Basic Principles of DOE (Design of Experiments)

The basic principles of doe (design of experiments or experimental design) are (i) Randomization, (ii) Replication, and (iii) Local Control. Let us discuss these important principles of experimental design in detail below.

Principles of DOE (Design of Experiments)

1. Randomization

   Randomization is the cornerstone underlying the use of statistical methods in experimental designs.  Randomization is the random process of assigning treatments to the experimental units. The random process implies that every possible allotment of treatments has the same probability. For example, if the number of treatments = 3 (say, $A, B$, and C) and replication =$r = 4$, then the number of elements = $t \times r$ = 3 \times 4 = 12 = n$. Replication means that each treatment will appear 4 times as $r = 4$. Let the design is

   A	C	B	C
   C	B	A	B
   A	C	B	A

   Note from the design elements 1, 7, 9, and 12 are reserved for Treatment $A$, elements 3, 6, 8, and 11 are reserved for Treatment $B$, and elements 2, 4, 5, and 10 are reserved for Treatment $C$. $P(A)= \frac{4}{12}, P(B)= 4/12$, and $P(C)=\frac{4}{12}$, meaning that Treatment $A, B$, and $C$ have equal chances of its selection.
2. Replication

   By replication, we mean the repetition of the basic experiments. For example, If we need to compare the grain yield of two varieties of wheat then each variety is applied to more than one experimental unit. The number of times these are applied to experimental units is called their number of replications. It has two important properties:

   • It allows the experimenter to obtain an estimate of the experimental error.
   • More replication would provide the increased precision by reducing the standard error (SE) of mean as $s_{\overline{y}}=\tfrac{s}{\sqrt{r}}$, where $s$ is sample standard deviation and $r$ is a number of replications. Note that increase in $r$ value $s_{\overline{y}}$ (standard error of $\overline{y}$).
3. Local Control

   Local control is the last important principle among the principles of doe. It has been observed that all extraneous source of variation is not removed by randomization and replication, i.e. unable to control the extraneous source of variation.
   Thus we need to refine the experimental technique. In other words, we need to choose a design in such a way that all extraneous source of variation is brought under control. For this purpose, we make use of local control, a term referring to the amount of (i) balancing, (ii) blocking, and (iii) grouping of experimental units.

Balancing: Balancing means that the treatment should be assigned to the experimental units in such a way that the result is a balanced arrangement of treatment.

Blocking: Blocking means that the like experimental units should be collected together to form relatively homogeneous groups. A block is also called a replicate.

The main objective/ purpose of local control is to increase the efficiency of experimental design by decreasing experimental error.

This is all about the Basic Principles of the Experimental Design. To learn more about DOE visit the link: Design of Experiments.

Real Life Example

Imagine a bakery trying to improve the quality of its bread. Factors that could affect bread quality include

• Flour type,
• Water
• Temperature, and
• Yeast quantity

By using DOE, the bakery can systematically test different combinations of these factors to determine the optimal recipe.

Randomization: Randomly assign different bread batches to different combinations of flour type, water temperature, and yeast quantity.

Replication: Bake multiple loaves of bread for each combination to assess variability.

Local Control: If the oven has different temperature zones, bake similar bread batches in the same zone to reduce temperature variation.

By following the Basic Principles of Design of Experiments, the bakery can efficiently identify the best recipe for its bread, improving product quality and reducing waste.

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