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The syringe length is measured during a pharmaceutical manufacturing process. The following table provides data (in inches) for 20 samples each of size 5. Construct

The syringe length is measured during a pharmaceutical manufacturing process. The following table provides data (in inches) for 20 samples each of size 5. Construct the control limits for both X and R charts and check if the process is in control or out of control. If the process is out of control, construct the revised control limits for both X and R charts.

Sample

x1

x2

x3

x4

x5

1

4.960

4.946

4.950

4.956

4.958

2

4.958

4.927

4.935

4.940

4.950

3

4.971

4.929

4.965

4.952

4.938

4

4.940

4.982

4.970

4.953

4.960

5

4.964

4.950

4.953

4.962

4.956

6

4.969

4.951

4.955

4.966

4.954

7

4.960

4.944

4.957

4.948

4.951

8

4.969

4.949

4.963

4.952

4.962

9

4.984

4.928

4.960

4.943

4.955

10

4.970

4.934

4.961

4.940

4.965

11

4.975

4.959

4.962

4.971

4.968

12

4.945

4.977

4.950

4.969

4.954

13

4.976

4.964

4.970

4.968

4.972

14

4.970

4.954

4.964

4.959

4.968

15

4.982

4.962

4.968

4.975

4.963

16

4.961

4.943

4.950

4.949

4.957

17

4.980

4.970

4.975

4.978

4.977

18

4.975

4.968

4.971

4.969

4.972

19

4.977

4.966

4.969

4.973

4.970

20

4.975

4.967

4.969

4.972

4.972

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