Question

Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) LOADING... for this problem. Sampling 4 pieces of​ precision-cut wire​ (to be used in computer​ assembly) every hour for the past 24 hours has produced the following​ results:                                                                                                                                                         Hour Bold x overbar R Hour Bold x overbar R Hour Bold x overbar R Hour Bold x overbar R 1 3.15​" 0.65​" 7 2.95​" 0.58​" 13 3.11​" 0.80​" 19 3.41​" 1.66​" 2 3.10 1.18 8 2.75 1.08 14 2.83 1.31 20 2.79 1.09 3 3.12 1.43 9 3.02 0.76 15 3.02 1.01 21 2.65 1.13 4 3.29 1.31 10 2.95 1.38 16 2.94 0.45 22 3.28 0.46 5 3.07 1.12 11 2.73 1.17 17 2.96 1.43 23 3.04 1.63 6 2.76 0.32 12 2.97 0.40 18 2.84 1.29 24 2.74 1.02 Based on the sampling​ done, the control limits for ​3-sigma x overbar chart are ​(round all intermediate calculations to three decimal places before proceeding with further ​calculations)​: Upper Control Limit ​(UCL Subscript x overbar​) ​= nothing inches ​(round your response to three decimal​ places).

Sample ​Size, n	Mean​ Factor, A2	Upper​ Range, D4	Lower​ Range, D3
2	1.880	3.268	0
3	1.023	2.574	0
4	0.729	2.282	0
5	0.577	2.115	0
6	0.483	2.004	0
7	0.419	1.924	0.076
8	0.373	1.864	0.136
9	0.337	1.816	0.184
10	0.308	1.777	0.223
12	0.266	1.716	0.284

Answer 1

The control charts are used to find whether the production process is under control or not. Here the constructed charts indicates even though the process is under control is needed some adjustments as 5 points continuously above the CL.