Compute the 3σ [latex]\overline{X}[/latex] chart upper and lower control limits for the moisture data in Table 10.1.

With sample 6 deleted, the value of [latex]\overline{\overline{X}}[/latex] is 2.658, and the value of [latex]\overline{R}[/latex] is 0.5836. The sample size is n = 5. From the table, A[latex]_2[/latex] = 0.577. Therefore the upper control limit is 2.658 + (0.577)(0.5836) = 2.995, and the lower control limit is 2.658 - (0.577) (0.5836) = 2.321.

Question 10.2: Compute the 3σ X chart upper and lower control limits for th...

Principles of Statistics for Engineers and Scientists

Compute the 3σ $\overline{X}$ chart upper and lower control limits for the moisture data in Table 10.1.

TABLE 10.1 Moisture content for salt packages, as a percentage of total weight
Sample	Sample Values					Mean( $\bar{X}$ )	Range (R)	SD (s)
1	2.53	2.66	1.88	2.21	2.26	2.308	0.780	0.303
2	2.69	2.38	2.34	2.47	2.61	2.498	0.350	0.149
3	2.67	2.23	2. 10	2.43	2.54	2.394	0.570	0.230
4	2.10	2.26	2.51	2.58	2.28	2.346	0.480	0.196
5	2.64	2.42	2.56	2.51	2.36	2.498	0.280	0.111
6	2.64	1.63	2.95	2.12	2.67	2.402	1.320	0.525
7	2.58	2.69	3.01	3.01	2.23	2.704	0.780	0.327
8	2.31	2.39	2.60	2.40	2.46	2.432	0.290	0.108
9	3.03	2.68	2.27	2.54	2.63	2.630	0.760	0.274
10	2.86	3.22	2.72	3.09	2.48	2.874	0.740	0.294
11	2.71	2.80	3.09	2.60	3.39	2.918	0.790	0.320
12	2.95	3.54	2.59	3.31	2.87	3.052	0.950	0.375
13	3.14	2.84	3.77	2.80	3.22	3. 154	0.970	0.390
14	2.85	3.29	3.25	3.35	3.59	3.266	0.740	0.267
15	2.82	3.71	3.36	2.95	3.37	3.242	0.890	0.358
16	3.17	3.07	3.14	3.63	3.70	3.342	0.630	0.298
17	2.81	3.21	2.95	3.04	2.85	2.972	0.400	0.160
18	2.99	2.65	2.79	2.80	2.95	2.836	0.340	0.137
19	3.11	2.74	2.59	3.01	3.03	2.896	0.520	0.221
20	2.83	2.74	3.03	2.68	2.49	2.754	0.540	0.198
21	2.76	2.85	2.59	2.23	2.87	2.660	0.640	0.265
22	2.54	2.63	2.32	2.48	2.93	2.580	0.610	0.226
23	2.27	2.54	2.82	2.11	2.69	2.486	0.710	0.293
24	2.40	2.62	2.84	2.50	2.51	2.574	0.440	0.168
25	2.41	2.72	2.29	2.35	2.63	2.480	0.430	0. 186
26	2.40	2.33	2.40	2.02	2.43	2.316	0.410	0. 169
27	2.56	2.47	2.1 1	2.43	2.85	2.484	0.740	0.266
28	2.21	2.61	2.59	2.24	2.34	2.398	0.400	0.191
29	2.56	2.26	1.95	2.26	2.40	2.286	0.610	0.225
30	2.42	2.37	2. 13	2.09	2.41	2.284	0.330	0.161
31	2.62	2.11	2.47	2.27	2.49	2.392	0.510	0.201
32	2.21	2.15	2.18	2.59	2.61	2.348	0.460	0.231
						$\overline{\overline{X}}=2.6502$	$\bar{R}=0.6066$	$\bar{s}=0.2445$

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