Math Problem Statement

A producer of ink for grid paper is concerned about the amount of delamination (measure of ink migration off grid lines). This company uses a 1-10 scale to rate delamination (1-very poor; 10-no delamination). A rating value of 9 or higher is considered acceptable. See example below of different levels of ink delamination for grid paper (Attached file has additional pictorials for each rating). (Note: Treat the 1-10 ordinal rating as a continuous variable for analysis.) To better understand the causes of delamination, they run a fractional factorial experiment with 5 factors (listed below). The experiment is a (25-1) fractional design with 3 replications (Total of 16 combinations with 48 samples). The data is provided below: StdOrder RunOrder Replication A-Belt Speed B-Pot Life C-Oven Temp D-Oven Time E-Mesh Delamination 10 1 1 High 2 140 3 Wide 6 31 2 2 Low 4 160 3 Narrow 7 7 3 1 Low 4 160 2 Wide 9 23 4 2 Low 4 160 2 Wide 9 17 5 2 Low 2 140 2 Wide 10 19 6 2 Low 4 140 2 Narrow 10 9 7 1 Low 2 140 3 Narrow 8 33 8 3 Low 2 140 2 Wide 10 39 9 3 Low 4 160 2 Wide 6 29 10 2 Low 2 160 3 Wide 1 43 11 3 Low 4 140 3 Wide 9 35 12 3 Low 4 140 2 Narrow 7 15 13 1 Low 4 160 3 Narrow 7 12 14 1 High 4 140 3 Narrow 5 27 15 2 Low 4 140 3 Wide 7 13 16 1 Low 2 160 3 Wide 5 28 17 2 High 4 140 3 Narrow 9 41 18 3 Low 2 140 3 Narrow 10 22 19 2 High 2 160 2 Wide 9 24 20 2 High 4 160 2 Narrow 8 20 21 2 High 4 140 2 Wide 7 4 22 1 High 4 140 2 Wide 8 18 23 2 High 2 140 2 Narrow 9 6 24 1 High 2 160 2 Wide 10 37 25 3 Low 2 160 2 Narrow 9 14 26 1 High 2 160 3 Narrow 6 1 27 1 Low 2 140 2 Wide 9 42 28 3 High 2 140 3 Wide 2 21 29 2 Low 2 160 2 Narrow 10 38 30 3 High 2 160 2 Wide 7 45 31 3 Low 2 160 3 Wide 1 47 32 3 Low 4 160 3 Narrow 3 8 33 1 High 4 160 2 Narrow 4 36 34 3 High 4 140 2 Wide 8 16 35 1 High 4 160 3 Wide 2 5 36 1 Low 2 160 2 Narrow 6 34 37 3 High 2 140 2 Narrow 6 48 38 3 High 4 160 3 Wide 5 30 39 2 High 2 160 3 Narrow 1 46 40 3 High 2 160 3 Narrow 6 2 41 1 High 2 140 2 Narrow 8 40 42 3 High 4 160 2 Narrow 6 44 43 3 High 4 140 3 Narrow 8 26 44 2 High 2 140 3 Wide 4 32 45 2 High 4 160 3 Wide 2 25 46 2 Low 2 140 3 Narrow 4 3 47 1 Low 4 140 2 Narrow 5 11 48 1 Low 4 140 3 Wide 5 Factor Code= -1 Code=1 A-Belt Speed Low High B-Pot Life (hrs) 2 4 C-Oven Temp (°F) 140 160 D-Oven Time (hrs) 2 3 E-Mesh Narrow Wide Using the response optimizer, which of the following settings would yield the best performance (at least Y > 9.5)? Note: For consistency of results, Note: Include all main effects and any significant two-way interactions in response optimizer. a. A=High; B=2; C=140; D=2; E=Wide b. A=Low; B=3; C=150; D=2.5; E=Narrow c. A=High; B=2; C=140; D=2; E=Narrow d. A=Low; B=2; C=140; D=2; E=Wide

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Regression Analysis
Fractional Factorial Design

Formulas

Main Effects Model
Two-Way Interaction Model

Theorems

ANOVA (Analysis of Variance)
Response Optimization

Suitable Grade Level

Undergraduate/Graduate