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.

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

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 Skim

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 = .55 + (+1)(.36)/2 + (-1)(-.39)/2 =.55 +.375 = .925

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

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.

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.

II.2 Four Factors in Eight Runs: Examples Excess Length - Estimated Mean Response (EMR) For B = - , C = +, D=+: EMR = -.057 + (-1)(-.18)/2 + (+1)(-.09)/2 + (+1)(.07)/2 +(-1)(+1)(.12)/2 = -.057 + .02 = -.037 Don’t overthink need to assign D as well. Do EMR in Minitab

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.

II.2 Four Factors in Eight Runs: U-Do-It Exercise Shrinkage Skim/skip

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

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 Skim/skip

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. Skim/skip

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