Designing of Variables Modified Chain Sampling Plan Based on the Process Capability Index with Unknown Mean and Variance

Figures & data

Table 1. Optimal parameters of variables modified chain sampling plan based on C_pk (symmetric fraction non-conforming).

p1	p2	n	i	ka	kr	Pa (p1)	Pa (p2)
0.001	0.002	267	8	0.98299	0.96299	0.95012	0.09519
	0.003	90	8	0.91200	0.88200	0.95005	0.09882
	0.004	51	8	0.86100	0.82600	0.95023	0.09745
	0.006	27	7	0.79700	0.75200	0.95015	0.09535
	0.008	18	8	0.73000	0.70000	0.95036	0.09869
	0.010	13	8	0.68600	0.65100	0.95042	0.09838
	0.015	8	8	0.60101	0.57601	0.95019	0.09849
	0.020	6	7	0.55601	0.53101	0.95014	0.09762
0.0025	0.005	185	8	0.88400	0.85900	0.95048	0.09869
	0.010	37	8	0.75200	0.72200	0.95095	0.09783
	0.015	19	7	0.67900	0.64400	0.95043	0.09958
	0.020	12	7	0.62201	0.57701	0.95087	0.09551
	0.025	8	8	0.55701	0.51201	0.95035	0.09918
	0.030	7	7	0.53201	0.49701	0.95091	0.09806
	0.050	4	6	0.42901	0.40901	0.95074	0.09813
0.005	0.010	143	8	0.80400	0.77900	0.95052	0.09566
	0.015	48	8	0.72100	0.69100	0.95023	0.09911
	0.020	26	8	0.66000	0.62500	0.95039	0.09866
	0.030	13	8	0.56901	0.53901	0.95061	0.09999
	0.040	8	8	0.50201	0.46701	0.95018	0.09838
	0.050	6	8	0.44801	0.42301	0.95080	0.09685
	0.100	3	4	0.36301	0.31801	0.95069	0.09937
0.010	0.020	106	7	0.72100	0.69100	0.95079	0.09737
	0.030	37	8	0.62700	0.60700	0.95008	0.09568
	0.040	20	6	0.58000	0.54000	0.95035	0.09832
	0.050	13	7	0.51700	0.48700	0.95081	0.09680
	0.100	4	7	0.33701	0.30701	0.95074	0.09958
	0.150	3	3	0.34101	0.26101	0.95012	0.09942
	0.200	3	1	0.33901	0.32401	0.95018	0.09903
0.030	0.060	58	7	0.56300	0.53300	0.95029	0.09995
	0.090	19	8	0.45200	0.43200	0.95012	0.09529
	0.120	9	8	0.37101	0.33601	0.95036	0.09652
	0.150	6	7	0.31601	0.28101	0.95033	0.09938
	0.300	3	2	0.22301	0.21301	0.95073	0.09535
0.050	0.100	43	6	0.48600	0.45100	0.95027	0.09782
	0.150	12	8	0.35600	0.32100	0.95056	0.09598
	0.200	6	8	0.26500	0.22500	0.95030	0.09649
	0.250	4	8	0.18600	0.16100	0.95014	0.09954
	0.300	3	7	0.13801	0.10801	0.95031	0.09813

Table 2. Optimal parameters of variables modified chain sampling plan based on C_pk (asymmetric fraction non-conforming).

p1	p2	n	i	ka	kr	Pa (p1)	Pa (p2)
0.001	0.002	280	4	1.18199	1.10199	0.95066	0.09539
	0.003	105	7	0.92000	0.88500	0.95094	0.09600
	0.004	57	7	0.87100	0.83100	0.95061	0.09727
	0.006	28	8	0.78800	0.75300	0.95079	0.09889
	0.008	18	8	0.73400	0.69400	0.95074	0.09671
	0.010	14	7	0.70200	0.66200	0.95070	0.09942
	0.015	8	8	0.60701	0.57201	0.95088	0.09654
	0.020	6	7	0.55901	0.52901	0.95042	0.09959
0.0025	0.005	228	8	0.88000	0.85500	0.95008	0.09742
	0.010	40	8	0.75300	0.72300	0.95048	0.09948
	0.015	19	8	0.67100	0.63600	0.95056	0.09871
	0.020	12	8	0.60901	0.57401	0.95004	0.09942
	0.025	9	8	0.56201	0.53201	0.95067	0.09583
	0.030	5	7	0.47001	0.44001	0.95062	0.09752
	0.050	4	6	0.43601	0.40601	0.95036	0.09717
0.005	0.010	174	8	0.79900	0.77400	0.95002	0.09522
	0.015	54	8	0.72100	0.69100	0.95045	0.09915
	0.020	29	8	0.66100	0.63100	0.95074	0.09995
	0.030	15	7	0.58301	0.55801	0.95052	0.09742
	0.040	9	7	0.52001	0.48501	0.95038	0.09548
	0.050	6	7	0.46801	0.41801	0.95012	0.09546
	0.100	3	4	0.37101	0.31101	0.95075	0.09888
0.010	0.020	126	8	0.71000	0.68500	0.95054	0.09744
	0.030	38	8	0.62500	0.59500	0.95022	0.09956
	0.040	21	7	0.51700	0.53600	0.95083	0.09612
	0.050	13	7	0.51800	0.47800	0.95016	0.09772
	0.100	4	8	0.31801	0.30301	0.95013	0.09814
	0.150	2	8	0.20601	0.15601	0.95011	0.09735
	0.200	2	4	0.20701	0.19701	0.95031	0.09767
0.030	0.060	70	7	0.55600	0.52600	0.95035	0.09618
	0.090	20	8	0.44800	0.42300	0.95070	0.09785
	0.120	10	6	0.39500	0.34000	0.95035	0.09786
	0.150	6	8	0.30100	0.27100	0.95093	0.09903
	0.300	3	2	0.23500	0.20000	0.95007	0.09900
0.050	0.100	48	8	0.46300	0.43800	0.95097	0.09612
	0.150	13	8	0.34900	0.31900	0.95023	0.09948
	0.200	7	7	0.27100	0.24600	0.95024	0.09727
	0.250	4	8	0.18200	0.15200	0.95013	0.09884
	0.300	3	7	0.13500	0.10000	0.95029	0.09648

Table 3. Optimal parameters of variables modified chain sampling plan based on C_pk (asymmetric fraction non-conforming).

p1	p2	n	i	ka	kr	Pa (p1)	Pa (p2)
0.001	0.002	317	8	0.96899	0.94399	0.95042	0.09721
	0.003	110	8	0.90900	0.87900	0.95095	0.09962
	0.004	63	7	0.87200	0.83200	0.95080	0.09557
	0.006	29	8	0.79000	0.75000	0.95013	0.09927
	0.008	19	8	0.73700	0.69700	0.95039	0.09730
	0.010	15	7	0.70500	0.67000	0.95022	0.09971
	0.015	8	8	0.61201	0.56701	0.95056	0.09624
	0.020	6	7	0.56801	0.52301	0.95058	0.09720
0.0025	0.005	229	8	0.86900	0.84400	0.95051	0.09703
	0.010	42	8	0.75300	0.71800	0.95092	0.09594
	0.015	20	8	0.67200	0.63700	0.95035	0.09897
	0.020	13	8	0.61201	0.58201	0.95056	0.09773
	0.025	9	7	0.58001	0.52001	0.95021	0.09704
	0.030	4	6	0.44201	0.40201	0.95023	0.09765
	0.050	7	6	0.63400	0.57400	0.95287	0.09667
0.005	0.010	180	8	0.78600	0.76600	0.95049	0.09566
	0.015	22	7	0.68300	0.65300	0.95086	0.09887
	0.020	13	8	0.61201	0.58201	0.95056	0.09773
	0.030	7	8	0.52301	0.48801	0.95089	0.09759
	0.040	5	8	0.44701	0.43701	0.95055	0.09811
	0.050	4	6	0.44201	0.40201	0.95023	0.09765
	0.100	3	2	0.40901	0.39901	0.95025	0.09665
0.010	0.020	125	8	0.69700	0.67200	0.95060	0.09551
	0.030	39	8	0.62000	0.58500	0.95021	0.09564
	0.040	21	8	0.55600	0.52600	0.95084	0.09861
	0.050	13	8	0.50400	0.46900	0.95054	0.09907
	0.100	4	8	0.32201	0.29701	0.95066	0.09759
	0.150	3	4	0.29701	0.27201	0.95014	0.09932
	0.200	3	5	0.40301	0.34801	0.95498	0.09856
0.030	0.060	68	7	0.54000	0.51000	0.95064	0.09613
	0.090	20	7	0.44900	0.40900	0.95073	0.09918
	0.120	10	8	0.35900	0.33400	0.95063	0.09943
	0.150	6	8	0.29700	0.26200	0.95076	0.09725
	0.300	4	1	0.31000	0.21500	0.95076	0.09502
0.050	0.100	44	8	0.44500	0.41500	0.95064	0.09562
	0.150	14	8	0.32900	0.31900	0.95034	0.09959
	0.200	7	7	0.26000	0.23500	0.95092	0.09898
	0.250	4	8	0.17300	0.14300	0.95017	0.09759
	0.300	3	7	0.12300	0.09300	0.95036	0.09834

Table 4. ASN of proposed modified chain sampling plan and other sampling plans based on C_pk (symmetric fraction non-conforming case).

		ASN
p1	p2	SSP	Resampling Scheme	RGS	MChSP
0.001	0.002	1134	1041.53	452.77	267
	0.003	351	374.06	168.17	90
	0.004	166	216.86	89.06	51
	0.006	74	113.87	43.47	27
	0.008	47	78.88	29.26	18
	0.010	34	59.68	23.55	13
0.0025	0.005	822	750.74	319.83	185
	0.010	118	152.14	61.23	37
	0.015	53	78.60	29.07	19
	0.020	32	51.60	19.28	12
	0.025	24	40.67	13.37	8
	0.030	18	32.53	11.05	7
0.005	0.010	623	567.65	246.49	143
	0.015	186	195.21	79.39	48
	0.020	87	111.19	49.51	26
	0.030	37	56.95	22.99	13
	0.040	23	38.09	13.55	8
	0.050	17	27.12	9.41	6
0.010	0.020	449	407.29	187.96	106
	0.030	132	138.38	59.71	37
	0.040	61	75.93	32.88	20
	0.050	37	51.52	21.45	13
	0.100	11	19.97	5.80	4
	0.150	6	10.85	3.95	3
0.030	0.060	240	214.18	88.13	58
	0.090	68	67.81	29.40	19
	0.120	31	35.24	17.43	9
	0.150	18	24.41	10.02	6
	0.300	5	8.13	3.35	3
0.050	0.100	167	149.13	67.91	43
	0.150	46	46.08	19.71	12
	0.200	20	24.39	10.07	6
	0.250	12	13.55	6.68	4

Table 5. ASN of proposed modified chain sampling plan and other sampling plans based on C_pk (asymmetric fraction non-conforming case).

		ASN
p1	p2	SSP	Resampling Scheme	RGS	MChSP
0.001	0.003	350	86.87	172.31	110
	0.004	169	62.34	66.42	63
	0.006	74	40.67	30.85	29
	0.008	47	32.52	22.85	19
	0.010	35	24.39	17.00	15
0.0025	0.010	119	43.36	47.66	42
	0.015	51	27.10	21.23	20
	0.020	32	21.70	15.67	13
	0.025	23	16.27	11.49	9
	0.030	18	13.55	8.98	4
0.005	0.015	189	46.15	53.40	22
	0.020	87	32.59	32.90	13
	0.030	38	18.99	16.67	7
	0.040	23	13.56	11.82	5
	0.050	17	10.84	8.79	4
0.010	0.030	135	32.54	52.14	39
	0.040	61	21.68	25.56	21
	0.050	37	16.26	15.79	13
	0.100	11	8.13	5.84	4
	0.150	6	5.42	3.94	3
0.030	0.090	68	16.27	23.49	20
	0.120	31	10.84	13.01	10
	0.150	18	8.13	8.74	6
	0300	5	3.80	3.26	4
0.050	0.150	46	10.84	18.47	14
	0.200	13	5.42	9.90	7
	0.250	12	5.42	6.45	4