1. The following data are the production units from a manufacturing line for the past 5 weeks. The manager wants to know if the process is stable and in control. Produce X-bar and R charts and comment on the process
|
Week
|
Monday
|
Tuesday
|
Wednesday
|
Thursday
|
Friday
|
|
1
|
12
|
15
|
8
|
7
|
10
|
|
2
|
6
|
9
|
11
|
13
|
7
|
|
3
|
15
|
11
|
9
|
6
|
12
|
|
4
|
8
|
7
|
6
|
11
|
14
|
|
5
|
20
|
12
|
10
|
5
|
14
|
|
6
|
13
|
10
|
9
|
8
|
12
|
|
7
|
10
|
14
|
11
|
8
|
5
|
|
8
|
10
|
15
|
17
|
11
|
9
|
2. The internal diameter of a cylinder must be 60 centimeter. The tolerance is +1 and -0.5 centimeter. If the mean value of the process is 60.4 and the standard deviation is 0.5,
a. Calculate the process capability index (CP and CPk) and indicate if the process is capable.
b. Calculate the % of the cylinders produced that will meet the specifications
c. What should be the standard deviation in order for the process to become capable?
3. A product has specification limits of 18 to 20. If the process mean is 19.2 and the standard deviation is 0.6, calculate
a. The process capability for this production line.
b. What % of the products are out of specs
c. What should be the standard deviation in order for the process to become capable?