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Please need a correct answer and explain it clearly Given the data below, what is the...

Please need a correct answer and explain it clearly

Given the data below, what is the upper control limit for the Range control chart? Please enter your answer with at least 4 significant digits.

Data:

Observation 1 Observation 2 Observation 3 Observation 4 Observation 5
155.1759 164.4978 144.0894 149.1192 160.0421
161.1192 145.4001 162.7882 177.1397 162.4125
161.3671 143.0758 171.4366 158.8492 154.7023
166.1941 166.911 163.6076 151.8873 162.9515
158.7486 154.2805 180.887 178.2488 155.1188
159.233 160.6053 176.0102 175.6228 166.1402
170.6843 161.7413 169.6049 157.7824 172.9065
167.3616 148.0186 165.7245 162.1048 163.974
157.9749 148.492 167.2943 140.076 181.7458
155.6967 171.0943 152.6593 142.4727 160.5202
164.5217 157.1935 151.1438 158.0747 155.3919
167.979 141.8374 155.4931 149.2655 163.0297
163.8557 168.984 163.8254 150.4593 160.4368
171.5194 148.2178 163.5912 157.6182 161.8093
135.6434 186.8886 152.3281 137.6502 167.7435
173.4057 159.6673 155.0814 169.7719 179.3919
169.3266 158.3569 174.3621 173.9279 174.052
154.3969 146.7553 168.1947 148.4083 170.2388
151.6227 143.9714 164.887 142.5745 158.1103
176.3726 171.7192 158.2436 170.3528 167.8382
165.9762 150.7074 160.5092 158.1487 179.0462
177.6822 160.1059 185.147 186.0095 174.6436
166.6542 181.4711 138.1257 171.4638 160.0559
153.1734 165.9899 168.987 165.7046 148.5262
143.6162 152.5279 177.0654 160.5963 162.9247
165.9919 176.0156 158.9986 167.7788 169.1682
178.3369 157.5605 160.1486 177.0536 168.5923
154.2878 164.8663 158.5857 176.5919 176.6121
151.5038 170.4999 155.6362 153.6519 174.8804
173.1002 178.7034 177.8521 162.7629 161.4867
159.0639 179.3448 170.4143 154.9183 161.8192
173.56 150.7119 171.7711 151.7356 143.1589
156.3567 171.9441 159.2536 161.1486 158.9801
154.1641 151.0134 163.3826 169.4772 173.8932

There are more data but I can't post because it says the question is too large.

So, I need you to explain how to get the answer

engineering   Mechanical-Engineering   
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Homework Answers

Answer #1

follow the following steps:

  1. tabulate the observations in a table
  2. write the subgroup numbers on the left side of the table. if it is given then note down the same subgroups which are given to you.
  3. for range control chart use the following formulas for calculations
  4. range (r)= xmax - xmin

ex: for subgroup (n=1), range (r)= 164.4978-144.0894 = 20.4084

  likewise, follow the same formula for whole subgroups.

5. r bar= (r1+r2+.........rn) / n

  here, there are 34 subgroups. so, n=34

and, r bar= (20.4084+31.7396+28.3608+.........+22.8798) / 34

therefore, r bar = 24.29441

6. upper critical limit (UCLR) and lower critical limits (LCLR) of r chart can be found by using the following formulas

UCLR = D4* r bar and LCLR = D3* r bar

these D4 and D3 should be given along with the question. Or these can be found out by using control chart constants, and this depends on the subgroup number as well.

The SHEWHART Procedure Means and Ranges Chart Summary for response 3 Sigma Limits with n=4 for 3 Sigma Limits with n=4 for Me

ex: for subgroup 4, sample size 34, D4 = UPPER LIMIT OF RANGE = 9.3963507,

D3 = LOWER LIMIT OF RANGE= 0

So, UCLR =9.3963507 * r bar and LCLR = 0 * r bar

sample observation 1 observation 2 observation 3 observation 4 observation 5 range (r)
1 155.1759 164.4978 144.0894 149.1192 160.0421 20.4084
2 161.1192 145.4001 162.7882 177.1397 162.4125 31.7396
3 161.3671 143.0758 171.4366 158.8492 154.7023 28.3608
4 166.1941 166.911 163.6076 151.8873 162.9515 15.0237
5 158.7486 154.2805 180.887 178.2488 155.1188 26.6065
6 159.233 160.6053 176.0102 175.6228 166.1402 16.7772
7 170.6843 161.7413 169.6049 157.7824 172.9065 15.1241
8 167.3616 148.0186 165.7245 162.1048 163.974 19.343
9 157.9749 148.492 167.2943 140.076 181.7458 41.6698
10 155.6967 171.0943 152.6593 142.4727 160.5202 28.6216
11 164.5217 157.1935 151.1438 158.0747 155.3919 13.3779
12 167.979 141.8374 155.4931 149.2655 163.0297 26.1416
13 163.8557 168.984 163.8254 150.4593 160.4368 18.5247
14 171.5194 148.2178 163.5912 157.6182 161.8093 23.3016
15 135.6434 186.8886 152.3281 137.6502 167.7435 51.2452
16 173.4057 159.6673 155.0814 169.7719 179.3919 24.3105
17 169.3266 158.3569 174.3621 173.9279 174.052 16.0052
18 154.3969 146.7553 168.1947 148.4083 170.2388 23.4835
19 151.6227 143.9714 164.887 142.5745 158.1103 22.3125
20 176.3726 171.7192 158.2436 170.3528 167.8382 18.129
21 165.9762 150.7074 160.5092 158.1487 179.0462 28.3388
22 177.6822 160.1059 185.147 186.0095 174.6436 25.9036
23 166.6542 181.4711 138.1257 171.4638 160.0559 43.3454
24 153.1734 165.9899 168.987 165.7046 148.5262 20.4608
25 143.6162 152.5279 177.0654 160.5963 162.9247 33.4492
26 165.9919 176.0156 158.9986 167.7788 169.1682 17.017
27 178.3369 157.5605 160.1486 177.0536 168.5923 20.7764
28 154.2878 164.8663 158.5857 176.5919 176.6121 22.3243
29 151.5038 170.4999 155.6362 153.6519 174.8804 23.3766
30 173.1002 178.7034 177.8521 162.7629 161.4867 17.2167
31 159.0639 179.3448 170.4143 154.9183 161.8192 24.4265
32 173.56 150.7119 171.7711 151.7356 143.1589 30.4011
33 156.3567 171.9441 159.2536 161.1486 158.9801 15.5874
34 154.1641 151.0134 163.3826 169.4772 173.8932 22.8798
r bar=

24.29441
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