Table 2.

ARL₀ values for the $T^2$ and MEWMA control charts (gamma distribution with different shape parameter and $\mathrm{\text{β}}=1$).

	α
ARL0 $T^2$	0.5	1	2	3	4	8	16	64	256	1024
$\varphi$ = 0
$T_{\text{total}}^{\text{2}}$	19.12	25.21	36.29	45.12	52.64	76.99	105.966	162.86	187.58	198.50
$T_{\text{stage2}}^{\text{2}}$	37.38	50.45	71.62	90.16	104.42	154.60	209.03	326.85	374.62	395.45
$T_{\text{stage1}}^{\text{2}}$	37.17	49.83	70.24	89.12	104.32	152.61	214.97	321.56	377.11	388.78
$\varphi$ = 0.1
$T_{\text{total}}^{\text{2}}$	18.76	25.89	35.25	44.98	52.23	77.03	106.43	161.83	188.61	197.65
$T_{\text{stage2}}^{\text{2}}$	37.19	50.57	70.91	90.25	106.11	156.22	214.58	327.33	377.65	389.17
$T_{\text{stage1}}^{\text{2}}$	37.17	49.73	71.74	90.28	106.46	153.97	215.25	323.97	378.60	395.03
$\varphi$ = 0.5
$T_{\text{total}}^{\text{2}}$	18.96	25.19	35.64	45.03	52.88	78.06	107.12	162.38	188.39	197.95
$T_{\text{stage2}}^{\text{2}}$	37.55	49.89	71.47	88.48	104.91	155.30	211.32	324.49	371.37	391.19
$T_{\text{stage1}}^{\text{2}}$	38.01	50.06	72.96	90.53	105.48	152.23	213.18	326.98	382.84	391.93
$\varphi$ = 0.9
$T_{\text{total}}^{\text{2}}$	18.71	25.09	35.960	45.45	53.34	76.63	107.87	161.11	190.23	200.23
$T_{\text{stage2}}^{\text{2}}$	36.59	49.68	70.24	88.36	106.83	154.32	215.42	321.60	384.99	397.39
$T_{\text{stage1}}^{\text{2}}$	37.55	50.26	71.74	90.81	105.95	153.67	211.11	326.80	372.92	391.53
	α
ARL0 MEWMA	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5
$\varphi$ = 0
$\text{MEWM}{\text{A}}_{\text{total}}$	61.09	82.43	108.86	125.95	136.59	162.21	182.07	193.86	200.86	201.35
$\text{MEWM}{\text{A}}_{\text{stage2}}$	120.94	164.06	219.33	252.82	273.67	320.81	355.48	388.38	392.37	402.21
$\text{MEWM}{\text{A}}_{\text{stage1}}$	118.77	160.45	216.21	251.24	274.82	324.34	354.44	382.30	397.93	398.51
$\varphi$ = 0.1
$\text{MEWM}{\text{A}}_{\text{total}}$	61.21	80.35	108.9798	127.53	139.09	162.76	178.55	202.66	201.48	202.28
$\text{MEWM}{\text{A}}_{\text{stage2}}$	122.09	161.81	213.05	249.11	271.53	324.39	358.51	385.49	399.16	402.04
$\text{MEWM}{\text{A}}_{\text{stage1}}$	122.79	163.09	217.62	251.60	275.54	322.13	354.92	386.23	398.21	399.37
$\varphi$ = 0.5
$\text{MEWM}{\text{A}}_{\text{total}}$	60.89	80.52	109.83	125.22	135.47	160.92	183.06	199.99	203.14	200.98
$\text{MEWM}{\text{A}}_{\text{stage2}}$	119.44	161.83	212.66	247.26	274.49	328.05	355.83	386.66	398.29	400.51
$\text{MEWM}{\text{A}}_{\text{stage1}}$	118.77	160.45	216.21	251.24	274.82	324.34	354.44	382.30	397.93	398.51
$\varphi$ = 0.9
$\text{MEWM}{\text{A}}_{\text{total}}$	60.79	82.43	109.82	125.59	137.46	164.08	183.10	195.99	204.29	201.49
$\text{MEWM}{\text{A}}_{\text{stage2}}$	122.03	164.38	216.24	247.53	274.83	326.17	355.53	391.86	399.78	402.52
$\text{MEWM}{\text{A}}_{\text{stage1}}$	119.70	160.57	213.38	249.06	272.14	323.72	355.88	390.71	398.27	401.63