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The diameter of the casting is an important quality characteristic. A coordinate measuring machine is used to measure the diameter of each casting at five different locations. Data for 20 castings are shown below. Perform a process capability study using x-bar and R charts. The specification limits are: Lower specification limit: 11.7; Upper specification limit: 11.8
Note: Provide your answer under each bullet
Measurements
Casting
1
2
3
4
5
11.7629
11.7403
11.7511
11.7474
11.7374
11.8122
11.7506
11.7787
11.7736
11.8412
11.7742
11.7114
11.753
11.7532
11.7773
11.7833
11.7311
11.7777
11.8108
11.7804
11.7134
11.687
11.7305
11.7419
11.6642
6
11.7925
11.7611
11.7588
11.7012
7
11.6916
11.7205
11.6958
11.744
11.7062
8
11.7109
11.7832
11.7496
11.7318
9
11.7984
11.8887
11.7729
11.8485
11.8416
10
11.7914
11.7613
11.7356
11.7628
11.707
11
11.726
11.7329
11.7424
11.7645
11.7571
12
11.7202
11.7537
11.7328
11.7582
11.7265
13
11.8356
11.7971
11.8023
11.7802
11.7903
14
11.7069
11.7112
11.7492
11.7289
15
11.7116
11.7978
11.7982
11.7429
11.7154
16
11.7165
11.7284
11.7597
11.7317
17
11.8022
11.8127
11.7864
11.7917
11.8167
18
11.7775
11.7372
11.7241
11.7543
19
11.7753
11.787
11.7574
11.762
11.7673
20
11.7572
11.7626
11.7523
11.7395
11.7884
a)Set up the x-bar and r-charts for this process, assuming the measurements on each casting form a rational subgroup. Show the xbar and r-charts for the stable process. Ensure you have a stable process.Calculate the Cp and Cpk indices based on the stable process.Do your capability analysis using Minitab and show Minitab output.Is the process capable?Is the process centered?
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