Lab 3 General Factorials - for PLAR

Lab 6: General Factorial Design and RSM The objective of this lab is to explore the last topic of General Factorial modeling. There will also be some time dedicated to reviewing previous topics from the course, as well as furthering analysis exploration using factorial and contour plots. At the end of this lab, you should know how to: 1. Discriminate between types of designs 2. Design general factorial and RSM models. 3. Analyze general factorial and RSM models. 4. Analyze data from experimental designs to determine optimal settings, significant factors and future design possibilities. 5. Select factors and responses; determine levels; select model terms; decide on design resolution and control aliasing. 6. Discriminate between types of designs. 7. Utilize Factorial and Contour plots to further analyze non-linear responses LAYOUT: Create the needed graphs and data outputs in Minitab, then place the appropriate analysis and questions with the Minitab content . Explain what you can learn about this data to a parent/boss/etc. Answer each question with a full sentence and show only the Minitab output needed to answer each question. Marks will be deducted for formatting, layout and style. You may use this document as a template. Remove the question text but leave the numbers. Marks are noted beside each question. DUE: Your data (project file), and completed report (Activity 3.1 & 3.2) This Final Report is 100% your original individual work . Use another student’s work, or content from the internet or other sources, in your report will receive a 0 Minitab/General Factorials and RSM Page 1

Lab Activity 3.1: General Factorial and RSM Designs 1) Why is it important to follow a randomized run order in an experiment rather than a design matrix standard order? /2 2) In an experiment you want to carefully analyze main, 2-way, and 3-way interaction, and are certain higher order interactions are small or non-existent. What minimum design resolution will ensure your main, 2-way, and 3-way interactions are not aliased together or with each other? Show your work /3 3) If a fractional factorial model has it’s 3-way and 4-way interactions aliased with each other, what is the resolution of the model? Show you work /2 Create and Analyze a General Factorial Designs Researchers at a motor vehicle bureau compared driving correction times (sec) between beginner and advanced drivers on three types of roads, with 4 different tire brands. Eight experienced and eight non-experienced drivers were included. Each driver drove on all three road types, once for each of the 4 brands of tire based on a randomized list of combinations. 4) Choose the appropriate design and number of factors; name factors; and define factor settings : a. Choose Stat  DOE  Factorial  Create Factorial Design b. Under Type of Design chose General full factorial. Number of factors, choose 3 c. Click “Designs…”.  Type in each factor name, type, and the number of levels for each: 2 for Experience and 3 for Road Type , and 4 for Tire .  Enter 1 for number of replicates.  Click OK. d. Click : “Factors…” Enter in the factor levels  Experience : Beginner, Advanced  Road Type : Paved, Gravel, Dirt  Tire : A, B, C, D e. Click: OK f. Keep (and include in this report/template):  Design Summary You now have a design worksheet in Minitab (with your own randomized run order!). /3 5) Collect the response data, and enter it into worksheet: /3 Minitab/General Factorials and RSM Page 2 Road Type Tire Paved Gravel Dirt Experience Beginner A 28 12 32 B 18 15 27 C 21 20 24 D 10 13 14 Advanced A 9 17 16 B 4 21 18 C 8 33 11 D 1 16 17

settings : 14) Choose Stat  DOE  Response Surface  Create Response Surface Design a. Under Type of Design chose Central composite. Number of factors, choose 2 b. Click “Designs…”. Choose Full with 13 runs {first option}. Leave other options as they are. Click OK c. Click : “Factors…” • Select Cube Points • Rename the factors Temperature and Pressure • Leave the levels as -1, 1. (In general these are better set to the actual values though) • Click OK. d. Click: OK. Keep: (and include in this report/template): • Design Summary • Note: α=1.41421 is because of -1, and 1 levels and some basic trigonometry (see notes for diagram) • Point Types - You should have 4 factorial points (cube), 5 centre points, and 4 axial (13 runs) You now have a design worksheet in Minitab (with your own randomized run order!). Note that the centre points and axial runs are randomized with the factorial points. 15) Collect the response data, enter into worksheet: a. Name the last column, C7, to “Filtration time(sec)” b. Sort the worksheet on StdOrder c. Enter the responses into the Filtration Time (C7) column. Be careful to match the correct run combinations!! 16) Choose Stat > DOE > Response Surface>Analyze a. Response Surface Design b. In Responses, select Filtration Time (C7) c. Click “Terms…”. Choose Full quadratic. - Click OK. d. Click “Graphs…”. Under Residuals Plots, choose Four in one. - Click OK e. Click OK. Keep: (and include in this report/template): • Coded Coefficients • Model Summary • Residual Plots /5 17) Do the residual plots so any major issues with our model? /1 18) Which factors should be considered significant? /2 19) How much of the variability in the filtration times can be explained by Temperature, pressure and their interactions? /1 20) Based on the main factor coefficients, what levels (-1, or 1) of Temperature and Pressure would yield the lowest Filtration time? /1 Minitab/General Factorials and RSM Page 4 Temperature (°C) Pressure (Atm) Filtration Time(sec) -1 -1 53 -1 1 45 1 -1 31 1 1 47 -1.414 0 50 1.414 0 54 0 -1.414 47 0 1.414 51 0 0 42 0 0 38 0 0 45 0 0 43 0 0 39

21) Create Factorial Plots Keep: (and include in this report/template): • Main Effects Plot and the Interaction Plot /1 22) What can you see in the factorial plots about the relationship between the levels for each factor? /2 23) Create a Contour Plot Keep: (and include in this report/template): • Contour Plot /1 24) According to the contour plot our minimum filtration time is 40sec. Do only maximum settings get us this time? Explain what settings could still keep our filtration time below 45sec. /3 Minitab/General Factorials and RSM Page 5