1. II.2 Four Factors in Eight Runs Some Fiber Optics Examples and Exercises*
Some 24-1 DOE’s
Responses:
Shrinkage (S)
Excess Length (L)
Factors: some are trade secrets and others include
Time
Temperature
Fiber Tension
Draw Ratio
Line Speed
Fiber Conditioning
* Examples are based on some 24-1 DOE studies done at the Pirelli’s Lexington, SC plant
Discuss only a few highlights. Shrinkage is measured by diameter (Target is best). For Excess Length, a target of zero is best.

2. II.2 Four Factors in Eight Runs: Examples Shrinkage
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3. II.2 Four Factors in Eight Runs: Examples Shrinkage - Discussion and Interpretation
The 24-1 Fractional Factorial Used Here (D=ABC or ABCD=I) is called a Resolution IV Design. This Means That, Assuming that 3-way and 4-way Interactions are NEGLIGIBLE , Factors B and C Affect Shrinkage Without a Significant Interaction. (More About Resolution Later)
We Estimate That
Setting B Hi Increases Shrinkage .36 over Setting it Lo
Setting C Lo Increases the Shrinkage .39 over Setting it Hi
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4. II.2 Four Factors in Eight Runs: Examples Shrinkage - Estimated Mean Response (EMR)
EMR isn’t any more complex. Our answer will differ from Minitab’s due to rounding error.
For B = + and C = -, EMR = (+1)(.36)/2 +
(-1)(-.39)/2 = = .925

5. II.2 Four Factors in Eight Runs: Examples Excess Length
Excess length is both positive and negative.

6. II.2 Four Factors in Eight Runs: Examples Excess Length - Discussion and Interpretation
The 24-1 Fractional Factorial Used Here is Again the Resolution IV Design, D=ABC (or ABCD=I). Thus, Assuming that 3-way and 4-way Interactions are NEGLIGIBLE, Factors B, C and D Affect Excess Length But There Appears To Be A Significant Interaction, (AD or BC, or Both).
Since B and C signaled but A did not, We Shall ASSUME that the BC interaction is Significant for Interpretation Purposes.
A somewhat strong assumption here, since D signaled too, which could suggest AD is large.

7. II.2 Four Factors in Eight Runs: Example Excess Length - Discussion and Interpretation
Noise Factors/Control Factors
If Factor C was Hard to Control (a Noise Factor), But B was not (a Control Factor), Setting B Hi mitigates the effect of C
Similarly, Setting C Hi mitigates the effect of B
Ideally, The Excess Length should be 0.
Setting B Lo and C Hi Give the Smallest Magnitude of Excess Length with Excess Length at about -.07.
In addition, changing D from Lo to Hi increases Excess Length
Thus, Set B Lo, and C and D both Hi.
The plot could also be a BC+AD plot, or a AD plot (Minitab forces a choice). B low, C high is closest to 0.

8. II.2 Four Factors in Eight Runs: Examples Excess Length - Estimated Mean Response (EMR)
For B = - , C = +, D=+:
EMR = (-1)(-.18)/2 + (+1)(-.09)/2 + (+1)(.07)/ (-1)(+1)(.12)/2 = = -.037
Don’t overthink need to assign D as well. Do EMR in Minitab

9. II.2 Four Factors in Eight Runs: U-Do-It Exercise
Completed Signs Tables and Normal Probability Plots are Provided for Two Other 24-1 Experiments (D=ABC or ABCD=I) Involving Shrinkage and Excess Length
Analyze These Experiments
Calculate the EMR for Shrinkage and Excess Length when A and B are both Lo and C and D are both Hi
Another example.

10. II.2 Four Factors in Eight Runs: U-Do-It Exercise Shrinkage
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11. II.2 Four Factors in Eight Runs: U-Do-It Exercise Excess Length
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12. II.2 Four Factors in Eight Runs: U-Do-It Exercise Shrinkage Solution - Discussion and Interpretation
C+ABD is Statistically Significant. Thus, Assuming that 3-way and 4-way Interactions are NEGLIGIBLE , Factor C Affects Shrinkage. There are No Significant Two-way Interactions.
We Estimate That
Setting C Hi Increases the Shrinkage .206 over Setting it Lo
When C = +, EMR = (+1)(.206)/2 = = .795
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13. II.2 Four Factors in Eight Runs: U-Do-It Exercise Excess Length Solution - Discussion and Interpretation
A+BCD, C+ABD and AC+BD are Statistically Significant. Thus, Assuming that 3-way and 4-way Interactions are NEGLIGIBLE , Factors A and C Affect Excess Length. To interpret AC+BD, we will ASSUME that BD is Negligible Since A and C are Significant.
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14. II.2 Four Factors in Eight Runs: Exercises Excess Length Solution - Discussion and Interpretation
Ideally, Excess Length should be 0.
Setting A Lo and C Hi Reduces the Magnitude of Excess Length with Excess Length at about -.04.
For A = - and C = +, EMR = (-1)(.107)/2 + (+1)(-.07)/2 +(-1)(+1)(.045)/2 = = -.037
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