[Degree of freedom calculations] An industrial engineer is studying hand inserti
ID: 3354439 • Letter: #
Question
[Degree of freedom calculations]
An industrial engineer is studying hand insertion of electronic components on printed circuit boards to improve the speed of an assembly operation. She designed three assembly fixtures and two workplace layouts that seem promising for use. Since operators will be required to use the apparatus, four operators are randomly selected to test each combination of fixtures and layouts. Since the layouts are in different locations of a plant, a different set of four operators is used for each layout but all operators experience all three fixture designs. During testing the fixtures were presented to operators in random order with replication and assembly times were recorded in seconds (s). See the below data table.
(A) Prepare a table of degrees of freedom (DoF) for all effects/factors in your model.
(B) What is the total number of DoFs available for data analysis based on the data collection
table.
(C) How many DoFs are pooled in the error term of the model?
Layout 2 Layout 1 4 2 27 25 30 27 26 24 4 26 28 29 28 27 25 28 25 24 23 24 27 24 23 28 30 28 27 Operator 28 29 30 32 27 25 25 23 27 25 26 23 Fixture 1 22 24 24 29 28 24 Fixture 2 30 27 25 21 Fixture 3Explanation / Answer
Answer:
(A) Prepare a table of degrees of freedom (DoF) for all effects/factors in your model.
Source
DoF
Layout
1
Operator
2
Interaction
2
Error
42
Total
47
(B) What is the total number of DoFs available for data analysis based on the data collection
table.
total number of DoFs = 47
(C) How many DoFs are pooled in the error term of the model?
Error DoF = 42
Source
DoF
Layout
1
Operator
2
Interaction
2
Error
42
Total
47
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