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## Chapter 28

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**Chapter 28**Design of Experiments (DOE)**Objectives**• Define basic design of experiments (DOE) terminology. • Apply DOE principles. • Plan, organize, and evaluate experiments.**Terminology**• Design of experiments (DOE) is a statistical approach to designing and conducting experiments in an efficient and economical manner. • The objective of the experiment is to generate knowledge about a product or process and establish the mathematical relationship y = f(x), where x is the independent variable and y is the dependent variable.**Definitions**• An effect is the relationship between a factor and a response variable. • The response variable is the output variable that shows the observed results or values of an experimental treatment. • A factor is an independent variable (input variable) that may affect the response.**Design Principles**• Concepts underlying experimental design: • 1. Power and sample size: Power (ability to detect small differences) increases as the sample size increases. • 2. Replication: increases the precision of the estimates of the effects in an experiment. Entire experiment is repeated n times in a row. • 3. Repetition: Each run is repeated n times in a row. Allows to determine the variability in the measurement system. • 4. Confounding: or aliasing occurs when factors or interactions are not distinguishable from one another. • 5. Order: Sequence in which the runs of the experiment are conducted.**Design Principles**• 6. Randomization: each unit has an equal chance of being assigned a particular treatment. • 7. Blocking: collection of experimental units more homogenous than the full set. • 8. Main effect: impact of a single factor on the mean of the response variable. • 9. Interaction effect: when the influence of one factor on the response variable depends on one or more other factors. • 10. Balanced design: All treatment combinations have the same number of observations. • 12. Resolution: numbered with roman numerals – number of levels in a design. See example on page 307.**Planning Experiments**• The first consideration is, “What question are we seeking to answer?” • Example: Find the inspection procedure that provides optimum precision. • The objective must be related to the enterprise’s goals and objectives. • It must also be measurable. • So the primary objective of an experimental design is to identify what independent variables explain most of the variation in a response variable and to determine what levels of the independent variables minimizes or maximizes the response variable.**Selecting Factors and Levels**• People with the most experience and knowledge about the product or process should be consulted to determine what factors and what levels of each factor are important to achieve the objective. • The next step is to choose the appropriate design. • Typically 20 to 40% of the available budget is allocated to the first experiment – more modest screening design. • Statistical analysis of the data. • Conclusions and recommendations – in terms management and operations people can understand.**Summary**• Design of experiments (DOE) is a statistical approach to designing and conducting experiments in an efficient and economical manner. • Concepts underlying experimental design: 1. Power and sample size, 2. Replication, 3. Repetition, 4. Confounding, 5. Order, 6. Randomization, 7. Blocking, 8. Main effect, 9. Interaction effect, 10. Balanced design, 12. Resolution. • People with the most experience and knowledge about the product or process should be consulted to determine what factors and what levels of each factor are important to achieve the objective. • Conclusions and recommendations – in terms management and operations people can understand.**Home Work**• 1. What is the objective of the experiment? • 2. What is a response variable? • 3. What is the relationship between power and sample size? • 4. How do you determine what factors and what levels of each factor are important?