DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS MODULE - 13 MODULE TITLE: Design of Experiments with Several Factors LEARNING OBJECTIVES: After finishing this module, you are expected to: 1. Design and conduct engineering experiments involving several factors using the factorial design approach 2. Know how to analyze and interpret main effects and interactions 3. Understand how the ANOVA is used to analyze the data from these experiments 4. Assess model adequacy with residual plots 5. Know how to use the two-level series of factorial designs TOPICS: 1. 2. 3. 4. 5. 6. Factorial Experiments Two-Factor Factorial Experiments 2k Factorial Design Blocking and Confounding in the 2k Design Fractional Replication of the 2k Design Response Surface Methods WARM UP: A. Give three things that you expect you will learn in this module. 1. ______________________________________________ 2. ______________________________________________ 3. ______________________________________________ B. Pre-Test: Answer the following: 1. Parts manufactured in an injection-molding process are showing excessive shrinkage, which is causing problems in assembly operations upstream from the injection-molding area. In an effort to reduce the shrinkage, a qualityimprovement team has decided to use a designed experiment to study the injection-molding process. The team investigates six factors—mold temperature (A), screw speed (B), holding time (C), cycle time (D), gate size (E), and holding pressure (F)—each at two levels, with the objective of learning how each factor affects shrinkage and obtaining preliminary information about how the factors interact. Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS OVERVIEW/INTRODUCTION: An experiment is just a test or series of tests. Experiments are performed in all engineering and scientific disciplines and are an important part of the way we learn about how systems and processes work. The validity of the conclusions that are drawn from an experiment depends to a large extent on how the experiment was conducted. Therefore, the design of the experiment plays a major role in the eventual solution of the problem that initially motivated the experiment. In this chapter we focus on experiments that include two or more factors that the experimenter thinks may be important. The factorial experimental design will be introduced as a powerful technique for this type of problem. Generally, in a factorial experimental design, experimental trials (or runs) are performed at all combinations of factor levels. For example, if a chemical engineer is interested in investigating the effects of reaction time and reaction temperature on the yield of a process, and if two levels of time (1 and 1.5 hours) and two levels of temperature (125 and 150F) are considered important, a factorial experiment would consist of making experimental runs at each of the four possible combinations of these levels of reaction time and reaction temperature. Most of the statistical concepts introduced in Chapter 13 for single-factor experiments can be extended to the factorial experiments of this chapter. The analysis of variance (ANOVA), in particular, will continue to be used as one of the primary tools for statistical data analysis. We will also introduce several graphical methods that are useful in analyzing the data from designed experiments. LESSON PROPER: Factorial Experiments When several factors are of interest in an experiment, a factorial experimental design should be used. As noted previously, in these experiments factors are varied together. Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS TWO-FACTOR FACTORIAL EXPERIMENTS Statistical Analysis of the Fixed-Effects Model Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Example 14-1: Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Model Adequacy Checking Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS 2k Factorial Design Single Replicate of the 2k Design Example 14-5: Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS BLOCKING AND CONFOUNDING IN THE 2k DESIGN Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Example 14-6: Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS FRACTIONAL REPLICATION OF THE 2k DESIGN One-Half Fraction of the 2k Design Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Example 14-7: Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS RESPONSE SURFACE METHODS AND DESIGNS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS Example S14-3: Engr. Belen B. Magistrado Instructor 1 (BSCE) DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS PERFORMANCE TASK: ✓ Analyze the principle of Design of experiments with several factors. TARGET SKILLS: ✓ Determine the factorial experiments. LEARNING ACTIVITIES ✓ Participate in discussion forum thru google meet or zoom meeting ✓ Read the entire content of Module ✓ Working through sample problems ✓ Collaborative online learning ASSESSMENT TASK ✓ Recitation ✓ Pre-test / Quiz References: ❖ http://meteo.edu.vn/GiaoTrinhXS/e-book/PQ220-6234F.Ch-14.pdf ❖ Ronald-E.-Walpole-Raymond-H.-Myers-Sharon-L.-Myers-Keying-E.-Ye-ProbabilityStatistics-for-Engineers-Scientists-Pearson-2016 Engr. Belen B. Magistrado Instructor 1 (BSCE)
