# Design of Experiments - 230414 Flashcards

What is design of Experiments?

Influence of multiple inputs (factors) in outputs (responses), experiment with all the factors at the same time.

Goal: More results, less experiments.

Agriculture: what factors are important to get an outcome. Medicine, Pharmaceutical companies: which of the factors influence the other ones?

Factors: temp, humidity. Response: thickness of coating.

Non optimal examples

Trial and error, not very good method:

* Temperature, time -> Yield.

* Adjust one of them -> Yield. Adjust another one -> Yield.

OFAT (One Factor at a Time):

* More efficient, but could still fail. Not exploring the whole behavior of the system in the design space.

Full factorial DOE

Full factorial DOE: Test the extremal points (+1 max and -1 min values) and its combinations (2^k).

Discover trends, not necessarily the optimal solution, less tests.

Do it twice to find if the order of the experiments does not generate any unexpected interaction and evaluate statistical scattering.

Why DOE?

Shorter testing, cost effective, statistical tolerancing.

General process

Expert knowledge (or random numbers and evaluate after that), select factors and response, design space, choose DOE design,

Run experiments, Find optimal settings, Test runs with optimal parameter, Modify process

Two general conditions

- Measurability: pressure, temperature, material types, fyber content.
- Adjustability:

Statistics’ uses in DOE

Factors: construction of design spaces.

Responses: Real effects vs. Random results, prediction of process results (approximation function)

Axioms of Probability

- Each probability goes from 0 to 1.
- Safe event: 1
- Probability of two events that are mutually exclusive: 0

How does the density function relates to the cumulability frequency?

- Failure probability is the integral of the density function.

Number of fringes

square root of the number of elements

Why is the Weibull distribution so used?

Same distribution, variation in Weibull parameters result in different shapes (exponential and normal)

t test

Hypothesis tests. Only for normally distributed data.

Null hypothesis: mean values are identical. Otherwise: there is an actual effect on the factor.