A218 Lesson 6 (Team Deliverable) by CHOO YEN YING

DESIGN OF EXPERIMENT

22038685 — 2023-05-29 07:39:16 UTC

Full factorial Design Experiment

22035870_2 — 2023-05-29 07:40:47 UTC

Types of Experimental Process

22038685 — 2023-05-29 07:41:42 UTC

k-factor

22024339_2 — 2023-05-29 07:42:49 UTC

A 2^k full factorial design is an experimental design of k factors with each factor having 2 levels.
The design will have a total of 2^k runs.

k= number of factors

example

22024339_2 — 2023-05-29 07:44:17 UTC

2^3 = 8 runs

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

22038685 — 2023-05-29 07:44:29 UTC

Full factorial design results

22038685 — 2023-05-29 07:46:07 UTC

i.e. cube plots, factorial regression, analysis of variance table, normal plots, Pareto chart, residual plots, normal probability plot.

full factorial design

22035870_2 — 2023-05-29 07:46:34 UTC

TO BE USED WHEN WE WANT TO:
- Effectively calculate each factor's influence on the response.
- to calculate how one or more elements may combine to affect the outcome.
- By integrating center points in the design, check for curvature in the response.

A full factorial design is a design in which researchers measure responses at all combinations of the factor levels. which Minitab offers us two types of full factorial designs:

2-level full factorial designs that contain only 2-level factors.
general full factorial designs that contain factors with more than two levels.

The number of runs necessary for a 2-level full factorial design is 2^k where k is the number of factors. As the number of factors in a 2-level factorial design increases, the number of runs necessary to do a full factorial design increases quickly.

For example, a 2-level full factorial design with 6 factors requires 64 runs; a design with 9 factors requires 512 runs. A half-fraction, fractional factorial design would require only half of those runs.

Cube plots

22038685 — 2023-05-29 07:47:19 UTC

E.g. Current at 11kA, 16 Cycles and Force at 4kN gives the highest strength of 508.

Yates Order

22024339_2 — 2023-05-29 07:47:26 UTC

its a systematic way to place the experimental factor level of total factorial effect in a standard order

yates

22024339_2 — 2023-05-29 07:55:00 UTC

1st factor: Group as a cluster
2nd factor: Writing out the variable in each level twice as shown
3rd factor: Writing out the variable in each level 4 times as shown.

Normal Plot of Standardized Effects

22038685 — 2023-05-29 07:56:31 UTC

Pareto Chart

22038685 — 2023-05-29 07:58:29 UTC

- Factors that cross the red dotted line = factors affect significantly
- Factors that did not cross the red dotted line = factors DOES NOT affect significantly

replication

22024339_2 — 2023-05-29 08:04:36 UTC

- all measurements are usually subjected to variation and uncertainty
- measurements of the same setting are often repeated, and the full set of experiment is replicated
- replication of experiment will help to identify the sources of variation and to better estimate teh true effects of the treatment

22024339_2 — 2023-05-29 08:05:39 UTC

replication

22024339_2 — 2023-05-29 08:08:01 UTC

-replication helps in verifying the results and gives better estimation o fthe experimental variability and the effects of the factors
- more replicates, the more precise will be the model

Factorial Regression Table

22018807_2 — 2023-05-29 11:36:43 UTC

p-value < alpha value -> factor affect significantly
-> there is interaction between the factors
p-value > alpha value -> factor DOES NOT affect significantly
-> there is NO interaction between the factors

Analysis of Variance

22018807_2 — 2023-05-29 11:38:47 UTC

Model Summary

22018807_2 — 2023-05-29 11:44:23 UTC

Regression Equation

22018807_2 — 2023-05-29 11:47:09 UTC

If the factors are numeric, it can be used to PREDICT the results using the equation.

Main Effects Plot

22018807_2 — 2023-05-29 11:54:35 UTC

STEEPER gradient -> MORE SIGNIFICANT the factor is on the response.

Interaction plot

22018807_2 — 2023-05-29 11:55:29 UTC

Fit and Diagnostics for Unusual Observations

22038685 — 2023-05-29 13:43:57 UTC

- Shows unusual observation that could be outliers.

E.g. Observation 24 from the data is UNUSUAL.

Residual Plots

22038685 — 2023-05-29 13:59:15 UTC

22038685 — 2023-05-29 14:05:04 UTC

22038685 — 2023-05-29 14:08:04 UTC

22038685 — 2023-05-29 14:13:20 UTC

22038685 — 2023-05-29 14:15:28 UTC

THERE ARE TWO TYPES OF FACTORIAL DESIGNS: FULL FACTORIAL DESIGN AND FRACTIONAL FACTORIAL DESIGN

22035870_2 — 2023-05-30 09:21:22 UTC

A factorial design is a type of designed experiment that lets us study the effects that several factors which can have on a response.

When conducting an experiment, varying the levels of all factors at the same time instead of one at a time lets you study the interactions between the factors.
such as determining the variable which would have the strongest influence on the response.