# Ffacdes1

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### Purpose

Output a fractional factorial design matrix.

### Synopsis

- desgn = ffacdes1(k,
*p*) - [desgn, col_ID, alias_ID, res] = ffacdes1(k,p,options)

### Description

FFACDES1 outputs a 2^{(k-p)} fractional factorial design of experiments. The design is constructed such that the highest order interaction term is confounded. This is one way to select a fractional factorial. Input `k` is the total number of factors in the design and `p` is the number of confounded factors {default: `p` = 1}. Note that it is required that `p < k`. Output `desgn` is the experimental design matrix.

#### Inputs

**k**= total number of factors in the design.

#### Optional Inputs

**p**= numerical indicator of the fraction desired (default = 1)

- 1 : Half Fraction
- 2 : Quarter Fraction
- 3 : Eighth Fraction
- 4 : Sixteenth Fraction
- Note: Only fractionation up to 1/16 presently supported

#### Outputs

**desgn**= experimental design matrix

If the dso option is false, the outputs include:

**desgn**= is a matrix of the experimental design in uncoded form**col_ID**= is a cell array of strings describing the multiplicative origin of each column; one col for each coefficient to potentially be calculated where:- the first k cells describe the original main factors
- the remaining cells describe the various interactions among main factors.

**alias_ID**= is a cell array of logicals describing the alias structure of the selected design; one row per coefficient/X-column. Multiplying a given logical by the full set of characters representing the factors yields the alias relationship for that row/coefficient.

ABCDEF .* [1 0 0 1 1 0] = ADE

**res**= resolution of the selected design.