Auto pistons at yongpin zhou’s plant in shanghai are produced in a

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S6.7: Auto pistons at Yongpin Zhou’s plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean the range of this diameter have been as follows:

Day

Mean (mm)

Range(mm)

1

156.9

4.2

2

153.2

4.6

3

153.6

4.1

4

155.5

5

5

156.6

4.5

 

a.What is the value x bar?

b. What is the value of R bar?

c. What are the UCL_x bar and LCL_x bar using 3 sigma?

S.6.15: The results of inspection of DNA samples taken over the past 10 days are given below. Sample size is 100.

Day

1

2

3

4

5

6

7

8

9

10

Defectives

7

6

6

9

5

6

0

8

9

1

 

a) Construct a 3-sigma p-chart using this information.

 

b) If the number of defectives on the next three days are 12, 5 and 13, is the process in control?