A218 Lesson 6 mindmap by

Design of Experiment (DOE)

2022-11-23 11:32:15 UTC

Comparison between OFAT and Factorial experiment

jirehpuibyl — 2022-11-23 13:13:30 UTC

One-factor-at-a-time (OFAT)

jirehpuibyl — 2022-11-23 13:14:35 UTC

• Purpose: To evaluate the effect of only one factor on the outcome while keeping all other factors constant.

• Unable to estimate the interaction between factors
• Unable to predict the optimization well.

Factorial Experiment

jirehpuibyl — 2022-11-23 13:20:58 UTC

Purpose: Experiment which consists of two or more of the factors with different levels to be investigated simultaneously.
• Able to estimate interaction between factors systematically
• Improved prediction of the response, resulting in a more efficient process optimization.

jirehpuibyl — 2022-11-23 13:22:59 UTC

Hence, Factorial experiment is mroe beneficial than OFAT

What is DOE

21014357_2 — 2022-11-23 13:37:56 UTC

It is a method that is used to study and determine the relationship between different input factors and help us see which variables can improve the output

Factorial Regression

jirehpuibyl — 2022-11-23 13:42:50 UTC

Interactive effects
- In this example, there are two coded coefficients that have a P-value that is less than the confidence level of 95%, Egg, and Egg*Flour.
- However, only Egg*Flour has an interactive effect as it has at least 2 different factors involved.
-Interactive effects can be applied when there are 3 different factors as well.

When P-Value < 0.05(95% confidence level), there is an interactive effect
When P-value > 0.05(i5% confidence level), there is no interactive effect

Having an interactive effect means that...
Egg: When P < 0.05, Using a different egg has a significant effect. Hence the effect of varying is significant.
Egg*Flour: When P < 0.005, one of the factors (Egg or Flour) depends on one another. Egg*Flour is significant to the response as there is an interactive effect.

Normal Probability Plot

jirehpuibyl — 2022-11-23 14:15:39 UTC

On the normal probability plot, there are some values which lies far from the straight line which represents the average. And the interactive effect between egg and flour is far from the line meaning that it is significant.

Pareto Chart

jirehpuibyl — 2022-11-23 14:26:28 UTC

On the Pareto chart, it can be seen that egg and egg*flour is passed 2.145 the refrence number, showing that egg and egg*flour is significant values that will affect the end result.

Interaction Plot

21014357_2 — 2022-11-23 14:42:10 UTC

Sugar*egg has weak interaction as they have low angle and is nearly parallel so there is weak interactive effect.
Sugar*flour has some interaction as they have angle but doesn't cross each other so there is some weak interactive effect.
Egg*Flour has strong interaction as they both have high angle and cross each other so there is a stronger interactive effect.

Main effect plot

21014357_2 — 2022-11-23 14:45:10 UTC

Egg has the steepest angle so it affects the taste the most.
Flour and sugar has low steepness so it does not affect the taste.

Cube Plot

21021276_2 — 2022-11-24 12:01:48 UTC

With the Cube plot we can derive the average score of the response based on the different combination of factors represented by the different values. From hear we can see that the combination of White Sugar, Fine Flour and Chicken Egg has the highest average score/response.

With the help of This cube, if we are given the Average Score we are able to derive the combination of different factors in order to arrive at that score if the different factors have numerical value

Equation

21021276_2 — 2022-11-24 12:16:44 UTC

With the Help of Regression Equation, if the factors have numerical value and we are provided the numerical values of the factors, we are able to substitute the numerical values of the factors into the equation to derive the resultant score.

Methods used for DOE

2022-11-24 13:54:42 UTC

p-test (testing for significance in data factor, interaction, variance)

T and F-test are present but we do not use

Anova (Analysis of Variance) - test for variance in values across data blocks

What DOE show

210123271_2 — 2022-11-24 14:03:57 UTC

The variance between data blocks

Importance of data factors (whether they cause significant changes in data)

Mean of value to factor values

Interaction between data factors

Predictions of data