Table 9. The OOC RL characteristics (the first row contains ARL₁ values with SDRL₁ values in parenthesis, while MRL₁ values are in the second row) of the MA sign, EWMA sign, CUSUM sign, mixed EWMA-CUSUM, and the EWMA-MA sign control charts using arcsine transformation for various continuous distributions at n = 10 and ARL₀≅370.

Control Chart	δ									AEQL	RMI
	0.1	0.25	0.50	0.75	1.00	1.50	2.00	2.5	3.0
Normal distribution i.e. N(0,1)
MA Sign	171.7(169.5)	35.8(34.4)	7.3(5.5)	3.4(1.8)	2.3(1.0)	1.5(0.6)	1.2(0.4)	1.1(0.2)	1.0(0.1)	11.74	0.45
	119	25	6	3	2	2	1	1	1
EWMA Sign	73.2(57.8)	19.5(9.8)	8.3(2.8)	5.4(1.5)	4.1(1.0)	2.9(0.6)	2.4(0.5)	2.1(0.3)	2(0.2)	20.1	0.84
	57	17	8	5	4	3	2	2	2
CUSUM sign	92.8(80.9)	20.8(11.8)	8.3(2.8)	5.4(1.3)	4.3(0.8)	3.3(0.5)	3.0(0.2)	3.0 (0.0)	3.0 (0.0)	26.5	1.21
	68	18	8	5	4	3	3	3	3
EWMA-CUSUM sign	74.2(39.2)	31.2(8.0)	18.5(2.9)	13.9(1.8)	11.4(1.3)	8.9(0.8)	7.8 (0.6)	7.3(0.5)	7.1(0.3)	64.6	4.15
	64	30	18	14	11	9	8	7	7
EWMA-MA sign	64.1(55.7)	15.8(10.5)	5.9(3.6)	3.1(2.1)	1.9(1.2)	1.2(0.4)	1.0(0.1)	1.0(0.0)	1.0(0.0)	9.9	0
	49	14	6	3	1	1	1	1	1
Student’s t-distribution with df = 5
MA Sign	132.9(131.2)	22.5(20.5)	5.0(3.3)	2.7(1.2)	2.0(0.8)	1.5(0.5)	1.2(0.4)	1.1(0.3)	1.1(0.2)	11.19	0.46
	93	16	4	3	2	1	1	1	1
EWMA Sign	54.7 (40.4)	15.1 (6.8)	6.8 (2.1)	4.6 (1.2)	3.6 (0.9)	2.8 (0.6)	2.4 (0.5)	2.2 (0.4)	2.1 (0.3)	19.9	0.96
	44	14	7	5	3	3	2	2	2
CUSUM sign	65.3(54.0)	15.5(7.6)	6.8(2.0)	4.7(1.0)	3.9(0.7)	3.2(0.4)	3.0(0.2)	3.0(0.1)	3.0(0.0)	25.8	1.31
	49	14	6	4	4	3	3	3	3
EWMA-CUSUM sign	59.7(26.9)	26.8(5.9)	16.2(2.3)	12.4(1.5)	10.5(1.1)	8.7(0.7)	7.9(0.6)	7.5(0.5)	7.3(0.5)	64.7	4.58
	54	26	16	12	10	9	8	8	7
EWMA-MA sign	47.2(42.1)	11.9(7.5)	4.4(2.7)	2.3(1.5)	1.5(0.9)	1.1(0.4)	1.0(0.2)	1.0(0.1)	1.0(0.0)	9.3	0
	36	11	4	2	1	1	1	1	1
Laplace distribution i.e. $\mathit{L}\mathit{a}\mathit{p}\mathit{l}\mathit{a}\mathit{c}\mathit{e}\left(\mathbf{0},\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}\right)$
MA Sign	80.9(78.7)	13.1(11.6)	3.9(2.3)	2.5(1.1)	1.9(0.8)	1.5 (0.6)	1.3 (0.4)	1.1 (0.3)	1.1(0.3)	10.78	0.41
	57	10	3	2	2	1	1	1	1
EWMA Sign	35.1 (22.7)	11.4 (4.5)	5.9 (1.7)	4.3 (1.1)	3.5 (0.8)	2.8 (0.6)	2.5 (0.5)	2.3 (0.4)	2.1 (0.3)	20.0	0.99
	29	11	6	4	3	3	2	2	2
CUSUM sign	39.3(28.1)	11.5(4.7)	5.9(1.6)	4.5(0.9)	3.8(0.6)	3.3(0.5)	3.1(0.2)	3.0(0.1)	3.0(0.0)	25.7	1.34
	32	11	6	4	4	3	3	3	3
EWMA-CUSUM sign	44.5(15.6)	22.5(4.2)	14.8(2.0)	11.9(1.4)	10.4(1.1)	8.8(0.8)	8.0 (0.6)	7.6(0.5)	7.4(0.5)	65.0	4.76
	41	22	15	12	10	9	8	8	7
EWMA-MA sign	29.4(22.1)	8.6(5.3)	3.6(2.3)	2.1(1.4)	1.5(0.8)	1.1(0.4)	1.0(0.2)	1.0(0.1)	1.0(0.0)	9.0	0
	24	8	3	2	1	1	1	1	1
Logistic distribution i.e. $\mathit{L}\mathit{G}\left(\mathbf{0},\frac{\sqrt{\mathbf{3}}}{\mathit{\pi }}\right)$
MA Sign	149.4(148.0)	26.8(24.5)	5.7(4.0)	2.9(1.4)	2.1(0.8)	1.5(0.6)	1.2(0.4)	1.1(0.3)	1.0(0.2)	11.16	0.43
	102	19	5	3	2	1	1	1	1
EWMA Sign	60.4(45.8)	16.6(7.9)	7.3(2.4)	4.9(1.3)	3.8(0.9)	2.8(0.6)	2.4(0.5)	2.2(0.4)	2.1(0.3)	20.2	0.91
	48	15	7	5	4	3	2	2	2
CUSUM sign	74.5(63.1)	17.1(8.9)	7.3(2.3)	5.0(1.2)	4.1(0.7)	3.3(0.5)	3.0(0.2)	3.0(0.1)	3.0(0.0)	26.1	1.27
	55	15	7	5	4	3	3	3	3
EWMA-CUSUM sign	64.7(30.8)	28.3(6.5)	17.1(2.5)	13.0(1.6)	10.9(1.2)	8.8(0.8)	7.9(0.6)	7.5(0.5)	7.2(0.4)	64.8	4.43
	57	27	17	13	11	9	8	7	7
EWMA-MA sign	55.5(43.6)	13.4(8.5)	4.8(3.0)	2.6(1.7)	1.7(1.0)	1.1(0.4)	1.0(0.2)	1.0(0.1)	1.0(0.0)	9.5	0
	45	12	5	2	1	1	1	1	1
Contaminated Normal distribution with a 10% contamination proportion
MA Sign	152.2(151.5)	29.1(27.0)	6.1(4.4)	3.1(1.6)	2.2(0.9)	1.5(0.6)	1.2(0.4)	1.1(0.2)	1.0(0.1)	11.33	0.46
	106	21	5	3	2	1	1	1	1
EWMA Sign	64.0(49.6)	17.4(8.4)	7.6(2.5)	5.0(1.4)	3.9(1)	2.8(0.6)	2.4(0.5)	2.1(0.3)	2(0.2)	19.8	0.89
	50	16	7	5	4	3	2	2	2
CUSUM sign	78.3(66.7)	18.1(9.7)	7.6(2.5)	5.1(1.2)	4.1(0.7)	3.3(0.5)	3.0(0.2)	3.0(0.0)	3.0(0.0)	26.2	1.27
	58	16	7	5	4	3	3	3	3
EWMA-CUSUM sign	67.5(33.1)	29.2(6.9)	17.4(2.6)	13.3(1.7)	11.0(1.2)	8.8(0.8)	7.8(0.6)	7.3(0.5)	7.1(0.2)	64.1	4.33
	59	28	17	13	11	9	8	7	7
EWMA-MA sign	54.5(47.2)	14.0(9.0)	5.1(3.2)	2.7(1.8)	1.8(1.1)	1.1(0.4)	1.0(0.1)	1.0(0.0)	1.0(0.0)	9.6	0
	44	13	5	2	1	1	1	1	1
Gamma distribution, i.e., Gamma(3,1)
MA Sign	160.3(159.0)	32.5(30.5)	7.1(5.3)	3.4(1.9)	2.4(1.0)	1.6(0.6)	1.3(0.5)	1.1(0.3)	1.0(0.2)	11.9	0.46
	113	23	5	3	2	2	1	1	1
EWMA Sign	68.1(53.4)	18.5(9.2)	8.2(2.8)	5.4(1.5)	4.2(1.1)	3(0.7)	2.5(0.6)	2.2(0.4)	2.1(0.3)	20.9	0.88
	53	17	8	5	4	3	3	2	2
CUSUM sign	84.1(72.7)	19.4(10.6)	8.2(2.7)	5.5(1.4)	4.3(0.9)	3.4(0.5)	3.1(0.3)	3.0(0.1)	3.0(0.0)	26.6	1.22
	62	17	8	5	4	3	3	3	3
EWMA-CUSUM sign	70.4(35.7)	30.3(7.4)	18.3(2.9)	14.0(1.8)	11.7(1.3)	9.2(0.9)	8.2(0.6)	7.6(0.5)	7.3(0.4)	66.7	4.29
	61	29	18	14	12	9	8	8	7
EWMA-MA sign	59.9(49.8)	15.1(10.0)	5.6(3.5)	3.1(2.1)	2.0(1.3)	1.2(0.5)	1.0(0.2)	1.0(0.1)	1.0(0.0)	9.9	0
	47	13	6	3	2	1	1	1	1
Weibull distribution, i.e., Weibull(2,1)
MA Sign	198.4(197.0)	53.8(52.3)	14.0(12.0)	6.6(4.9)	4.4(2.7)	2.8(1.3)	2.2(0.9)	2.0(0.8)	1.8(0.7)	20.95	0.54
	137	37	10	5	4	3	2	2	2
EWMA Sign	89.7 (74.1)	25.5 (14.7)	11.6 (4.6)	7.9 (2.6)	6.3 (1.9)	4.7 (1.3)	4.0 (1.0)	3.5 (0.9)	3.3 (0.8)	32.5	0.74
	68	22	11	8	6	5	4	3	3
CUSUM sign	113.2(102.9)	27.8(17.5)	11.7(4.9)	7.9(2.6)	6.3(1.8)	4.8(1.1)	4.2(0.8)	3.8(0.6)	3.6(0.6)	34.6	0.85
	82	23	11	8	6	5	4	4	4
EWMA-CUSUM sign	86.6(48.3)	36.8(11.0)	22.8(4.3)	18.0(2.8)	15.4(2.1)	12.7(1.5)	11.2(1.3)	10.4(1.1)	9.7(1.0)	89.7	3.26
	74	35	22	18	15	13	11	10	10
EWMA-MA sign	82.7(76.2)	21.6(15.5)	8.8(5.3)	5.4(3.4)	3.9(2.5)	2.5(1.6)	1.8(1.1)	1.5(0.8)	1.3(0.7)	15.6	0
	60	18	8	5	3	2	1	1	1