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
|
|
1
|
11.7629
|
11.7403
|
11.7511
|
11.7474
|
11.7374
|
|
2
|
11.8122
|
11.7506
|
11.7787
|
11.7736
|
11.8412
|
|
3
|
11.7742
|
11.7114
|
11.753
|
11.7532
|
11.7773
|
|
4
|
11.7833
|
11.7311
|
11.7777
|
11.8108
|
11.7804
|
|
5
|
11.7134
|
11.687
|
11.7305
|
11.7419
|
11.6642
|
|
6
|
11.7925
|
11.7611
|
11.7588
|
11.7012
|
11.7611
|
|
7
|
11.6916
|
11.7205
|
11.6958
|
11.744
|
11.7062
|
|
8
|
11.7109
|
11.7832
|
11.7496
|
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
|
11.7329
|
11.7289
|
|
15
|
11.7116
|
11.7978
|
11.7982
|
11.7429
|
11.7154
|
|
16
|
11.7165
|
11.7284
|
11.7571
|
11.7597
|
11.7317
|
|
17
|
11.8022
|
11.8127
|
11.7864
|
11.7917
|
11.8167
|
|
18
|
11.7775
|
11.7372
|
11.7241
|
11.7773
|
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?