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II.2 Four Factors in Eight Runs Some Fiber Optics Examples and Exercises*. Some 2 4-1 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

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Ii 2 four factors in eight runs some fiber optics examples and exercises
II.2 Four Factors in Eight RunsSome 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



Ii 2 four factors in eight runs examples shrinkage discussion and interpretation
II.2 Four Factors in Eight Runs: ExamplesShrinkage - 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


Ii 2 four factors in eight runs examples shrinkage estimated mean response emr
II.2 Four Factors in Eight Runs: ExamplesShrinkage - Estimated Mean Response (EMR)

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

  • (-1)(-.39)/2 =.55 +.375 = .925



Ii 2 four factors in eight runs examples excess length discussion and interpretation
II.2 Four Factors in Eight Runs: ExamplesExcess 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.


Ii 2 four factors in eight runs example excess length discussion and interpretation
II.2 Four Factors in Eight Runs: ExampleExcess 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.


Ii 2 four factors in eight runs examples excess length estimated mean response emr
II.2 Four Factors in Eight Runs: ExamplesExcess Length - Estimated Mean Response (EMR)

  • For B = - , C = +, D=+:

  • EMR = -.057+ (-1)(-.18)/2 + (+1)(-.09)/2 + (+1)(.07)/2 +(-1)(.12)/2 = -.057+ .02 = -.037


Ii 2 four factors in eight runs u do it exercise
II.2 Four Factors in Eight Runs: U-Do-It Exercise

  • 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




Ii 2 four factors in eight runs u do it exercise shrinkage solution discussion and interpretation
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 = .692+ (+1)(.206)/2 = .692+ .103 = .795


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.


Ii 2 four factors in eight runs exercises excess length solution discussion and interpretation
II.2 Four Factors in Eight Runs: ExercisesExcess 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 = .074+ (-1)(.107)/2 + (+1)(-.07)/2 +(-1)(.045)/2 = .074- .111 = -.037


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