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## Description

OPTIMAL DESIGN 5mark

Optimal designs (or optimum designs]) are a class of experimental designs that
are optimal with respect to some statistical criterion.

In the design of experiments for estimating statistical models, optimal designs allow
parameters to be estimated without bias and with minimum variance. A non-optimal
design requires a greater number of experimental
runs to estimate the parameters with the same precisionas an optimal design. In
practical terms, optimal experiments can reduce the costs of experimentation.

The different type of optimal designs are

1. A-optimality (“average” or trace)
2. C-optimality
3. D-optimality (determinant)
4. E-optimality (eigenvalue)
5. T-optimality
6. G-optimality
7. I-optimality (integrated)
8. V-optimality (variance)

D optimal Design

D‐optimal designs are one form of design provided by a computer algorithm.

These types of computer‐aided designs are particularly useful when classical designs
do not apply.

Unlike standard classical designs such as factorials and fractional factorials, D‐
optimal design matrices are usually non‐orthogonal and effect estimates are correlated.

These types of designs are always an option regardless of the type of the model the
experimenter wishes to fit (for example, first order, first order plus some interactions,
full quadratic, cubic, etc.) or the objective specified for the experiment (for example,
screening, response surface, etc.).

The optimality criterion results in minimizing the generalized variance of the
parameter estimates for a pre‐specified model; the ‘optimality’ of a given D‐optimal
design is model dependent.

The experimenter must specify a model for the design and the total number of runs
allowed and the computer algorithm chooses the optimal set of design runs from a
candidate set. This candidate set usually consists of all possible combinations of
various factor levels that one wishes to use in the experiment.

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To put it in another way, the candidate set is a collection of treatment combinations
from which the D‐optimal algorithm chooses the treatment combinations to be
included in the design. The computer algorithm generally uses a stepping and
exchanging process to select the set of runs. Note that there is no guarantee that the
design the computer generates is actually D‐optimal.

The reasons for using D‐optimal designs instead of standard classical designs
generally fall into two categories:

The standard factorial or fractional factorial design requires too many runs for the
amount of resources or time allowed for the experiment or the design space is
constrained; i.e. the process space contains factor settings that are not feasible or are
impossible to run.

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