Example: Consider a measurement system to measure the internal diameter of the bearing.The quality engineer conducted an experiment with 10 pieces, three operators and three repetitions for each operator and piece. The data from this experiment are shown in the following table.
| measurement | piece | operator |
| 114.958 | 1 | 1 |
| 114.957 | 2 | 1 |
| 114.962 | 3 | 1 |
| 114.963 | 4 | 1 |
| 114.965 | 5 | 1 |
| 114.963 | 6 | 1 |
| 114.967 | 7 | 1 |
| 114.963 | 8 | 1 |
| 114.953 | 9 | 1 |
| 114.967 | 10 | 1 |
| 114.957 | 1 | 1 |
| 114.958 | 2 | 1 |
| 114.962 | 3 | 1 |
| 114.963 | 4 | 1 |
| 114.965 | 5 | 1 |
| 114.962 | 6 | 1 |
| 114.967 | 7 | 1 |
| 114.968 | 8 | 1 |
| 114.952 | 9 | 1 |
| 114.967 | 10 | 1 |
| 114.958 | 1 | 1 |
| 114.958 | 2 | 1 |
| 114.953 | 3 | 1 |
| 114.965 | 4 | 1 |
| 114.967 | 5 | 1 |
| 114.962 | 6 | 1 |
| 114.967 | 7 | 1 |
| 114.968 | 8 | 1 |
| 114.953 | 9 | 1 |
| 114.966 | 10 | 1 |
| 114.962 | 1 | 2 |
| 114.956 | 2 | 2 |
| 114.963 | 3 | 2 |
| 114.965 | 4 | 2 |
| 114.966 | 5 | 2 |
| 114.965 | 6 | 2 |
| 114.969 | 7 | 2 |
| 114.97 | 8 | 2 |
| 114.955 | 9 | 2 |
| 114.965 | 10 | 2 |
| 114.961 | 1 | 2 |
| 114.957 | 2 | 2 |
| 114.963 | 3 | 2 |
| 114.966 | 4 | 2 |
| 114.967 | 5 | 2 |
| 114.963 | 6 | 2 |
| 114.97 | 7 | 2 |
| 114.968 | 8 | 2 |
| 114.955 | 9 | 2 |
| 114.964 | 10 | 2 |
| 114.961 | 1 | 2 |
| 114.96 | 2 | 2 |
| 114.963 | 3 | 2 |
| 114.966 | 4 | 2 |
| 114.968 | 5 | 2 |
| 114.965 | 6 | 2 |
| 114.968 | 7 | 2 |
| 114.969 | 8 | 2 |
| 114.953 | 9 | 2 |
| 114.965 | 10 | 2 |
| 114.958 | 1 | 3 |
| 114.96 | 2 | 3 |
| 114.965 | 3 | 3 |
| 114.966 | 4 | 3 |
| 114.967 | 5 | 3 |
| 114.964 | 6 | 3 |
| 114.97 | 7 | 3 |
| 114.97 | 8 | 3 |
| 114.955 | 9 | 3 |
| 114.966 | 10 | 3 |
| 114.958 | 1 | 3 |
| 114.959 | 2 | 3 |
| 114.965 | 3 | 3 |
| 114.965 | 4 | 3 |
| 114.966 | 5 | 3 |
| 114.965 | 6 | 3 |
| 114.97 | 7 | 3 |
| 114.97 | 8 | 3 |
| 114.954 | 9 | 3 |
| 114.966 | 10 | 3 |
| 114.958 | 1 | 3 |
| 114.958 | 2 | 3 |
| 114.964 | 3 | 3 |
| 114.965 | 4 | 3 |
| 114.966 | 5 | 3 |
| 114.965 | 6 | 3 |
| 114.969 | 7 | 3 |
| 114.971 | 8 | 3 |
| 114.955 | 9 | 3 |
| 114.967 | 10 | 3 |
click here to download the data
To use the tool ANOVA - Random Factors the user must follow these steps:
1. Access the menu:
Action
ANOVA
ANOVA (Random Factors)
2. The following screen will be shown;
3. With the cursor in the field Data Set, select the columns that contain the data that will be analyzed;
4. The titles of the columns can also be selected. If only the data are selected, disable the option Columns with Name. Then, click the button Read;
5. Select the Response Variable, in the appropriate item;
6. In Factors, select the factors that will be used in the analysis, in this case Pieces and Operators;
7. In Show Results, choose one of the options. We suggest the option New Sheet, because Action does not have the undo command;
REMARK: The names of the columsn can not contain symbols, space or tab.
Results and Interpretation
Once the process is finished, the following results will be shown:
So, we conclude that there is significant difference between the operators and between the pieces.
