Optimal Designing of Variables Chain Sampling Plan by Minimizing the Average Sample Number

Table 1

Variables chain sampling plans indexed by AQL and LQL for 𝛼 = 5% and 𝛽 = 10%.

𝑝1	𝑝2	Known sigma				Unknown sigma
		𝑛𝜎	𝑖𝜎	𝑘^′𝜎	𝑘𝜎	𝑛𝑆	𝑖𝑆	𝑘^′𝑆	𝑘𝑆
0.001	0.0020	119	1	2.883	3.013	650	1	2.888	3.013
	0.0025	68	2	2.810	2.965	361	1	2.834	2.984
	0.003	46	1	2.776	2.961	242	1	2.774	2.964
	0.004	31	2	2.740	2.885	147	1	2.716	2.921
	0.005	21	2	2.610	2.860	103	1	2.637	2.897
	0.006	19	4	2.597	2.807	84	2	2.599	2.829
	0.007	15	3	2.534	2.789	72	3	2.532	2.792
	0.008	13	3	2.495	2.765	62	3	2.518	2.768
	0.009	12	3	2.521	2.736	51	2	2.470	2.765
	0.010	12	6	2.517	2.697	45	2	2.425	2.750
	0.012	9	4	2.331	2.686	40	3	2.414	2.694
	0.015	7	3	2.237	2.657	34	4	2.387	2.637
	0.020	7	6	2.414	2.539	27	5	2.335	2.565
	0.025	6	6	2.370	2.485	20	3	2.197	2.552
	0.030	5	6	2.264	2.454	19	5	2.231	2.476
0.0025	0.004	230	2	2.658	2.738	1131	2	2.676	2.736
	0.005	105	2	2.598	2.703	474	2	2.585	2.705
	0.006	64	2	2.530	2.675	282	1	2.533	2.698
	0.0075	39	2	2.441	2.641	171	1	2.464	2.669
	0.010	26	3	2.379	2.579	106	1	2.430	2.610
	0.012	19	2	2.335	2.555	76	1	2.321	2.601
	0.015	16	4	2.296	2.491	55	1	2.237	2.572
	0.020	12	4	2.260	2.425	38	1	2.139	2.529
	0.025	10	6	2.206	2.366	32	2	2.163	2.413
	0.030	8	5	2.114	2.334	29	5	2.107	2.342
	0.035	7	6	2.307	2.297	25	5	2.092	2.302
	0.040	6	6	1.884	2.274	21	5	1.952	2.282
0.005	0.0075	259	1	2.434	2.524	1113	2	2.442	2.512
	0.010	86	1	2.326	2.486	347	1	2.348	2.483
	0.012	53	1	2.277	2.457	211	1	2.299	2.454
	0.015	33	1	2.211	2.421	128	1	2.233	2.418
	0.020	24	4	2.161	2.316	75	2	2.100	2.345
	0.025	16	3	2.046	2.281	55	2	2.083	2.293
	0.030	14	6	1.989	2.224	43	3	1.974	2.249
	0.035	12	6	2.002	2.182	36	3	1.979	2.209
	0.040	10	4	1.976	2.156	31	3	1.964	2.174
	0.050	8	5	1.893	2.098	25	4	1.925	2.105
0.0075	0.010	505	2	2.339	2.384	1817	1	2.329	2.394
	0.012	173	1	2.259	2.369	690	2	2.278	2.353
	0.015	78	1	2.185	2.335	286	1	2.182	2.337
	0.020	43	2	2.146	2.251	133	1	2.083	2.293
	0.025	29	5	2.008	2.198	83	1	2.003	2.258
	0.030	19	2	1.968	2.178	61	1	1.984	2.214
	0.035	17	5	1.888	2.123	47	1	1.925	2.190
	0.040	13	3	1.837	2.107	41	3	1.851	2.111
	0.050	10	3	1.792	2.052	28	2	1.756	2.081
	0.060	9	5	1.792	1.982	26	4	1.815	1.990
0.010	0.015	248	1	2.212	2.257	786	1	2.187	2.267
	0.020	74	1	2.090	2.220	247	1	2.071	2.226
	0.025	42	1	2.027	2.177	135	1	2.011	2.186
	0.030	27	1	1.906	2.161	93	2	1.954	2.124
	0.035	21	2	1.846	2.096	66	1	1.900	2.125
	0.040	18	3	1.804	2.054	53	2	1.846	2.066
	0.045	15	3	1.762	2.027	46	3	1.811	2.026
	0.050	13	3	1.731	2.001	39	2	1.824	2.004
	0.060	11	5	1.662	2.942	30	3	1.730	1.955
	0.070	9	5	1.573	1.903	26	4	1.728	1.898
	0.080	7	3	1.486	1.891	21	5	1.579	1.869
0.02	0.030	187	2	1.896	1.976	528	1	1.886	1.991
	0.035	96	2	1.835	1.945	272	2	1.831	1.946
	0.040	59	1	1.779	1.939	169	2	1.770	1.920
	0.045	45	2	1.749	1.889	117	1	1.734	1.919
	0.050	34	2	1.693	1.868	88	1	1.683	1.903
	0.060	22	2	1.563	1.833	63	2	1.670	1.820
	0.070	18	3	1.544	1.779	44	2	1.577	1.792
	0.080	14	3	1.434	1.749	36	3	1.525	1.745
	0.090	13	4	1.502	1.697	27	2	1.423	1.737
	0.10	10	2	1.436	1.691	22	1	1.386	1.766
	0.11	10	4	1.457	1.632	23	4	1.476	1.636
	0.12	7	1	1.235	1.725	17	1	1.379	1.699
	0.13	8	5	1.360	1.580	17	4	1.356	1.596
	0.15	6	4	1.110	1.560	14	5	1.279	1.544
0.030	0.040	341	2	1.771	1.821	1027	5	1.771	1.816
	0.045	157	1	1.711	1.811	416	2	1.704	1.799
	0.050	96	1	1.650	1.795	253	1	1.679	1.789
	0.060	52	2	1.566	1.736	126	1	1.585	1.760
	0.070	33	1	1.508	1.728	81	1	1.539	1.724
	0.080	26	3	1.427	1.657	62	2	1.514	1.659
	0.090	23	5	1.449	1.609	44	2	1.401	1.641
	0.100	17	3	1.378	1.593	36	2	1.384	1.609
	0.110	13	2	1.268	1.588	29	2	1.305	1.590
	0.120	11	1	1.270	1.605	26	3	1.274	1.549
	0.130	11	4	1.204	1.514	23	3	1.289	1.519
	0.150	10	6	1.273	1.443	18	3	1.230	1.475
	0.200	6	5	0.950	1.365	12	5	1.134	1.354
0.04	0.060	145	2	1.568	1.663	339	2	1.564	1.664
	0.070	73	1	1.513	1.643	166	1	1.507	1.647
	0.080	50	2	1.478	1.588	102	1	1.425	1.625
	0.090	34	2	1.394	1.564	71	1	1.374	1.600
	0.100	27	3	1.324	1.529	53	1	1.315	1.580
	0.110	24	5	1.309	1.489	42	1	1.294	1.554
	0.120	18	3	1.233	1.478	34	1	1.234	1.539
	0.130	14	2	1.130	1.475	31	2	1.271	1.461
	0.140	14	4	1.158	1.423	27	3	1.193	1.433
	0.150	11	2	1.108	1.428	23	3	1.130	1.415
	0.170	10	4	1.070	1.360	17	2	1.061	1.396
	0.200	8	5	0.990	1.295	15	4	1.120	1.290
0.050	0.070	188	1	1.487	1.582	427	2	1.485	1.570
	0.080	93	1	1.408	1.558	203	1	1.422	1.557
	0.090	60	2	1.359	1.509	127	2	1.365	1.510
	0.100	46	3	1.331	1.471	86	1	1.331	1.506
	0.110	33	2	1.288	1.453	63	1	1.261	1.491
	0.120	26	1	1.270	1.450	49	1	1.213	1.473
	0.130	20	1	1.157	1.452	45	3	1.235	1.395
	0.140	19	3	1.160	1.375	34	2	1.148	1.393
	0.150	17	4	1.108	1.348	30	2	1.165	1.365
	0.160	13	2	1.011	1.356	25	1	1.134	1.384
	0.170	12	2	1.045	1.330	24	3	1.112	1.312
	0.200	11	6	1.059	1.229	17	3	1.023	1.258