full factorial design3

8/21/2019 Full Factorial Design3

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Design of Experiments (DOE)

Planning phase

Designing phase

Conducting phase

Analyzing phase


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Planning phase

(a) Problem recognition and formulation-A clear and succinct statement of problem can create better understanding

of what needs to be done.

-The statement should contain a specific and measurable objective that can

yield practical value to the company.

Examples:

oDevelopment of new products

oImprovement of the process/product performance (relative to demands of

customers).

(b) Selection of response or quality characteristic

-the selection of a suitable response is critical to the success of any

industrial designed experiment.

-Examples: viscosity, strength, etc.


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(c) Selection of process variables or design parameters

-indentify process variables: the use of engineering knowledge of the

process, historical data, cause and effect analysis and brainstorming.

(d) Classification of process variables

-Classify all the process variables into controllable and un-controllable

variables. (controllable can be controlled by engineers; un-controllable

are difficult to control or expensive to control).

(e) Determining the level of process variables

-For quantitative process variables: two levels are generally required.

-For qualitative variables: two or more levels are required

-For a non-linear function is expected by the experimenter, then it is

advisable to study variables at 3 or more levels.

(f) List all the interactions of interest

-In order to effectively interpret the results of experiment, it is highly

desirable to have a good understanding of interaction between two

process variables.


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Designing phase

The size of the experiment is dependent on the number of factors/,

interaction to be studied, the number of levels of each factor, budget and

resources allocation for carrying out the experiment.

Conducting Phase

-The planned experiment is carried out and the results are evaluated.-Several considerations are recognized as being recommended prior to

executing an experiment:

1. Selection of suitable location, ensure not affected by any external

sources of noise (eg: humidity, vibration),

2. Availability of materials/parts, machines, operators, etc.,3. Assessment of the viability of an action in monetary terms by utilising

cost-benefit analysis.


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Analyzing phase

Having performed the experiment, the next phase is to analyse and

interpret the results so that valid and sound conclusions can be derived.

The following are the possible objectives to be achieved from this phase:

Determine the design parameters or process variables that affect the

mean process performance.

Determine the design parameters or process variables that influenceperformance variability.

Determine the design parameter levels that yield the optimum

performance.

Determine further improvement is possible.


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Analytical tools of DOEMain Effects Plot- A plot of the mean response values at each level of a design parameter or process

variables.

- This plot can be used to compare relative strength of the effect of variousfactors.

- The sign and magnitude of a main effect would tell the following:

1. The direction of the effect (the average response increases or decreases),

2. The strength of the effect.

- If the effect of a design/process parameter is positive, implies the averageresponse is higher at high level than low level of parameter setting.

- The effect of a process or design parameter (or factor) can be mathematically

calculated as below, where, F(+1)= average response at high level of a factor, F(-1)=average response at low level setting of a factor.

Interactions Plots- An interaction plot is a powerful graphical tool which plots the mean response of

two factors at all possible combinations of their settings.

- If the lines are parallel, then it connotes that there is an interaction between the

factors. Non-parallel lines is an indication of the presence of interaction betweenthe factors.

)1()1( FFEf


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Example: A cutting tool life optimization study with 3 tools parameters; cutting

speed, tool geometry and cutting angle.


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Cube Plots- Display the average response values at all combinations of process or design

parameter setting.

- Can easily define the best and the worst combinations of factor levels for

achieving the desired optimum response.


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Pareto Plots of Factor Effects- The Pareto plot allows one to detect the factor and interaction effects which are

most important to the process or design optimization.

- It displays the absolute values of the effects, and draw a reference line on the

chart.- Any effect that extends past his reference line is potentially important.

- Significance level is the risk saying that a factor is significant when in fact it is

not.


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Example:

A process to produce chemical substance depends on three factors which

are temperature, pressure and type of catalyst in used.Each of these factors will influence the chemical yield either individually or

through interactions with each others.

Significance level used is 5 %

One of the common approaches adapted by engineers to find out the effects

of parameters is using One-Variable-At-a-Time (OVAT) method where only

single parameter is varied while others parameters are fixed.


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Run T P R Response

1 -1 -1 -1 420

2 +1 -1 -1 370

3 -1 +1 -1 410

4 +1 +1 -1 350

5 -1 -1 +1 450

6 +1 -1 +1 380

7 -1 +1 +1 400

8 +1 +1 +1 330

full factorial design3

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