# Example 3 - Two Level Fractional Factorial Design

**Download Example File for Version
10 (*.rsgz10) or
Version 9 (*.rsr9) **

## Background

Consider a manufacturing process for an integrated circuit.* The objective is to improve the process yield. The five factors that may affect the process are:

Factor |
Name |
Unit |
Low |
High |

A | Aperture Setting | - | small | large |

B | Exposure Time | min | 20 | 30 |

C | Develop Time | s | 30 | 45 |

D | Mask Dimension | - | small | large |

E | Etch Time | min | 14.5 | 15.5 |

It is too expensive to run a full factorial design, which would
require 2^{5}
= 32 runs. Therefore, the engineers decide to run a half fractional
factorial design using generator E = ABCD.

## Experiment Design

To find the important factors, the experimenters use the standard
design folio in DOE++ to create a two level factorial design.
On the Design tab of the folio, the following design settings are
specified. *The design matrix and response data are given on the
Data tab of the "Fractional
Factorial Design" folio.*

## Analysis Part I - Screening

**Step 1:** When the design is built, the experiment runs are
shown in a randomized order on the Data tab. After performing the
runs in the displayed order and recording the results, the experimenters enter the
data set into the folio, as shown next.

**Step 2:** Next, the analysis settings are specified. The data set will be analyzed using the default risk
(significance) level of 0.1. In addition, the test statistic for the effects
will be calculated using the partial sum of squares, and
the ANOVA table will show the results for each individual term.

**Step 3:** An effect probability plot is created, as shown next. The plot shows that
the main effects A, B and C, and the interaction effect AB, are
significant.

## Analysis Part II - Optimization

*The results for the reduced model are given in the "Reduced
Model" folio*.

**Step 1:** The design folio is duplicated and the copy is renamed
to "Reduced Model."

**Step 2:** In the Select Effects window, only the significant
effects are selected to calculate the new model, as shown next.

**Step 3:** The reduced model is calculated. The Regression
Information table in the detailed
summary of results shows the following coefficients for the included
terms.

Term |
Coefficient |

A | 5.5625 |

B | 16.9375 |

C | 5.4375 |

AB | 3.4375 |

## Conclusions

Each of the effects in the reduced model has a positive effect on the yield (as indicated by the positive coefficients). Therefore, in order to increase the yield, the high levels of factors A, B, and C should be applied. For the remaining factors, the low or high levels could be used.

* Montgomery, D. C. Design and Analysis of Experiments, 5th edition, John Wiley & Sons, New York, 2001.