. 2020 Jul 11;48(12):2178–2204. doi: 10.1080/02664763.2020.1787356

Table 4. The ARL values of the RR $_{r, s} - γ^{2}$ control charts in the presence of measurement errors for $γ_{0} = 0.05$ (left side), $γ_{0} = 0.1$ (middle) and $γ_{0} = 0.2$ (right side), and for different values of η, $θ = 0.05$ , τ, n, B = 1, m = 1.

Charts	τ	$η = 0$	$η = 0.1$	$η = 0.2$	$η = 0.3$	$η = 0.5$	$η = 1$
n = 5
RR $_{2, 3} - γ^{2}$	0.5	$(8.92, 8.85, 8.98)$	$(8.94, 8.85, 8.99)$	$(8.92, 8.84, 8.99)$	$(8.92, 8.86, 9.01)$	$(8.90, 8.84, 9.06)$	$(8.87, 8.87, 9.24)$
	0.7	$(29.38, 29.11, 29.54)$	$(29.45, 29.14, 29.58)$	$(29.35, 29.06, 29.57)$	$(29.40, 29.13, 29.65)$	$(29.29, 29.09, 29.80)$	$(29.19, 29.18, 30.42)$
	0.8	$(93.12, 92.52, 93.41)$	$(93.28, 92.44, 93.58)$	$(93.15, 92.24, 93.38)$	$(93.20, 92.54, 93.68)$	$(92.90, 92.39, 93.98)$	$(92.74, 92.60, 95.22)$
	1.3	$(28.57, 28.83, 29.93)$	$(28.57, 28.84, 29.94)$	$(28.57, 28.85, 29.99)$	$(28.58, 28.87, 30.06)$	$(28.59, 28.92, 30.30)$	$(28.66, 29.19, 31.45)$
	1.5	$(9.07, 9.17, 9.62)$	$(9.07, 9.17, 9.62)$	$(9.07, 9.18, 9.64)$	$(9.07, 9.19, 9.67)$	$(9.07, 9.21, 9.77)$	$(9.10, 9.32, 10.24)$
	2.0	$(3.70, 3.74, 3.92)$	$(3.70, 3.74, 3.92)$	$(3.70, 3.74, 3.92)$	$(3.70, 3.75, 3.94)$	$(3.70, 3.76, 3.98)$	$(3.71, 3.80, 4.16)$
RR $_{3, 4} - γ^{2}$	0.5	$(6.01, 6.02, 6.11)$	$(6.02, 6.02, 6.12)$	$(6.02, 6.02, 6.12)$	$(6.01, 6.02, 6.13)$	$(6.01, 6.02, 6.15)$	$(6.01, 6.05, 6.26)$
	0.7	$(17.69, 17.71, 18.09)$	$(17.71, 17.71, 18.11)$	$(17.71, 17.71, 18.11)$	$(17.70, 17.73, 18.15)$	$(17.71, 17.73, 18.25)$	$(17.68, 17.82, 18.68)$
	0.8	$(64.10, 64.21, 65.33)$	$(64.20, 64.19, 65.35)$	$(64.22, 64.17, 65.37)$	$(64.13, 64.24, 65.47)$	$(64.22, 64.25, 65.78)$	$(64.07, 64.48, 67.06)$
	1.3	$(28.92, 29.17, 30.21)$	$(28.92, 29.17, 30.22)$	$(28.92, 29.18, 30.26)$	$(28.93, 29.20, 30.34)$	$(28.93, 29.25, 30.56)$	$(29.00, 29.51, 31.63)$
	1.5	$(10.01, 10.12, 10.55)$	$(10.01, 10.12, 10.55)$	$(10.01, 10.12, 10.57)$	$(10.02, 10.13, 10.60)$	$(10.02, 10.15, 10.69)$	$(10.05, 10.26, 11.14)$
	2.0	$(4.67, 4.71, 4.89)$	$(4.67, 4.71, 4.89)$	$(4.67, 4.72, 4.90)$	$(4.67, 4.72, 4.91)$	$(4.68, 4.73, 4.95)$	$(4.69, 4.77, 5.13)$
RR $_{4, 5} - γ^{2}$	0.5	$(5.64, 5.65, 5.71)$	$(5.64, 5.65, 5.71)$	$(5.64, 5.65, 5.72)$	$(5.64, 5.65, 5.72)$	$(5.64, 5.65, 5.74)$	$(5.64, 5.67, 5.81)$
	0.7	$(13.75, 13.79, 14.09)$	$(13.76, 13.80, 14.10)$	$(13.76, 13.81, 14.12)$	$(13.75, 13.81, 14.13)$	$(13.76, 13.81, 14.20)$	$(13.76, 13.89, 14.52)$
	0.8	$(50.44, 50.60, 51.63)$	$(50.49, 50.63, 51.67)$	$(50.51, 50.66, 51.74)$	$(50.45, 50.66, 51.78)$	$(50.46, 50.67, 52.03)$	$(50.48, 50.96, 53.14)$
	1.3	$(30.17, 30.42, 31.45)$	$(30.18, 30.43, 31.46)$	$(30.19, 30.43, 31.51)$	$(30.18, 30.45, 31.57)$	$(30.20, 30.51, 31.80)$	$(30.25, 30.76, 32.85)$
	1.5	$(11.17, 11.27, 11.70)$	$(11.17, 11.27, 11.71)$	$(11.17, 11.27, 11.73)$	$(11.17, 11.28, 11.76)$	$(11.17, 11.30, 11.85)$	$(11.20, 11.41, 12.30)$
	2.0	$(5.68, 5.72, 5.90)$	$(5.68, 5.72, 5.90)$	$(5.68, 5.72, 5.91)$	$(5.68, 5.72, 5.92)$	$(5.68, 5.73, 5.96)$	$(5.69, 5.78, 6.14)$
n = 15
RR $_{2, 3} - γ^{2}$	0.5	$(2.12, 2.12, 2.13)$	$(2.12, 2.12, 2.13)$	$(2.12, 2.12, 2.13)$	$(2.12, 2.12, 2.13)$	$(2.12, 2.12, 2.14)$	$(2.12, 2.12, 2.15)$
	0.7	$(4.12, 4.08, 4.18)$	$(4.12, 4.08, 4.18)$	$(4.12, 4.08, 4.18)$	$(4.11, 4.08, 4.19)$	$(4.11, 4.08, 4.22)$	$(4.09, 4.10, 4.35)$
	0.8	$(19.86, 19.42, 19.97)$	$(19.83, 19.43, 20.02)$	$(19.83, 19.45, 20.02)$	$(19.80, 19.45, 20.06)$	$(19.73, 19.43, 20.20)$	$(19.56, 19.55, 21.01)$
	1.3	$(9.68, 9.81, 10.41)$	$(9.68, 9.82, 10.41)$	$(9.68, 9.82, 10.44)$	$(9.68, 9.83, 10.48)$	$(9.69, 9.86, 10.61)$	$(9.72, 10.01, 11.22)$
	1.5	$(3.32, 3.36, 3.52)$	$(3.32, 3.36, 3.52)$	$(3.32, 3.36, 3.53)$	$(3.32, 3.36, 3.54)$	$(3.32, 3.37, 3.58)$	$(3.33, 3.41, 3.75)$
	2.0	$(2.13, 2.14, 2.17)$	$(2.13, 2.14, 2.17)$	$(2.13, 2.14, 2.18)$	$(2.13, 2.14, 2.18)$	$(2.13, 2.14, 2.19)$	$(2.13, 2.15, 2.23)$
RR $_{3, 4} - γ^{2}$	0.5	$(3.02, 3.02, 3.03)$	$(3.02, 3.02, 3.03)$	$(3.02, 3.02, 3.03)$	$(3.02, 3.02, 3.03)$	$(3.02, 3.02, 3.03)$	$(3.02, 3.03, 3.03)$
	0.7	$(4.02, 4.02, 4.09)$	$(4.02, 4.02, 4.09)$	$(4.01, 4.02, 4.10)$	$(4.01, 4.02, 4.10)$	$(4.01, 4.03, 4.12)$	$(4.01, 4.04, 4.20)$
	0.8	$(13.91, 13.92, 14.41)$	$(13.92, 13.91, 14.42)$	$(13.90, 13.91, 14.44)$	$(13.90, 13.92, 14.48)$	$(13.89, 13.95, 14.59)$	$(13.87, 14.06, 15.13)$
	1.3	$(9.77, 9.89, 10.42)$	$(9.77, 9.90, 10.42)$	$(9.78, 9.90, 10.44)$	$(9.78, 9.91, 10.48)$	$(9.78, 9.94, 10.59)$	$(9.81, 10.07, 11.13)$
	1.5	$(4.10, 4.13, 4.28)$	$(4.10, 4.13, 4.28)$	$(4.10, 4.14, 4.29)$	$(4.10, 4.14, 4.30)$	$(4.10, 4.14, 4.33)$	$(4.11, 4.18, 4.48)$
	2.0	$(3.09, 3.10, 3.12)$	$(3.09, 3.10, 3.13)$	$(3.09, 3.10, 3.13)$	$(3.09, 3.10, 3.13)$	$(3.09, 3.10, 3.14)$	$(3.09, 3.11, 3.17)$
RR $_{4, 5} - γ^{2}$	0.5	$(4.01, 4.01, 4.01)$	$(4.01, 4.01, 4.01)$	$(4.01, 4.01, 4.01)$	$(4.01, 4.01, 4.01)$	$(4.01, 4.01, 4.01)$	$(4.01, 4.01, 4.01)$
	0.7	$(4.58, 4.59, 4.64)$	$(4.58, 4.59, 4.64)$	$(4.58, 4.59, 4.64)$	$(4.58, 4.59, 4.65)$	$(4.58, 4.59, 4.66)$	$(4.58, 4.60, 4.71)$
	0.8	$(12.09, 12.14, 12.55)$	$(12.09, 12.14, 12.56)$	$(12.09, 12.14, 12.58)$	$(12.09, 12.15, 12.61)$	$(12.09, 12.17, 12.70)$	$(12.09, 12.27, 13.15)$
	1.3	$(10.37, 10.48, 10.97)$	$(10.37, 10.48, 10.98)$	$(10.37, 10.49, 11.00)$	$(10.37, 10.49, 11.03)$	$(10.38, 10.52, 11.14)$	$(10.40, 10.64, 11.64)$
	1.5	$(4.97, 5.00, 5.13)$	$(4.97, 5.00, 5.13)$	$(4.97, 5.00, 5.14)$	$(4.97, 5.00, 5.15)$	$(4.97, 5.01, 5.18)$	$(4.98, 5.04, 5.32)$
	2.0	$(4.07, 4.08, 4.10)$	$(4.07, 4.08, 4.10)$	$(4.07, 4.08, 4.10)$	$(4.07, 4.08, 4.10)$	$(4.07, 4.08, 4.11)$	$(4.07, 4.08, 4.13)$

Table 4. The ARL values of the RR r,s−γ2 control charts in the presence of measurement errors for γ0=0.05 (left side), γ0=0.1 (middle) and γ0=0.2 (right side), and for different values of η, θ=0.05, τ, n, B = 1, m = 1.

Table 4. The ARL values of the RR $_{r, s} - γ^{2}$ control charts in the presence of measurement errors for $γ_{0} = 0.05$ (left side), $γ_{0} = 0.1$ (middle) and $γ_{0} = 0.2$ (right side), and for different values of η, $θ = 0.05$ , τ, n, B = 1, m = 1.