spc problem

Excel file with the data for the three questions.

  • Piston rings for an automotive engine are produced by a forging process. We wish to establish statistical control of the inside diameter of the rings manufactured. Twenty-five samples, each of size five, have been taken to analyze the process. The inside diameter measurement data from theses samples are shown in the following table:
  • Fifteen additional samples from the piston ring manufacturing process were collected after the control charts were established. The data from theses new samples are shown in the following table:
  • You are the newly appointed assistant administrator at a local hospital, and your first project is to investigate the quality of the patient meals put out by the food-service department. You conducted a 10-day survey by submitting a simple questionnaire to the 400 patients with each three meals, asking that they simply check-off that the meal was either satisfactory or unsatisfactory. The results are:

Observations

1

2

3

4

5

Mean (X)

Range (R)

1

74.03

74.002

74.019

73.992

74.008

74.010

0.038

2

73.995

73.992

74.001

74.011

74.004

74.001

0.019

3

73.988

74.024

74.021

74.005

74.002

74.008

0.036

4

74.002

73.996

73.993

74.015

74.009

74.003

0.022

5

73.992

74.007

74.015

73.989

74.014

74.003

0.026

6

74.009

73.994

73.997

73.985

73.993

73.996

0.024

7

73.995

74.006

73.994

74.000

74.005

74.000

0.012

8

73.985

74.003

73.993

74.015

73.998

73.999

0.030

9

74.008

73.995

74.009

74.005

74.004

74.004

0.014

10

73.998

74.000

73.990

74.007

73.995

73.998

0.017

11

73.994

73.998

73.994

73.995

73.990

73.994

0.008

12

74.004

74.000

74.007

74.000

73.996

74.001

0.011

13

73.983

74.002

73.998

73.997

74.012

73.998

0.029

14

74.006

73.967

73.994

74.000

73.984

73.990

0.039

15

74.012

74.014

73.998

73.999

74.007

74.006

0.016

16

74.000

73.984

74.005

73.998

73.996

73.997

0.021

17

73.994

74.012

73.986

74.005

74.007

74.001

0.026

18

74.006

74.010

74.018

74.003

74.000

74.007

0.018

19

73.984

74.002

74.003

74.005

73.997

73.998

0.021

20

74.000

74.010

74.013

74.020

74.003

74.009

0.020

21

73.988

74.001

74.009

74.005

73.996

74.000

0.021

22

74.004

73.999

73.990

74.006

74.009

74.002

0.019

23

74.010

73.989

73.990

74.009

74.014

74.002

0.025

24

74.015

74.008

73.993

74.000

74.010

74.005

0.022

25

73.982

73.984

73.995

74.017

74.013

73.998

0.035

  • What is the value of and ?
  • Construct -charts and R-charts for this problem. Is the process in control?

Observations

1

2

3

4

5

Mean (X)

Range (R)

26

74.012

74.015

74.030

73.986

74.000

74.009

0.044

27

73.995

74.010

73.990

74.015

74.001

74.002

0.025

28

73.987

73.999

73.985

74.000

73.990

73.992

0.015

29

74.008

74.010

74.003

73.991

74.006

74.004

0.019

30

74.003

74.000

74.003

73.986

73.997

73.998

0.017

31

73.994

74.003

74.015

74.020

74.004

74.007

0.026

32

74.008

74.002

74.018

73.995

74.005

74.006

0.023

33

74.001

74.004

73.990

73.996

73.998

73.998

0.014

34

74.015

74.000

74.016

74.025

74.000

74.011

0.025

35

74.030

74.005

74.000

74.016

74.012

74.013

0.030

36

74.001

73.990

73.995

74.010

74.024

74.004

0.034

37

74.015

74.020

74.024

74.005

74.019

74.017

0.019

38

74.035

74.010

74.012

74.015

74.026

74.020

0.025

39

74.017

74.013

74.036

74.025

74.026

74.023

0.023

40

74.010

74.005

74.029

74.000

74.020

74.013

0.029

Is the process now in control? What conclusion can we make?

Day

Unsatisfactory meals

Sample size

1

74

1,000

2

39

1,100

3

64

1,050

4

86

1,000

5

35

1,078

6

50

950

7

65

1,141

8

70

988

9

67

750

10

75

1,010

Total

625

10,067

  • Construct a p-chart based on the questionnaire results.
  • What comments can you make about the results of the survey?

Note: in the attachment you will find an Excel file with the data for the three, please use the attachment for questions

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