Generalized Performance Measures of Control Charts Based on Different Sampling Schemes

Table 2

Performance measures through Monte Carlo simulation method (MCSM) and numerical method (NM) for varying choices of , , , and .

(a) and

Method	0.00		0.10		0.20		0.30		0.40		0.50
	SRS	MCSM	0.0027	370.37	0.0032	312.50	0.0056	178.57	0.0104	96.15	0.0174	57.47	0.0299	33.44
NM		0.0027	370.37	0.0034	294.12	0.0056	178.57	0.0101	99.01	0.0177	56.50	0.0299	33.44
RSS	MCSM	0.0027	370.37	0.0049	204.08	0.0122	81.97	0.0303	33.00	0.0662	15.11	0.1289	7.76
	NM	0.0027	370.37	0.0047	212.77	0.0122	81.97	0.0300	33.33	0.0659	15.17	0.1285	7.78
MRSS	MCSM	0.0027	370.37	0.0053	188.68	0.0148	67.57	0.0389	25.71	0.0904	11.06	0.1782	5.61
	NM	0.0027	370.37	0.0052	192.31	0.0151	66.23	0.0392	25.51	0.0908	11.01	0.1787	5.60
ERSS	MCSM	0.0027	370.37	0.0046	217.39	0.0105	95.24	0.0252	39.68	0.0538	18.59	0.1031	9.70
	NM	0.0027	370.37	0.0044	227.27	0.0107	93.46	0.0251	39.84	0.0534	18.73	0.1029	9.72
DRSS	MCSM	0.0027	370.37	0.0064	156.25	0.0205	48.78	0.0572	17.48	0.1335	7.49	0.2631	3.80
	NM	0.0027	370.37	0.0063	158.73	0.0201	49.75	0.0571	17.51	0.1340	7.46	0.2634	3.80
DMRSS	MCSM	0.0027	370.37	0.0135	74.07	0.0763	13.11	0.2547	3.93	0.5499	1.82	0.8178	1.22
	NM	0.0027	370.37	0.0133	75.19	0.0759	13.18	0.2552	3.92	0.5502	1.82	0.8181	1.22
MDRSS	MCSM	0.0027	370.37	0.0084	119.05	0.0376	26.60	0.1203	8.31	0.2837	3.52	0.5149	1.94
	NM	0.0027	370.37	0.0085	117.65	0.0372	26.88	0.1199	8.34	0.2841	3.52	0.5154	1.94
DERSS	MCSM	0.0027	370.37	0.0057	175.44	0.0151	66.23	0.0375	26.67	0.0834	11.99	0.1646	6.08
	NM	0.0027	370.37	0.0055	181.82	0.0148	67.57	0.0371	26.95	0.0837	11.95	0.1645	6.08
EDRSS	MCSM	0.0027	370.37	0.0055	181.82	0.0153	65.36	0.0402	24.88	0.0889	11.25	0.1748	5.72
	NM	0.0027	370.37	0.0052	192.31	0.0150	66.67	0.0399	25.06	0.0892	11.21	0.1751	5.71

(b) and

Method	0.00		0.10		0.20		0.30		0.40		0.50
	SRS	MCSM	0.0027	370.37	0.0037	270.27	0.0077	129.87	0.0161	62.11	0.0305	32.79	0.0558	17.92
NM		0.0027	370.37	0.0038	262.74	0.0076	130.86	0.0159	62.98	0.0309	32.41	0.0562	17.79
RSS	MCSM	0.0027	370.37	0.0074	135.14	0.0317	31.55	0.0981	10.19	0.2319	4.31	0.4362	2.29
	NM	0.0027	370.37	0.0077	130.24	0.0314	31.84	0.0976	10.24	0.2323	4.30	0.4358	2.29
MRSS	MCSM	0.0027	370.37	0.0096	104.17	0.0461	21.69	0.1524	6.56	0.3536	2.83	0.6112	1.64
	NM	0.0027	370.37	0.0097	103.36	0.0458	21.85	0.1519	6.58	0.3539	2.83	0.6109	1.64
ERSS	MCSM	0.0027	370.37	0.0058	172.41	0.0196	51.02	0.0532	18.79	0.1248	8.01	0.2456	4.07
	NM	0.0027	370.37	0.0059	170.79	0.0191	52.44	0.0535	18.68	0.1252	7.99	0.2459	4.07
DRSS	MCSM	0.0027	370.37	0.0134	74.63	0.0729	13.72	0.2490	4.02	0.5386	1.86	0.8102	1.23
	NM	0.0027	370.37	0.0131	76.41	0.0732	13.67	0.2489	4.02	0.5382	1.86	0.8098	1.23
DMRSS	MCSM	0.0027	370.37	0.0628	15.92	0.4792	2.09	0.9232	1.08	0.9980	1.00	1.0000	1.00
	NM	0.0027	370.37	0.0631	15.86	0.4789	2.09	0.9229	1.08	0.9981	1.00	1.0000	1.00
MDRSS	MCSM	0.0027	370.37	0.0257	38.91	0.1882	5.31	0.5689	1.76	0.8908	1.12	0.9894	1.01
	NM	0.0027	370.37	0.0261	38.31	0.1885	5.31	0.5693	1.76	0.8912	1.12	0.9890	1.01
DERSS	MCSM	0.0027	370.37	0.0081	123.46	0.0322	31.06	0.1017	9.83	0.2397	4.17	0.4497	2.22
	NM	0.0027	370.37	0.0079	126.15	0.0322	31.09	0.1013	9.87	0.2401	4.16	0.4501	2.22
EDRSS	MCSM	0.0027	370.37	0.0075	133.33	0.0284	35.21	0.0838	11.93	0.1999	5.00	0.3849	2.60
	NM	0.0027	370.37	0.0073	137.34	0.0280	35.73	0.0842	11.88	0.2005	4.99	0.3853	2.60

(c) and

Method	0.00		0.10		0.20		0.30		0.40		0.50
	SRS	MCSM	0.0027	370.37	0.0041	243.90	0.0092	108.70	0.0200	50.00	0.0410	24.39	0.0782	12.79
NM		0.0027	370.37	0.0041	244.14	0.0091	109.97	0.0202	49.61	0.0414	24.17	0.0781	12.81
RSS	MCSM	0.0027	370.37	0.0108	92.59	0.0528	18.94	0.1769	5.65	0.4069	2.46	0.6759	1.48
	NM	0.0027	370.37	0.0106	94.51	0.0528	18.93	0.1769	5.65	0.4066	2.46	0.6753	1.48
MRSS	MCSM	0.0027	370.37	0.0145	68.97	0.0854	11.71	0.2893	3.46	0.5999	1.67	0.8577	1.17
	NM	0.0027	370.37	0.0145	69.09	0.0851	11.75	0.2888	3.46	0.6002	1.67	0.8576	1.17
ERSS	MCSM	0.0027	370.37	0.0072	138.89	0.0272	36.76	0.0828	12.08	0.1991	5.02	0.3800	2.63
	NM	0.0027	370.37	0.0071	140.24	0.0273	36.57	0.0831	12.03	0.1995	5.01	0.3804	2.63
DRSS	MCSM	0.0027	370.37	0.0218	45.87	0.1459	6.85	0.4730	2.11	0.8204	1.22	0.9698	1.03
	NM	0.0027	370.37	0.0215	46.42	0.1462	6.84	0.4728	2.12	0.8198	1.22	0.9701	1.03
DMRSS	MCSM	0.0027	370.37	0.1765	5.67	0.8721	1.15	0.9994	1.00	1.0000	1.00	1.0000	1.00
	NM	0.0027	370.37	0.1765	5.67	0.8725	1.15	0.9993	1.00	1.0000	1.00	1.0000	1.00
MDRSS	MCSM	0.0027	370.37	0.0545	18.35	0.4220	2.37	0.8842	1.13	0.9955	1.00	1.0000	1.00
	NM	0.0027	370.37	0.0548	18.25	0.4218	2.37	0.8846	1.13	0.9953	1.00	1.0000	1.00
DERSS	MCSM	0.0027	370.37	0.0106	94.34	0.0510	19.61	0.1673	5.98	0.3899	2.56	0.6566	1.52
	NM	0.0027	370.37	0.0104	96.18	0.0506	19.77	0.1676	5.97	0.3904	2.56	0.6562	1.52
EDRSS	MCSM	0.0027	370.37	0.0093	107.53	0.0408	24.51	0.1336	7.49	0.3152	3.17	0.5599	1.79
	NM	0.0027	370.37	0.0091	109.36	0.0410	24.39	0.1337	7.48	0.3158	3.17	0.5603	1.78

(d) and

Method	0.00		0.10		0.20		0.30		0.40		0.50
	SRS	MCSM	0.0027	370.37	0.0033	303.03	0.0056	178.57	0.01	100	0.0176	56.82	0.0298	33.56
NM		0.0027	370.37	0.0034	294.12	0.0056	178.57	0.01	100	0.0177	56.5	0.0299	33.44
RSS	MCSM	0.0027	370.37	0.0038	263.16	0.0075	133.33	0.0154	64.94	0.0299	33.44	0.0545	18.35
	NM	0.0027	370.37	0.0038	263.16	0.0075	133.33	0.0154	64.94	0.0299	33.44	0.0544	18.38
MRSS	MCSM	0.0027	370.37	0.0037	270.27	0.0077	129.87	0.0163	61.35	0.0321	31.15	0.059	16.95
	NM	0.0027	370.37	0.0038	263.16	0.0078	128.21	0.0163	61.35	0.0321	31.15	0.059	16.95
ERSS	MCSM	0.0027	370.37	0.0038	263.16	0.0081	123.46	0.0174	57.47	0.0348	28.74	0.0643	15.55
	NM	0.0027	370.37	0.0039	256.41	0.0082	121.95	0.0174	57.47	0.0348	28.74	0.0644	15.53
DRSS	MCSM	0.0027	370.37	0.004	250	0.0093	107.53	0.0209	47.85	0.0432	23.15	0.0817	12.24
	NM	0.0027	370.37	0.0041	243.9	0.0093	107.53	0.0209	47.85	0.0432	23.15	0.0817	12.24
DMRSS	MCSM	0.0027	370.37	0.0041	243.9	0.0089	112.36	0.0195	51.28	0.0397	25.19	0.0744	13.44
	NM	0.0027	370.37	0.0041	243.9	0.0089	112.36	0.0195	51.28	0.0397	25.19	0.0745	13.42
MDRSS	MCSM	0.0027	370.37	0.0037	270.27	0.0071	140.85	0.0143	69.93	0.0277	36.1	0.05	20
	NM	0.0027	370.37	0.0037	270.27	0.0072	138.89	0.0144	69.44	0.0277	36.1	0.05	20
DERSS	MCSM	0.0027	370.37	0.0037	270.27	0.0078	128.21	0.0162	61.73	0.0321	31.15	0.058	17.24
	NM	0.0027	370.37	0.0038	263.16	0.0078	128.21	0.0163	61.35	0.0321	31.15	0.059	16.95
EDRSS	MCSM	0.0027	370.37	0.0039	256.41	0.0079	126.58	0.0164	60.98	0.0325	30.77	0.0596	16.78
	NM	0.0027	370.37	0.0039	256.41	0.0079	126.58	0.0165	60.61	0.0325	30.77	0.0597	16.75