1. II.2 Four Factors in Eight Runs Some Fiber Optics Examples and Exercises* Some 2 4-1 DOE’s Some 2 4-1 DOE’s Responses: Responses: –Shrinkage (S) –Excess Length (L) Factors: some are trade secrets and others include Factors: some are trade secrets and others include –Time –Temperature –Fiber Tension –Draw Ratio –Line Speed –Fiber Conditioning * Examples are based on some 2 4-1 DOE studies done at the Pirelli’s Lexington, SC plant

2. II.2 Four Factors in Eight Runs: Examples Shrinkage

3. II.2 Four Factors in Eight Runs: Examples Shrinkage - Discussion and Interpretation The 2 4-1 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) The 2 4-1 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 We Estimate That –Setting B Hi Increases Shrinkage.36 over Setting it Lo –Setting C Lo Increases the Shrinkage.39 over Setting it Hi

4. II.2 Four Factors in Eight Runs: Examples Shrinkage - Estimated Mean Response (EMR) For B = + and C = -, EMR =.55  + (+1)(.36)/2 + For B = + and C = -, EMR =.55  + (+1)(.36)/2 + (-1)(-.39)/2 =.55 +.375 =.925 (-1)(-.39)/2 =.55 +.375 =.925

5. II.2 Four Factors in Eight Runs: Examples Excess Length

6. II.2 Four Factors in Eight Runs: Examples Excess Length - Discussion and Interpretation The 2 4-1 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). The 2 4-1 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. Since B and C signaled but A did not, We Shall ASSUME that the BC interaction is Significant for Interpretation Purposes.

7. II.2 Four Factors in Eight Runs: Example Excess Length - Discussion and Interpretation Noise Factors/Control Factors 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. 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. Noise Factors/Control Factors 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. 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.

8. II.2 Four Factors in Eight Runs: Examples Excess Length - Estimated Mean Response (EMR) For B = -, C = +, D=+: For B = -, C = +, D=+: EMR = -.057  + (-1)(-.18)/2 + (+1)(-.09)/2 + (+1)(.07)/2 +(-1)(.12)/2 = -.057  +.02 = -.037 EMR = -.057  + (-1)(-.18)/2 + (+1)(-.09)/2 + (+1)(.07)/2 +(-1)(.12)/2 = -.057  +.02 = -.037

9. II.2 Four Factors in Eight Runs: U-Do-It Exercise Completed Signs Tables and Normal Probability Plots are Provided for Two Other 2 4-1 Experiments (D=ABC or ABCD=I) Involving Shrinkage and Excess Length Completed Signs Tables and Normal Probability Plots are Provided for Two Other 2 4-1 Experiments (D=ABC or ABCD=I) Involving Shrinkage and Excess Length Analyze These Experiments 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 Calculate the EMR for Shrinkage and Excess Length when A and B are both Lo and C and D are both Hi

10. II.2 Four Factors in Eight Runs: U-Do-It Exercise Shrinkage

11. II.2 Four Factors in Eight Runs: U-Do-It Exercise Excess Length

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. 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 We Estimate That –Setting C Hi Increases the Shrinkage.206 over Setting it Lo When C = +, EMR =.692  + (+1)(.206)/2 =.692+.103 =.795 When C = +, EMR =.692  + (+1)(.206)/2 =.692+.103 =.795

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. 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.

14. II.2 Four Factors in Eight Runs: Exercises Excess Length Solution - Discussion and Interpretation Ideally, Excess Length should be 0. 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 Ideally, Excess Length should be 0. 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