Design of Experiments DOE 1 2 3 4

Design of Experiments (DOE) 1. 2. 3. 4. 5. 6. 7. What is DOE? Purpose of DOE? Choose the design (Eg. Box-Behnhen) Principle of selected design How it works? How do you calculate? Conclusion

Design of Experiments Factorial design Regression analysis Mathematical model Statistical model Response surface methodology Central composite Box-Behnhen design Plackett Burmann model and etc.

Design of Experiments (DOE) • 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.

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.

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.

• 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

EXAMPLE: CONCLUSIONS • In statistical language, one would conclude that whether is not statistically significant at a 5% level of significance since the p-value is greater than 5% (0. 05).

2 k 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 2 k 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.

Interactions for 2 k Designs (k = 3)

2 k 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)