II.2 Four Factors in Eight Runs Some Fiber Optics Examples and Exercises*

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II.2 Four Factors in Eight Runs Some Fiber Optics Examples and Exercises*

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II.2 Four Factors in Eight Runs Some Fiber Optics Examples and Exercises*

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- 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

- 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

- For B = + and C = -, EMR = .55+ (+1)(.36)/2 +
- (-1)(-.39)/2 =.55 +.375 = .925

- 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.

- 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.

- For B = - , C = +, D=+:
- EMR = -.057+ (-1)(-.18)/2 + (+1)(-.09)/2 + (+1)(.07)/2 +(-1)(.12)/2 = -.057+ .02 = -.037

- Completed Signs Tables and Normal Probability Plots are Provided for Two Other 24-1Experiments (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

- 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 = .692+ (+1)(.206)/2 = .692+ .103 = .795

- 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.

- 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 = .074+ (-1)(.107)/2 + (+1)(-.07)/2 +(-1)(.045)/2 = .074- .111 = -.037