Question

((Note: The answer has to be typed, not hand written nor a picture.)) Thank you.   

GAGE R & R EXERCISE

in this example, we do a gage R&R study on two data sets: one in which measurement system variation contributes little to the overall observed variation (GAGEAIAG.MTW), and one in which measurement system variation contributes a lot to the overall observed variation (GAGE2.MTW). For comparison, we analyze the data using both the ANOVA and the Xbar and R method.

The GAGEAIAG data was taken from Measurement Systems Analysis Reference Manual, 3rd edition. (Chrysler, Ford, General Motors Supplier Quality Requirements Task Force). Ten parts were selected that represent the expected range of the process variation. Three operators measured the ten parts, three times per part, in a random order.

For the GAGE2 data, three parts were selected that represent the expected range of the process variation. Three operators measured the three parts, three times per part, in a random order

Part 1: Use the ANOVA method with GAGEAIAG data

1    Open the worksheet GAGEAIAG.MTW.

2    Choose Stat > Quality Tools > Gage Study > Gage R&R Study (Crossed).

3    In Part numbers, enter Part.

4    In Operators, enter Operator.

5    In Measurement data, enter Measurement.

6    Under Method of Analysis, choose ANOVA.

7    Click Options. Under Process tolerance, choose Upper spec - Lower spec and enter 8.

8    Click OK in each dialog box.

Answer the following questions

1. In the session window output, what is the percent contribution for part-to-part? _____

2. In the session window output, what is the percent contribution for total Gage R & R? _____

3. After answer questions 1 and 2 above, which do you, believe causes more of the variation, part-to- part or the measuring system? ________________________________

4. If you knew that according to Automobile Industry Action Group (AIAG) that you can determine whether or not your measurement system is acceptable using the following guidelines.

If the Total Gage R&R percentage in the %Study Var column (% Tolerance, %Process) is:                       PAGE 1

          

                           Gage R  & R EXERCISE

Less than 10% - the measurement system is acceptable

Between 10% and 30% - the measurement system is acceptable depending on the application, the cost of the measuring device, cost of repair, or other factors

Greater than 30% - the measurement system is unacceptable and should be improved

If you are looking at the % Contribution column, the corresponding standards are:

Less than 1% - the measurement system is acceptable

Between 1% and 9% - the measurement system is acceptable depending on the application, the cost of the measuring device, cost of repair, or other factors.

What have you determined about this measurement system based on the %Study Var column for total Gage R &R?___________________________________________________

_________________________________________________________________

5. Looking at the graph window output, what does the components of variation graph in the top upper left hand corner indicate?__________________________________________________

__________________________________________________________________________

6. Looking at the measurement by operator graph, which operator seems to measure differently than the others? ________________

Step 2: Use the ANOVA method with GAGE2 data

1    Open the file GAGE2.MTW.

2    Choose Stat > Quality Tools > Gage Study > Gage R&R Study (Crossed).

3    In Part numbers, enter Part.

4    In Operators, enter Operator.

5    In Measurement data, enter Response.

6    Under Method of Analysis, choose ANOVA.

7    Click OK.                                                                                                                                     PAGE 2

                                          GAGE R & R EXERCISE

Answer the following questions

1. In the session window output, what is the percent contribution for Total Gage R&R? _____

2. In the session window output, what is the percent contribution for total part-to-part? _____

3. After answer questions 1 and 2 above, which do you, believe causes more of the variation, part-to- part or the measuring system? ________________________________

4. If you knew that according to Automobile Industry Action Group (AIAG) that you can determine whether or not your measurement system is acceptable using the (criteria from part 1)

What have you determined about this measurement system based on the %Study Var column for total Gage R &R?___________________________________________________

5. Looking at the graph window output, what does the components of variation graph in the top upper left hand corner indicate?__________________________________________________

__________________________________________________________________________

6. Looking at the repsonse by operator graph, which operator seems to measure differently than the others? ________________

Answer 1

Answer:

By using given data,

Part-1

Results for: Gageaiag.MTW as follows bellow

Gage R&R Study - Here, ANOVA Method is followed

Two-Way ANOVA Table With Interaction

Source           DF       SS       MS        F      P

Part              9 88.3619 9.81799 492.291 0.000

Operator          2   3.1673 1.58363   79.406 0.000

Part * Operator 18   0.3590 0.01994    0.434 0.974

Repeatability    60   2.7589 0.04598

Total            89 94.6471

α to remove interaction term is = 0.05

Two-Way ANOVA Table Without Interaction

Source         DF       SS       MS        F      P

Part            9 88.3619 9.81799 245.614 0.000

Operator        2   3.1673 1.58363   39.617 0.000

Repeatability 78   3.1179 0.03997

Total          89 94.6471

Gage R&R

                            %Contribution

Source             VarComp   (of VarComp)

Total Gage R&R     0.09143           7.76

Repeatability    0.03997           3.39

Reproducibility 0.05146           4.37

    Operator       0.05146           4.37

Part-To-Part       1.08645          92.24

Total Variation    1.17788         100.00

Process tolerance = 8

                                Study Var %Study Var %Tolerance

Source             StdDev (SD)   (6 × SD)       (%SV) (SV/Toler)

Total Gage R&R         0.30237    1.81423       27.86       22.68

Repeatability        0.19993    1.19960       18.42       14.99

Reproducibility      0.22684    1.36103       20.90       17.01

    Operator           0.22684    1.36103       20.90       17.01

Part-To-Part           1.04233    6.25396       96.04       78.17

Total Variation        1.08530    6.51180      100.00       81.40

Number of Distinct Categories are = 4

(1) The percent contribution for part-to-part =92.24%

(2) The percent contribution for total Gage R & R =7.76%

(3) We believe part-to-part causes more of the variation

(4) We observe that Total Gage R&R percentage in the %Study Var column is 27.86%. So, the measurement system is acceptable depending on the application, the cost of the measuring device, cost of repair, or other factors

(5) This shows, that part-to part contribute more towards variations as compared to other factors.

(6) Looking at the measurement by operator graph, operator-C seems to measure differently than the others

Results for: Gage2.MTW is follows bellow

Gage R&R Study - Here ANOVA Method is followed

Two-Way ANOVA Table With Interaction

Source           DF      SS       MS        F      P

Part              2   38990 19495.2 2.90650 0.166

Operator          2     529    264.3 0.03940 0.962

Part * Operator   4   26830   6707.4 0.90185 0.484

Repeatability    18 133873   7437.4

Total            26 200222

α to remove interaction term = 0.05

Two-Way ANOVA Table Without Interaction

Source         DF      SS       MS        F      P

Part            2   38990 19495.2 2.66887 0.092

Operator        2     529    264.3 0.03618 0.965

Repeatability 22 160703   7304.7

Total          26 200222

Gage R&R

                            %Contribution

Source             VarComp   (of VarComp)

Total Gage R&R     7304.67          84.36

Repeatability    7304.67          84.36

Reproducibility     0.00           0.00

    Operator          0.00           0.00

Part-To-Part       1354.50          15.64

Total Variation    8659.17         100.00

Process tolerance = 8

                                Study Var %Study Var %Tolerance

Source             StdDev (SD)   (6 × SD)       (%SV) (SV/Toler)

Total Gage R&R         85.4673    512.804       91.85     6410.05

Repeatability        85.4673    512.804       91.85     6410.05

Reproducibility       0.0000      0.000        0.00        0.00

    Operator            0.0000      0.000        0.00        0.00

Part-To-Part           36.8036    220.821       39.55     2760.27

Total Variation        93.0547    558.328      100.00     6979.10

Number of Distinct Categories = 1

Gage R&R for Response

                                          GAGE R & R EXERCISE

Answers for the questions are

(1) The percent contribution for Total Gage R&R=84.36

(2) The percent contribution for total part-to-part=15.64

(3) We believe measuring system causes more of the variation

(4) We observe that Total Gage R&R percentage in the %Study Var column is 91.85% Greater than 30% -so the measurement system is unacceptable and should be improved.

(5) Looking at the graph window output, the components of variation graph in the top upper left hand corner indicate that the measurement system explained most of the variaiton and within this repeatability explained most variation.

(6) Looking at the repsonse by operator graph, operator-1 seems to measure differently than the others.