Lab 2 Blocking - for PLAR

Lab 2: Design of Experiments 2k Factorial Design The objective of this lab is to learn how to design and analyze 2 k-1 fractional factorial experiments using Minitab. The student will use their design results to determine optimal settings, significant factors, and consider future design possibilities. At the end of this lab, you should know how to: 1. Discriminate between types of fractional designs. 2. Select factors and responses; determine levels; select model terms; decide on design resolution and control aliasing. 3. Design and create an experimental worksheet for data collection. 4. Predict future experimental results. 5. Interpret output from the analysis of the experimental data 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 2.1 & 2.2) 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

Activity 2.1: Four factor full design Mark s A materials engineer at a plastic manufacturing company wants to increase the tensile strength of a plastic product. The engineer identifies several factors to evaluate as possible contributors to tensile strength, including processing temperature, additive, agitation rate, and processing time. A 2-level full factorial design unreplicated (which means the design has one replicate in Minitab) is the initial experiment. You will also be exploring blocking and centre points. To make analysis easier, you will be analysing with coded levels (+1, -1) only. 1) Full-factorial, no block . a) Create the design worksheet in Minitab (4 factors with 1 replicate) . Carefully fill out the command windows. You will have a design worksheet with 16 runs. b) Enter the response data into the worksheet in standard order from the table. c) Analyze this factorial experiment and include all terms in the model. For Graphs, just create the Pareto chart of effects. d) Analyze again and include only terms up to order 2 . For Graphs, just create the Pareto chart of effects. Include your MiniTab here :  For initial Analysis o Coded Coefficients Table o Model Summary o Pareto Chart  For Reduced Design o Coded Coefficients Table o Model Summary o Pareto Chart /7 2) Compare the Pareto Charts of effects. Explain why, based evidence in these charts, we can drop all terms above two-factor interactions. What benefit in experimentation does this provide? /3 3) Full-factorial, block on replicate The engineer would like to use two processing ovens. To do so, she has obtained the budget to run all factorial combinations twice resulting in a total of 32 runs. The oven is not a factor in the experiment but it may cause possible nuisance variation that can be reduced by blocking. Each replicate of the design will be run as one block a) Again, create the factorial design worksheet in Minitab this time using 4 factors and 2 replicates . Carefully fill out the command windows including: /4 Temp Additive Rate Time Tensile Strength -1 -1 -1 -1 59.5 1 -1 -1 -1 58.5 -1 1 -1 -1 57.4 1 1 -1 -1 51.9 -1 -1 1 -1 56.5 1 -1 1 -1 61.3 -1 1 1 -1 58.1 1 1 1 -1 66.2 -1 -1 -1 1 53.2 1 -1 -1 1 59.5 -1 1 -1 1 57.5 1 1 -1 1 66.8 -1 -1 1 1 56.4 1 -1 1 1 68.5 -1 1 1 1 63.9 1 1 1 1 70.8

b) Enter the response data into the worksheet in standard order from the table below. “Blocks” on your worksheet will be the Oven : Analyze this factorial experiment and include only terms up to order 2 . For Graphs, just create the Half Normal Plot of effects. Include your MiniTab here :  Coded Coefficients Table  Model Summary  Half Normal Plot 6) Discuss Oven as a blocking variable. Was it necessary to block based on this output? Why or why not? Provide evidence from the output. Discuss the method for blocking…issues? 7) Centre points in a full-factorial. The engineer would like to use centre points to explore potential non- linearity in the factors. a) Create a new design worksheet in Minitab with 4 factors , 1 replicate, 1 block and 3 centre points. You will have a design worksheet with 19 runs with three centre points. b) Enter the response data into the worksheet in standard order from the table: c) Analyze this factorial experiment and include only terms up to order 2 . For Graphs, just create the Pareto Plot of effects. Include your MiniTab here :  Coded Coefficients Table  Model Summary  Pareto Chart 8) What evidence do we have/do not have for curvature? What benefit did adding centre points to Oven Temp Additive Rate Time Tensile Strength 1 1 -1 -1 -1 58.5 1 -1 1 -1 -1 57.4 1 -1 -1 1 -1 56.5 1 1 1 1 -1 66.2 1 -1 -1 -1 1 53.2 1 1 1 -1 1 66.8 1 1 -1 1 1 68.5 1 -1 1 1 1 63.9 2 -1 -1 -1 -1 59.5 2 1 1 -1 -1 51.9 2 1 -1 1 -1 61.3 2 -1 1 1 -1 58.1 2 1 -1 -1 1 59.5 2 -1 1 -1 1 57.5 2 -1 -1 1 1 56.4 2 1 1 1 1 70.8 Temp Additive Rate Time Tensile Strength -1 -1 -1 -1 59.5 1 -1 -1 -1 58.5 -1 1 -1 -1 57.4 1 1 -1 -1 51.9 -1 -1 1 -1 56.5 1 -1 1 -1 61.3 -1 1 1 -1 58.1 1 1 1 -1 66.2 -1 -1 -1 1 53.2 1 -1 -1 1 59.5 -1 1 -1 1 57.5 1 1 -1 1 66.8 -1 -1 1 1 56.4 1 -1 1 1 68.5 -1 1 1 1 63.9 1 1 1 1 70.8 0 0 0 0 62.3 0 0 0 0 65.4 0 0 0 0 60.2

this experiment provide? Activity 2.2: Four factor fractional design The effect of four factors are being considered on cracks in components used for jet turbine engines. The four factors are (A) pouring temp, (B) titanium content, (C) heat method (categorical), and (D) amount of grain refiner. The length of cracks produced is the response being measured. Goal: minimize length 9) Full Factorial: In Minitab, design a 2 4 full factorial (16 combinations) for this experiment with 1 replicate (16 runs).  Use the data given to analyse the experiment and determine the best model  Initially (I.), use all terms in the model (up through order 4).  Reduce (II.) the model as needed, by removing higher order terms (*remember the model hierarchy!)  Remember to sort by StdOrder before copying the data to MiniTab Include your MiniTab here : I. For initial analysis : a. Table of coded coefficients b. Model Summary c. Half normal plot of the effects II. For reduced model: d. Table of coded coefficients e. Model Summary f. Half normal plot of the effects /6 10) Compare the results between the full factorial and the ½ fractional factorial. Which factors are significant? What differences do you see in the coefficients? Do you come to the same conclusion(s) with both designs? /3 11) What would be the benefit of the fractional design? What would be the “risk” of running the fractional design? /2 12) Fractional Factorial: Now consider that only a one-half fraction of this 2 4 design (2 4-1 ) could be run (8 combinations). a) Create the 2 4-1 in Minitab using the generator D=ABC (this is the default…no need to do anything). Reference Step (1) of the Activity above to complete the design. The design is un-replicated (replicates = 1) and there is no blocking (blocks = 1). StdOrder Effect Pour temp(°C) Titanium content(%) Heat method Grain refiner(%) Length of crack 1 (1) 1000 3 Convection 5 7.0 2 a 1500 3 Convection 5 15.0 3 b 1000 4 Convection 5 11.0 4 ab 1500 4 Convection 5 17.0 5 c 1000 3 Fin 5 10.0 6 ac 1500 3 Fin 5 4.0 7 bc 1000 4 Fin 5 9.0 8 abc 1500 4 Fin 5 13.0 9 d 1000 3 Convection 10 8.5 10 ad 1500 3 Convection 10 17.0 11 bd 1000 4 Convection 10 14.0 12 abd 1500 4 Convection 10 19.0 13 cd 1000 3 Fin 10 12.0 14 acd 1500 3 Fin 10 6.0 15 bcd 1000 4 Fin 10 11.0 16 abcd 1500 4 Fin 10 16.0

3) Play around with the other design options; specifically: a) What does it mean “specify generators”? How would you use this option and for what? b) For what would you use the “General full factorial design”? Give examples. /2 /5