Table 5. The ARL values of the RR ${}_{r,s}-{\gamma }^2$ control charts in the presence of measurement errors for ${\gamma }_0=0.05$ (left side), ${\gamma }_0=0.1$ (middle) and ${\gamma }_0=0.2$ (right side), and for different values of θ, $\eta =0.28$, τ, n, B = 1, m = 1.

Charts	τ	$\theta =0$	$\theta =0.01$	$\theta =0.02$	$\theta =0.03$	$\theta =0.04$	$\theta =0.05$
n = 5
RR ${}_{2,3}-{\gamma }^2$	0.5	$(8.11,8.06,8.22)$	$(8.28,8.21,8.38)$	$(8.43,8.35,8.53)$	$(8.59,8.52,8.69)$	$(8.75,8.69,8.84)$	$(8.93,8.85,9.01)$
	0.7	$(26.88,26.65,27.19)$	$(27.38,27.15,27.71)$	$(27.87,27.55,28.15)$	$(28.36,28.10,28.66)$	$(28.87,28.62,29.12)$	$(29.42,29.13,29.64)$
	0.8	$(87.72,87.23,88.36)$	$(88.96,88.30,89.56)$	$(89.94,89.12,90.51)$	$(90.85,90.33,91.69)$	$(91.95,91.30,92.44)$	$(93.24,92.53,93.63)$
	1.3	$(25.84,26.13,27.35)$	$(26.38,26.67,27.88)$	$(26.93,27.21,28.42)$	$(27.47,27.76,28.96)$	$(28.02,28.31,29.50)$	$(28.58,28.86,30.04)$
	1.5	$(8.09,8.20,8.68)$	$(8.28,8.39,8.87)$	$(8.47,8.59,9.07)$	$(8.67,8.78,9.26)$	$(8.87,8.98,9.46)$	$(9.07,9.18,9.66)$
	2.0	$(3.38,3.42,3.61)$	$(3.44,3.48,3.67)$	$(3.50,3.55,3.73)$	$(3.57,3.61,3.80)$	$(3.63,3.68,3.87)$	$(3.70,3.75,3.93)$
RR ${}_{3,4}-{\gamma }^2$	0.5	$(5.60,5.61,5.71)$	$(5.68,5.69,5.80)$	$(5.76,5.77,5.88)$	$(5.84,5.85,5.96)$	$(5.93,5.93,6.04)$	$(6.01,6.02,6.12)$
	0.7	$(16.15,16.20,16.62)$	$(16.47,16.50,16.93)$	$(16.76,16.78,17.24)$	$(17.07,17.10,17.53)$	$(17.38,17.40,17.84)$	$(17.70,17.72,18.14)$
	0.8	$(59.75,59.92,61.22)$	$(60.70,60.79,62.12)$	$(61.56,61.53,63.02)$	$(62.38,62.49,63.79)$	$(63.26,63.35,64.67)$	$(64.20,64.24,65.45)$
	1.3	$(26.28,26.56,27.72)$	$(26.80,27.08,28.23)$	$(27.33,27.60,28.75)$	$(27.86,28.13,29.27)$	$(28.39,28.66,29.79)$	$(28.92,29.19,30.31)$
	1.5	$(9.05,9.16,9.63)$	$(9.24,9.35,9.82)$	$(9.43,9.54,10.01)$	$(9.62,9.73,10.20)$	$(9.82,9.93,10.39)$	$(10.02,10.13,10.59)$
	2.0	$(4.35,4.39,4.58)$	$(4.41,4.46,4.64)$	$(4.48,4.52,4.70)$	$(4.54,4.58,4.77)$	$(4.61,4.65,4.84)$	$(4.67,4.72,4.91)$
RR ${}_{4,5}-{\gamma }^2$	0.5	$(5.37,5.39,5.46)$	$(5.43,5.44,5.51)$	$(5.48,5.49,5.56)$	$(5.53,5.54,5.61)$	$(5.58,5.59,5.67)$	$(5.64,5.65,5.72)$
	0.7	$(12.65,12.70,13.04)$	$(12.87,12.92,13.25)$	$(13.09,13.14,13.47)$	$(13.31,13.35,13.68)$	$(13.53,13.58,13.90)$	$(13.76,13.80,14.13)$
	0.8	$(46.80,47.00,48.23)$	$(47.56,47.75,48.90)$	$(48.26,48.47,49.65)$	$(49.00,49.14,50.35)$	$(49.70,49.91,51.07)$	$(50.47,50.63,51.74)$
	1.3	$(27.55,27.82,28.97)$	$(28.07,28.34,29.48)$	$(28.60,28.86,29.99)$	$(29.13,29.39,30.51)$	$(29.65,29.92,31.04)$	$(30.19,30.44,31.56)$
	1.5	$(10.18,10.30,10.77)$	$(10.38,10.49,10.96)$	$(10.57,10.68,11.15)$	$(10.77,10.88,11.35)$	$(10.97,11.08,11.55)$	$(11.17,11.28,11.75)$
	2.0	$(5.34,5.39,5.58)$	$(5.41,5.45,5.64)$	$(5.47,5.52,5.71)$	$(5.54,5.58,5.77)$	$(5.61,5.65,5.84)$	$(5.68,5.72,5.91)$
n = 15
RR ${}_{2,3}-{\gamma }^2$	0.5	$(2.09,2.09,2.10)$	$(2.09,2.09,2.10)$	$(2.10,2.10,2.11)$	$(2.11,2.11,2.12)$	$(2.11,2.11,2.13)$	$(2.12,2.12,2.13)$
	0.7	$(3.79,3.76,3.87)$	$(3.85,3.82,3.94)$	$(3.92,3.89,4.00)$	$(3.98,3.95,4.06)$	$(4.04,4.02,4.12)$	$(4.12,4.08,4.19)$
	0.8	$(17.85,17.59,18.24)$	$(18.22,17.94,18.60)$	$(18.65,18.32,18.96)$	$(19.00,18.68,19.31)$	$(19.39,19.08,19.68)$	$(19.82,19.40,20.05)$
	1.3	$(8.66,8.81,9.44)$	$(8.86,9.01,9.64)$	$(9.06,9.21,9.84)$	$(9.26,9.41,10.05)$	$(9.47,9.62,10.26)$	$(9.68,9.83,10.47)$
	1.5	$(3.07,3.11,3.28)$	$(3.12,3.16,3.33)$	$(3.17,3.21,3.38)$	$(3.22,3.26,3.43)$	$(3.27,3.31,3.48)$	$(3.32,3.36,3.54)$
	2.0	$(2.08,2.09,2.13)$	$(2.09,2.10,2.14)$	$(2.10,2.11,2.15)$	$(2.11,2.12,2.16)$	$(2.12,2.13,2.17)$	$(2.13,2.14,2.18)$
RR ${}_{3,4}-{\gamma }^2$	0.5	$(3.01,3.02,3.02)$	$(3.02,3.02,3.02)$	$(3.02,3.02,3.02)$	$(3.02,3.02,3.02)$	$(3.02,3.02,3.03)$	$(3.02,3.02,3.03)$
	0.7	$(3.83,3.84,3.91)$	$(3.87,3.87,3.95)$	$(3.90,3.91,3.99)$	$(3.94,3.95,4.02)$	$(3.98,3.98,4.06)$	$(4.02,4.02,4.10)$
	0.8	$(12.64,12.68,13.22)$	$(12.89,12.92,13.47)$	$(13.14,13.16,13.71)$	$(13.38,13.41,13.97)$	$(13.64,13.67,14.22)$	$(13.91,13.92,14.46)$
	1.3	$(8.87,9.00,9.56)$	$(9.04,9.18,9.74)$	$(9.22,9.36,9.92)$	$(9.41,9.54,10.10)$	$(9.59,9.72,10.28)$	$(9.78,9.91,10.47)$
	1.5	$(3.88,3.91,4.06)$	$(3.92,3.96,4.11)$	$(3.97,4.00,4.15)$	$(4.01,4.04,4.20)$	$(4.06,4.09,4.25)$	$(4.10,4.14,4.29)$
	2.0	$(3.06,3.06,3.09)$	$(3.07,3.07,3.10)$	$(3.07,3.08,3.10)$	$(3.08,3.08,3.11)$	$(3.09,3.09,3.12)$	$(3.09,3.10,3.13)$
RR ${}_{4,5}-{\gamma }^2$	0.5	$(4.00,4.00,4.00)$	$(4.00,4.00,4.01)$	$(4.00,4.00,4.01)$	$(4.01,4.01,4.01)$	$(4.01,4.01,4.01)$	$(4.01,4.01,4.01)$
	0.7	$(4.46,4.47,4.52)$	$(4.48,4.49,4.54)$	$(4.51,4.51,4.57)$	$(4.53,4.54,4.59)$	$(4.55,4.56,4.62)$	$(4.58,4.59,4.64)$
	0.8	$(11.10,11.17,11.62)$	$(11.29,11.36,11.82)$	$(11.48,11.55,12.01)$	$(11.69,11.75,12.21)$	$(11.89,11.94,12.40)$	$(12.09,12.14,12.60)$
	1.3	$(9.50,9.63,10.15)$	$(9.67,9.79,10.32)$	$(9.84,9.97,10.49)$	$(10.02,10.14,10.67)$	$(10.19,10.31,10.85)$	$(10.37,10.49,11.02)$
	1.5	$(4.77,4.80,4.93)$	$(4.81,4.84,4.97)$	$(4.85,4.88,5.02)$	$(4.89,4.92,5.06)$	$(4.93,4.96,5.10)$	$(4.97,5.00,5.15)$
	2.0	$(4.05,4.05,4.07)$	$(4.05,4.05,4.07)$	$(4.06,4.06,4.08)$	$(4.06,4.06,4.09)$	$(4.07,4.07,4.09)$	$(4.07,4.08,4.10)$