# 2010-08-30_045519_Twelve_samples__each_containing_five_parts

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```					Please put the answer on excel. Please show computations Twelve samples, each containing five parts, were taken from a p

Sample                                         Sample
Sample      mean(in.)        Range (in.)      Sample       mean(in.)   Range(in.)
1         10.002            0.011             7          10.001       0.008
2         10.002            0.014             8          10.005       0.013
3          9.991            0.007             9           9.995       0.004
4         10.006            0.022            10          10.001       0.011
5          9.997            0.013            11          10.001       0.014
6          9.999            0.012            12          10.006       0.009

(a) For x-bar chart, LCL = 9.9937 in and UCL = 10.0071 in
Mean of the sample means is 10.0005 in

For the R chart, LCL = 0 and UCL = 0.0243 in
Mean of the sample ranges is 0.0115 in

(b) See the sheets XBar chart and Rchart

(c) The process is not in control

(d) The process is not in control because the sample 3 (Mean = 9.991) lies below the LCL.
e parts, were taken from a process that produces steel rods. The length of each rod in the samples was determined. The results were t

Sample     Sample Mean     Sample Range
1      10.002          0.011
2      10.002          0.014
3      9.991           0.007
4      10.006          0.022
5      9.997           0.013
6      9.999           0.012
7      10.001          0.008
8      10.005          0.013
9      9.995           0.004
10      10.001          0.011
11      10.001          0.014
12      10.006          0.009

Means =      10.0005          0.0115
as determined. The results were tabulated and sample means and ranges were computed. The results were: Sample Sample Mean (in.)
were: Sample Sample Mean (in.) Range (in.) 1 10.002 0.011 2 10.002 0.014 3 9.991 0.007 4 10.006 0.022 5 9.997 0.013 6 9.999 0.0
0.022 5 9.997 0.013 6 9.999 0.012 7 10.001 0.008 8 10.005 0.013 9 9.995 0.004 10 10.001 0.011 11 10.001 0.014 12 10.006 0.009
11 10.001 0.014 12 10.006 0.009 10.0005 0.0115 a) Determine the upper and lower control limits and the overall means for -charts an
d the overall means for -charts and R-charts. b) Draw the charts and plot the values of the sample means and ranges. c) Do the data in
ans and ranges. c) Do the data indicate a process that is in control? d) Why or why not?
Control Chart Calculations
10.008

UCL

10.006

10.004

10.002

XBar
Sample Mean

10
XBar
LCL-X
9.998                                                              Center-X
UCL-X

9.996

9.994                                                  LCL

9.992

9.99
0   2   4        6         8         10   12          14
Control Chart Calculations
0.03

0.025
UCL

0.02
Sample Range

Range
0.015
LCL-R
Center-R

RBar        UCL-R

0.01

0.005

0                                                   LCL
0   2   4        6         8         10   12          14
Number    XBar       Range     LCL-R       Center-R    UCL-R       LCL-X    Center-X   UCL-X
1      10.002      0.011         0      0.0115    0.024311    9.993865 10.0005    10.00714
2      10.002      0.014         0      0.0115    0.024311    9.993865 10.0005    10.00714
3        9.991     0.007         0      0.0115    0.024311    9.993865 10.0005    10.00714
4      10.006      0.022         0      0.0115    0.024311    9.993865 10.0005    10.00714
5        9.997     0.013         0      0.0115    0.024311    9.993865 10.0005    10.00714
6        9.999     0.012         0      0.0115    0.024311    9.993865 10.0005    10.00714
7      10.001      0.008         0      0.0115    0.024311    9.993865 10.0005    10.00714
8      10.005      0.013         0      0.0115    0.024311    9.993865 10.0005    10.00714
9        9.995     0.004         0      0.0115    0.024311    9.993865 10.0005    10.00714
10      10.001      0.011         0      0.0115    0.024311    9.993865 10.0005    10.00714
11      10.001      0.014         0      0.0115    0.024311    9.993865 10.0005    10.00714
12      10.006      0.009         0      0.0115    0.024311    9.993865 10.0005    10.00714
A                         B               C          D           E      F      G         H
1   Control Chart Calculations
2                                                                   Control Chart Factors Table.
3                       Data                                     Subgroup size D3        D4     A2
4   Sample/Subgroup Size                                5                     2      0 3.267 1.880
5                                                                             3      0 2.575 1.023
6            R Chart Intermediate Calculations                                4      0 2.282 0.729
7   RBar                                           0.0115                     5      0 2.114 0.577
8   D3 Factor                                           0                     6      0 2.004 0.483
9   D4 Factor                                       2.114                     7 0.076 1.924 0.419
10                                                                             8 0.136 1.864 0.373
11               R Chart Control Limits                                        9 0.184 1.816 0.337
12   Lower Control Limit                                  0                   10 0.223 1.777 0.308
13   Center                                          0.0115                   11 0.256 1.744 0.285
14   Upper Control Limit                          0.024311                    12 0.283 1.717 0.266
15                                                                            13 0.307 1.693 0.249
16           XBar Chart Intemediate Calculations                              14 0.328 1.672 0.235
17   Average of Subgroup Averages                10.0005                      15 0.347 1.653 0.223
18   A2 Factor                                     0.577                      16 0.363 1.637 0.212
19   A2 Factor * RBar                         0.0066355                       17 0.378 1.622 0.203
20                                                                            18 0.391 1.609 0.194
21              XBar Chart Control Limits                                     19 0.404 1.596 0.187
22   Lower Control Limit                   9.9938645                          20 0.415 1.585 0.180
23   Center                                   10.0005                         21 0.425 1.575 0.173
24   Upper Control Limit                  10.0071355                          22 0.435 1.565 0.167
25                                                                            23 0.443 1.557 0.162
26                                                                            24 0.452 1.548 0.157
27                                                                            25 0.459 1.541 0.153
28                                                                                      Factor value not available. Possible er
Factor value not available. in sa
26 Factor value not available. Possible error Poss
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30                                                                Factor value not available. Possible error in sample/subgroup s
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Factor value not available. Possible error in sample/subgroup size.
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ble error in sample/subgroup size.

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