1. DESIGN OF EXPERIMENTS by R. C. Baker
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2. Role of DOE in Process Improvement
DOE is a formal mathematical method for systematically planning and conducting scientific studies that change experimental variables together in order to determine their effect of a given response.
DOE makes controlled changes to input variables in order to gain maximum amounts of information on cause and effect relationships with a minimum sample size.

3. Role of DOE in Process Improvement
DOE is more efficient that a standard approach of changing “one variable at a time” in order to observe the variable’s impact on a given response.
DOE generates information on the effect various factors have on a response variable and in some cases may be able to determine optimal settings for those factors.

4. Role of DOE in Process Improvement
DOE encourages “brainstorming” activities associated with discussing key factors that may affect a given response and allows the experimenter to identify the “key” factors for future studies.
DOE is readily supported by numerous statistical software packages available on the market.

5. BASIC STEPS IN DOE Four elements associated with DOE:
1. The design of the experiment,
2. The collection of the data,
3. The statistical analysis of the data, and
4. The conclusions reached and recommendations made as a result of the experiment.

6. TERMINOLOGY
Replication – repetition of a basic experiment without changing any factor settings, allows the experimenter to estimate the experimental error (noise) in the system used to determine whether observed differences in the data are “real” or “just noise”, allows the experimenter to obtain more statistical power (ability to identify small effects)

7. TERMINOLOGY
.Randomization – a statistical tool used to minimize potential uncontrollable biases in the experiment by randomly assigning material, people, order that experimental trials are conducted, or any other factor not under the control of the experimenter. Results in “averaging out” the effects of the extraneous factors that may be present in order to minimize the risk of these factors affecting the experimental results.

8. TERMINOLOGY
Blocking – technique used to increase the precision of an experiment by breaking the experiment into homogeneous segments (blocks) in order to control any potential block to block variability (multiple lots of raw material, several shifts, several machines, several inspectors). Any effects on the experimental results as a result of the blocking factor will be identified and minimized.

9. TERMINOLOGY
Confounding - A concept that basically means that multiple effects are tied together into one parent effect and cannot be separated. For example,
1. Two people flipping two different coins would result in the effect of the person and the effect of the coin to be confounded
2. As experiments get large, higher order interactions (discussed later) are confounded with lower order interactions or main effect.

10. TERMINOLOGY
Factors – experimental factors or independent variables (continuous or discrete) an investigator manipulates to capture any changes in the output of the process. Other factors of concern are those that are uncontrollable and those which are controllable but held constant during the experimental runs.

11. TERMINOLOGY
Responses – dependent variable measured to describe the output of the process.
Treatment Combinations (run) – experimental trial where all factors are set at a specified level.

12. TERMINOLOGY
Fixed Effects Model - If the treatment levels are specifically chosen by the experimenter, then conclusions reached will only apply to those levels.
Random Effects Model – If the treatment levels are randomly chosen from a population of many possible treatment levels, then conclusions reached can be extended to all treatment levels in the population.

13. PLANNING A DOE
Everyone involved in the experiment should have a clear idea in advance of exactly what is to be studied, the objectives of the experiment, the questions one hopes to answer and the results anticipated

14. PLANNING A DOE
Select a response/dependent variable (variables) that will provide information about the problem under study and the proposed measurement method for this response variable, including an understanding of the measurement system variability

15. PLANNING A DOE
Select the independent variables/factors (quantitative or qualitative) to be investigated in the experiment, the number of levels for each factor, and the levels of each factor chosen either specifically (fixed effects model) or randomly (random effects model).

16. PLANNING A DOE
Choose an appropriate experimental design (relatively simple design and analysis methods are almost always best) that will allow your experimental questions to be answered once the data is collected and analyzed, keeping in mind tradeoffs between statistical power and economic efficiency. At this point in time it is generally useful to simulate the study by generating and analyzing artificial data to insure that experimental questions can be answered as a result of conducting your experiment

17. PLANNING A DOE
Perform the experiment (collect data) paying particular attention such things as randomization and measurement system accuracy, while maintaining as uniform an experimental environment as possible. How the data are to be collected is a critical stage in DOE

18. PLANNING A DOE
Analyze the data using the appropriate statistical model insuring that attention is paid to checking the model accuracy by validating underlying assumptions associated with the model. Be liberal in the utilization of all tools, including graphical techniques, available in the statistical software package to insure that a maximum amount of information is generated

19. PLANNING A DOE
Based on the results of the analysis, draw conclusions/inferences about the results, interpret the physical meaning of these results, determine the practical significance of the findings, and make recommendations for a course of action including further experiments

20. FACTORIAL (2k) DESIGNS (k = 2): GRAPHICAL OUTPUT
Neither factor A nor Factor B have an effect on the response variable.

21. FACTORIAL (2k) DESIGNS (k = 2): GRAPHICAL OUTPUT
Factor A has an effect on the response variable, but Factor B does not.

22. FACTORIAL (2k) DESIGNS (k = 2): GRAPHICAL OUTPUT
Factor A and Factor B have an effect on the response variable.

23. FACTORIAL (2k) DESIGNS (k = 2): GRAPHICAL OUTPUT
Factor B has an effect on the response variable, but only if factor A is set at the “High” level. This is called interaction and it basically means that the effect one factor has on a response is dependent on the level you set other factors at. Interactions can be major problems in a DOE if you fail to account for the interaction when designing your experiment.

24. 2k DESIGNS (k > 2)
As the number of factors increase, the number of runs needed to complete a complete factorial experiment will increase dramatically. The following 2k design layout depict the number of runs needed for values of k from 2 to 5. For example, when k = 5, it will take 25 = 32 experimental runs for the complete factorial experiment.

25. 2k DESIGNS (k > 2)
Once the effect for all factors and interactions are determined, you are able to develop a prediction model to estimate the response for specific values of the factors. In general, we will do this with statistical software, but for these designs, you can do it by hand calculations if you wish.

26. 2k DESIGNS (k > 2)
For example, if there are no significant interactions present, you can estimate a response by the following formula. (for quantitative factors only)