Question: The data in the following table represent individual observations on molecular weight taken hourly from a chemical process. The target value of molecular weight is

The data in the following table represent individual observations on molecular weight taken hourly from a chemical process. The target value of molecular weight is 1,050 and the process standard deviation is thought to be about = 25.

Observation Number

x

Observation Number

x

1

1,045

11

1,139

2

1,055

12

1,169

3

1,037

13

1,151

4

1,064

14

1,128

5

1,095

15

1,238

6

1,008

16

1,125

7

1,050

17

1,163

8

1,087

18

1,188

9

1,125

19

1,146

10

1,146

20

1,167

a. Set up a tabular CUSUM for the mean of this process. Design the CUSUM to quickly detect a shift of 1, using h = 5.

b. At what point did the assignable cause that sent the process out of control occur (this is not the same as when it actually went out of control)?

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