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by: Kaya Schultz

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# Engr Statistics IME 2610

Kaya Schultz
WMU
GPA 3.69

Steven Butt

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COURSE
PROF.
Steven Butt
TYPE
Class Notes
PAGES
4
WORDS
KARMA
25 ?

## Popular in Industrial & Manufacturing Engineering

This 4 page Class Notes was uploaded by Kaya Schultz on Wednesday September 30, 2015. The Class Notes belongs to IME 2610 at Western Michigan University taught by Steven Butt in Fall. Since its upload, it has received 108 views. For similar materials see /class/216909/ime-2610-western-michigan-university in Industrial & Manufacturing Engineering at Western Michigan University.

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Date Created: 09/30/15
Chapter 11 Factorial Design Interaction Between Factors When a change in one factor produces a different change in the response variable at two levels of another factor there is an interaction between the two factors It is possible to test for the significance of an interaction only if more than one observation is taken for each experimental condition Constructing the ANOVA for TwoF actor Factorial Experiment Terms SSA Sum of Squares for Factor A SSB Sum of Squares for Factor B SSAB Sum of Squares for Interaction of A and B SSE Sum of Squares for Error variability within SST Total Sum of Squares SST SSA SSB SSAB SSE r c n 2 SST z z ng X i1j1k1 SSA uni 4 z SSB mi X1 z i il SSE Z i1j x I V ka Xi r c n 1k1 Chapter 1 1 1 Fixed Effects Analysis of Variance for Factorial Design ZFactor Example 1 Two Factor An experiment is conducted to study the in uence of operating temperature three levels and three types of faceplate glass in the light output of an oscilloscope tube Randomization There are 9 possible combinations of the factor levels If there are 3 replicates to be run at each combination then there are 27 observations to be collected The order in which the 27 observations are taken must be completely randomized The following data are collected Temperature Glass T 100 Chapter 1 1 2 General Linear Model Factor Levels Values Temperat 3 100 125 150 Glass 3 1 2 3 Analysis of Variance for Output source DE Seq 55 Ad 55 Ad Ms E Temperat 2 1970335 1970335 985167 269526 0000 Glass 2 150865 150865 75432 20637 0000 Temperameiass 4 290552 290552 72638 19873 0000 Error 18 6579 6579 366 Total 26 2418330 Interpretations When an interaction is significant one should be very cautious in interpreting the corresponding main effects A signi cant interaction means that the effect of one factor on another factor at a particular level is different at other levels If the main effects of two factors do not have a signi cant interaction then the two factors39 main effects can be treated separately in the interpretation phase Chapter 1 i The Tukey s Test again wnrks here MSE For Factor A Critical range Ta q on With r degrees of eedom numerator and rcn 1 degrees of freedom denominator MSE For Factor B Critical range Ta q 771 With c degrees of eedom numerator and rcn 1 degrees of freedom denominator MSE For Factor AB interaction Critical range Ta q 71 with re degrees of eedom numerator and rcn 1 degrees of freedom denominator MINITAB does the work for you Chapter 1 i ueew ueew 1200 1050 10010 O 750 500 Interaction Plot 25 Temperat Interact39 n Plot 150 Main Effects Temnem Chapter 1 1 Tampa Tukey Slmultaneous Tests Response Varlable Output All Palrwlse Comparlsons among Levels of Glass Glass 1 subtracted from Level mfference s of Glass of Means leference T 2 4403 9013 4536 3 41771 9013 41965 Glass 2 subtracted from Level mfference s of Glass of Means leference THValue 3 41200 9013 41429 Tukey Slmultaneous Tests Response Varlable Output Adjusted pHValue 00001 00000 Adjusted pHValue 00000 All Palrwlse Comparlsons among Levels of Temperat Temperat 100 subtracted from Level leference 50 of Tempe rat of Means lefe rence THValue 125 4927 9013 5466 150 6209 9013 6970 Temperat 125 subtracted from Level leference 50 of Temperat of Means leference THValue 150 1362 9013 1511 Tukey Slmultaneous Tests Response Varlable Output Adjusted pHValue 00000 00000 Adjusted pHValue 00000 All Palrwlse Comparlsons among Levels of GlassoTemperat Glass Tempe rat 1 100 subtracted from Level leference 50 of GlassoTemperat of Means mfference Ta 125 51467 1561 32970 0 F H m m H m m H m m m m m m H HHmmmmmm Chapter 1 1 Adjusted Glass 1 Tenperat 125 Level Glass Tempera 150 1 2 2 2 150 3 3 3 Glass 1 Tenperat 150 evel lass Tempera 100 Glass 2 Tenperat 100 evel lass Tempera 125 Glass 2 Tenperat 125 Level Glass Tempera 2 150 3 3 3 Glass 2 Tenperat 150 Level Glass Tempera 3 100 3 125 3 150 Glass 3 Tenperat 100 Level Glass Tempera 3 125 3 150 Chapter 1 1 subtracted from lefe rence subtracted from lefe rence subtracted from lefe rence subtracted from Difference of Means 2780 44617 197 41483 subtracted from lefe rence subtracted from lefe rence 513 of Difference 1561 513 of Difference 15 61 513 of Difference 1561 513 of Difference 15 61 15 61 TcValue 453 36 TcValue 30 877 48 686 1303 32137 21375 TcValue a 473 a TaValue 3083 2007 Adjusted Adjusted Pcvalue Adjusted Pcvalue Adjusted Adjusted Pcvalue Adjusted Pcvalue Glass Tenperat 125 subtracted from Level leference SE of Adjusted Glass Tempera of Means Difference TcValue Pcvalue 3 150 41680 1561 41076 00000 Example 2 T W0 Factor An experiment was conducted to determine if either firing temperature or furnace position affects the baked density of a carbon anode The data are shown below Temperature C Position 800 825 850 570 1063 565 1 565 1080 510 583 1043 590 528 988 526 2 547 1026 538 521 1004 532 Suppose we assume that no interaction exists What is the statistical model SST SSA SSB SSE Analysis of variance for Density No Interaction source DE seq 55 Ad 55 Ad Ms E P 472671 106926 0000 Position 1 7160 7160 7160 1620 0001 Error 14 6189 6189 442 Total 17 958691 Chapter 1 1 8

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