Risk Group	Reasons	Reference
Pregnant women	Methionine is metabolised to homocysteine and raised plasma homocysteine is associated with birth defects, pre-eclampsia, spontaneous abortion and placental abruption.	15, 16
Schizophrenic patients	Schizophrenic patients given 10–20 g methionine daily developed functional psychoses.	17
Patients with pre-existing cancer	Animal studies have shown that restriction of methionine intake blocks division and metastasis of tumour cells.	18,19
Ischaemic heart disease (IHD), peripheral vascular disease (PVD), stroke	Methionine is metabolised to homocysteine – raised homocysteine levels are associated with IHD, PVD and stroke.	20-22
Patients with chronic liver disease	The liver has an impaired ability to metabolise methionine.	22

Table 1: Nonparametric Two One-sided Tolerance Intervals: Sample Size Requirements so that

For one-side tolerance interval (p, 0.95) for p=0.8, 0.9, 0.95 and 0.99 can also be calculated with formula (7). The results are given in Table 2.

Sample Size	Values of K
Size	1	2	3	4	5	6	7	8	9	10
20	0.860	0.783	0.717	0.656	0.598	0.544	0.492	0.441	0.393	0.346
25	0.887	0.823	0.768	0.718	0.670	0.624	0.580	0.537	0.496	0.456
30	0.904	0.851	0.804	0.761	0.720	0.681	0.642	0.606	0.570	0.534
35	0.917	0.871	0.830	0.793	0.757	0.722	0.689	0.656	0.625	0.594
40	0.927	0.886	0.850	0.817	0.785	0.754	0.725	0.696	0.667	0.640
45	0.935	0.898	0.866	0.836	0.808	0.780	0.753	0.727	0.702	0.676
50	0.941	0.908	0.879	0.852	0.826	0.801	0.776	0.753	0.729	0.706
60	0.951	0.923	0.898	0.875	0.853	0.832	0.812	0.792	0.772	0.752
70	0.958	0.934	0.912	0.892	0.873	0.855	0.837	0.820	0.803	0.786
80	0.963	0.942	0.923	0.905	0.889	0.873	0.857	0.841	0.826	0.811
90	0.967	0.948	0.931	0.916	0.901	0.886	0.872	0.858	0.845	0.831
100	0.970	0.953	0.938	0.924	0.910	0.897	0.885	0.872	0.860	0.848
120	0.975	0.961	0.948	0.936	0.925	0.914	0.903	0.893	0.882	0.872
140	0.978	0.966	0.955	0.945	0.935	0.926	0.917	0.908	0.899	0.890
160	0.981	0.970	0.961	0.952	0.943	0.935	0.927	0.919	0.911	0.903
180	0.983	0.973	0.965	0.957	0.949	0.942	0.935	0.928	0.921	0.914
200	0.985	0.976	0.968	0.961	0.954	0.948	0.941	0.935	0.928	0.922

When an experimenter wants to determine the lower and upper limits of the specification that covers at least 90% of the product population, for a continuous attribute with unknown distribution, he needs to plan an experiment with at least sample size of 72. On the other hand, for k=1, (X(k),X(n-k+1)) is the range of minimum to maximum (table1). With sample size n=35, the range determined by (min, max) is 80% of the population centered at median (table3).

Table 4: Nonparametric One-sided Tolerance Intervals: True Coverage Probability (p) for a given Lower Tolerance Limit X(k) or Upper Tolerance Limit X_(n-k+1)

α= 0.05
Values of k	p =0.8	p =0.9	p =0.95	p =0.99
1	14	29	59	299
2	22	46	93	473
3	30	61	124	628
4	37	76	153	773
5	44	89	181	913
6	50	103	208	1049
7	57	116	234	1182
8	63	129	260	1312
9	69	142	286	1441
10	76	154	311	1568
11	82	167	336	1693
12	88	179	361	1818
13	94	191	386	1941
14	100	203	410	2064
15	106	215	434	2185
16	112	227	458	2306
17	118	239	482	2426
18	124	251	506	2546
19	129	263	530	2665
20	135	275	554	2784

α= 0.05
Values of k	p =0.8	p =0.9	p =0.95	p =0.99
1	14	29	59	299
2	22	46	93	473
3	30	61	124	628
4	37	76	153	773
5	44	89	181	913
6	50	103	208	1049
7	57	116	234	1182
8	63	129	260	1312
9	69	142	286	1441
10	76	154	311	1568
11	82	167	336	1693
12	88	179	361	1818
13	94	191	386	1941
14	100	203	410	2064
15	106	215	434	2185
16	112	227	458	2306
17	118	239	482	2426
18	124	251	506	2546
19	129	263	530	2665
20	135	275	554	2784

Tables at a glance

Figures at a glance