5\)

0.03

(2.25, 0.43)

(2.45, 0.47)

(2.67, 0.49)

(3.92, 1.27)

0.05

(2.28, 0.35)

(2.53, 0.41)

(2.89, 0.81)

(4.29, 2.74)

\(n=10\)

0.03

(2.51,0.38)

(2.68,0.48)

(2.59,1.29)

(4.39,1.95)

0.05

(2.74, 0.39)

(2.67,0.76)

(3.09, 1.50)

(4.76, 2.60)

0.10

(2.82, 0.47)

(3.202, 1.152)

(3.50, 2.14)

(4.98, 3.94)

0.20

(2.85, 0.59)

(3.09, 1.89)

(3.78, 2.28)

(5.38, 2.17)

\(n=15\)

0.03

(2.36, 0.37)

(2.50, 0.62)

(2.86, 1.58)

(4.07, 2.23)

0.05

(2.68, 0.41)

(2.66, 0.91)

(3.33, 1.58)

(4.57, 2.41)

0.10

(2.93, 0.67)

(3.09, 0.90)

(3.63, 1.66)

(5.27, 2.41)

0.20

(2.97, 0.80)

(3.37, 0.90)

(3.93, 1.65)

(5.55, 2.32)

\(n=20\)

0.03

(2.56, 0.40)

(2.70, 0.56)

(2.77, 1.55)

(4.17, 2.21)

0.05

(2.75, 0.55)

(2.70, 1.35)

(3.27, 1.91)

(4.65, 2.71)

0.10

(3.08, 0.60)

(3.10, 1.83)

(3.84, 2.27)

(5.85, 3.06)

0.20

(3.07, 0.79)

(3.43, 1.69)

(4.20, 2.08)

(5.93, 2.93)

\(n=5\)

0.03

(2.145, 0.534)

(2.48, 0.67)

(2.67, 0.67)

(3.86, 2.47)

0.05

(2.30, 0.40)

(2.63, 0.98)

(2.99, 0.83)

(4.31, 1.67)

\(n=10\)

0.03

(2.51, 0.53)

(2.67, 0.68)

(2.89, 1.08)

(4.39, 1.61)

0.05

(2.75, 0.54)

(2.78, 0.96)

(3.28, 1.41)

(4.48, 2.96)

0.10

(2.85, 0.57)

(2.99, 1.95)

(3.69, 1.44)

(5.09, 3.59)

0.20

(2.87, 0.68)

(3.15, 1.26)

(3.82, 2.22)

(5.38, 2.18)

\(n=15\)

0.03

(2.50, 0.47)

(2.50, 0.92)

(2.99, 1.58)

(4.29, 1.93)

0.05

(2.76, 0.54)

(2.96, 0.91)

(3.27, 1.91)

(4.79, 2.90)

0.10

(2.99, 0.91)

(3.19, 0.99)

(3.73, 1.97)

(5.28, 2.78)

0.20

(2.97, 1.21)

(3.41, 1.05)

(4.02, 2.36)

(5.65, 3.39)

\(n=20\)

0.03

(2.88,0.39)

(2.75, 0.66)

(3.17, 1.12)

(4.38, 1.62)

0.05

(2.75, 0.78)

(2.84, 1.07)

(3.46, 1.37)

(4.98, 1.85)

0.10

(3.09, 0.80)

(3.40, 1.55)

(4.24, 1.90)

(5.98, 2.70)

0.20

(3.17, 0.83)

(3.55, 1.28)

(4.22, 1.67)

(5.96, 2.79)