Types of Experiment Designs

We'll discuss three experiment designs:

1. Simple Design

2. Full Factorial Design

3. Fractional Design

Step 2: Vary the first factor, measuring performance at each level.

Example: For workload design, vary the CPU type first to see which CPU type is best.

Step 3: Repeat step 2 for each level.

Disadvantages:

• Design may give false conclusions about factor interaction

• Alternate design can give more information with same number of experiments

Exhaustively try every possible combination of all levels of all factors.

Total number of experiments required:

Example: In workstation design:

(Number experiments) = (3 CPUs)*(3 memory levels)*(4 disks)*

                            (3 workloads)*(3 educational levels)

                     = 324 experiments

Advantage:

• We can find effect of every factor (including secondary factors) and their interactions.

Disadvantage:

• Cost of study: Infeasible if number of factors or levels is large.

How to Reduce the Number of Experiments

• Reduce the number of levels for each factor:

  Extreme case: try just two levels for each factor: low and high value.

  A full factorial design with two levels for each factor is called 2**k design.

  One could start with a 2**k design, analyze the outcome, and then perform experiments with additional levels.

• Reduce the number of factors.

  Divide the factors into primary and secondary categories. Only vary the primary category.

• Use fractional factorial designs.

  Fractional Factorial Designs

  Use a fraction of the full factorial design. (Details are given later.)

  Consider a k factor study using a 2**k factorial design.

  If we perform half the experiments, we get a 2**(k-1) fractional factorial design. This is called a half-replicate of a 2**k design.

  In general, we perform a 2**(k-p) design for some integer p.

  The fractional factorial design is based on an algebraic method of calculating the contributions of factors to the total varance with fewer than a full factorial number of experiments.

  Example Fractional Factorial Design

  Consider the workstation study, with 324 experiments for a full factorial design.

  We first reduce the number of experiments by considering four or five factors (ignore number of disks).

  We are left with four factors, each with three levels. This is a 3**4 design, with 81 experiments.

  A 3**(4-2) fractional factorial design consisting of only nine experiments is shown below.

  CPU       Memory    Workload      Education     
  80386      4M       Managerial    High School
  80386      8M       Scientific    Postgraduate
  80386     16M       Secretarial   College
  
  80486      4M       Scientific    College
  80486      8M       Secretarial   High School
  80486     16M       Managerial    Postgraduate
  
  Pentium    4M       Secretarial   Postgraduate
  Pentium    8M       Managerial    College
  Pentium   16M       Scientific    High School
  

  Each of the four factors is used three times at each level.

  Advantage: Fewer experiments than full factorial design.

  Disadvantage: Indicates interactions among some but not all factors. (O.K. if you know a priori that certain interactions are negligible.)

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