INTRODUCTION TO DESIGN OF EXPERIMENT (DOE) (By Prof. V. A. Jideani)
Design of experiment (DOE) is a body of knowledge, based upon statistical and other scientific disciplines, for efficient and effective planning of experiments and for making sound inferences from experimental data. –
In an experiment, we deliberately change one or more process variables (or factors) in order to observe the effect the changes have on one or more response variables. The (statistical) design of experiments (DOE) is an efficient procedure for planning experiments so that the data obtained can be analyzed to yield valid and objective conclusions.
DOE begins with determining the objectives of an experiment and selecting the process factors for the study. An Experimental Design is the laying out of a detailed experimental plan in advance of doing the experiment. Well-chosen experimental designs maximize the amount of “information” that can be obtained for a given amount of experimental effort.
Used to evaluate which process inputs have a significant impact on the process output and what the target level of those inputs should be to achieve the desired result (Output).
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Design of experiment (DOE) defines the:
- Population to be studied,
- Randomization Process
- Administration of Treatments,
- Sample size requirement
- Method of statistical analysis
The process of DOE may seem too cumbersome and extensive to comprehend at the first try.
But, there is a need to understand the use of the design of experiment (DOE) in product and process research and development to achieve product excellence.
BASIC PRINCIPLES OF DESIGN OF EXPERIMENT
Following the Basic Principles of Design of Experiment (DOE) which include:
- Randomization
- Replication and
- Local Control
One can easily comprehend the Idea of DOE and easily implement it in product and process research.
Randomization
A random process of assigning treatments to the experimental units.
Experimental unit: the smallest division of the experimental material.
Treatment: a specific combination of factor levels whose effect is to be compared with other treatments.
Randomization: Removes bias and other sources of extraneous variation, which are not controllable.
Also, Randomisation accompanied by replication forms the basis of any valid statistical test.
Randomization can be performed:
- By a computer program such as Random Allocation Software
- Research Randomizer Online application here https://www.randomizer.org/
- From random number tables or
- Some physical mechanisms (e.g., 6 slips of paper in a box with 2 having level 1, 2 having level 2, and 2 having level 3. Before each run, one of the slips would be drawn blindly from the box and the level selected would be used for the next run of the experiment).
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Replication
Independent repetitions of an experiment under identical experimental conditions.
An individual repetition is called a replicate.
Purpose of Replication includes the following:
- To secure a more accurate estimate of the experimental error, a term that represents the differences that would be observed if the same treatments were applied several times to the same experimental units.
- Decreases the experimental error and thereby to increase precision, which is a measure of the variability of the experimental error.
- It obtains a more precise estimate of the mean effect of a treatment.
Local Control
Extraneous sources of variation are not removed by randomization and replication.
The general rule is: Block what you can randomize what you cannot.
Purpose: to decrease the experimental error.
Local control is the amount of balancing, blocking, and grouping of the experimental units.
- Balancing: the treatments should be assigned to the experimental units in such a way that the result is a balanced arrangement of the treatments.
- Blocking: experimental units should be collected together to form a relatively homogeneous group. A block is also a replicate.
- Blocking removes the effects of a few of the most important nuisance variables. Randomization reduces the contaminating effects of the remaining nuisance variables.
The statistical theory underlying DOE generally begins with the concept of process models
Process Models of Design of Experiment (DOE)
Experimental data can be used to derive an empirical (approximation) model linking the outputs and inputs.
These empirical models contain first and second-order terms.
The most common empirical models fit- Linear form
Linear form:
Y= β0 + β1 X1 + β2 X2 + β12 X1 X2 + experimental error
What are the uses of DOE?
- Choosing between alternatives (Comparative experiment)
- Selecting the Key Factors Affecting a Response (Screening experiment)
- Response Surface Modelling to:
- Hit a Target
- Reduce Variability
- Maximize or Minimize a Response
- Make a Process Robust (i.e., the process gets the “right” results even though there are uncontrollable “noise” factors)
- Seek Multiple Goals
- Mixture Design
- Regression Modelling
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Design of Experiment (DOE) Steps
DOE begins with determining the objectives of an experiment and selecting the process factors for the study.
- Set objectives
- Select experimental (or Sampling) unit and process variables
- Select an experimental design (treatment structure and design structure)
- Execute the design
- Check that the data are consistent with the experimental assumptions
- Analyze and interpret the results and
- Use/present the results (may lead to further runs or DOE)
You can get the complete Guide on how to set objectives for the Surface response method (RSM), Regression Model Objective, and Mixture Design.
Also, Select Experimental (or sampling) Unit and Process Variables, process variables such as Nuisance factors, Types, and cures, treatment factor such as Fixed effect treatment factors, and Random effect treatment factors.
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