- You are a statistical consultant for a company’s research and development center.

- Your boss assigns you to a project where a new process is being developed. The team of process specialists has been brainstorming potential important factors in this process. Your boss informs you that they came up with 9 potential factors and ran a screening design and found that 5 factors were significant. She says resources are scarce, so they started out with 48 runs before the first experiment was run. Using the tools we have learned so far and the remaining resources, come up with a
__feasible__strategy to optimize the process. Include any type of design (or designs) that you might use and how you would allocate the runs (there is more than one correct answer for this, make sure that you justify your choice of strategy). - At this same company, a 3-day seminar in 2
^{k}factorials is being given by a colleague. Someone in R&D comes to your office and tells you that they learned during this seminar that for 2^{k}full and fractional factorials, the standard error of a regression coefficient for a factor is one-half of the standard error of its effect, but they don’t know why this is. How would you explain it to them?

- The following are the experimental results from a designed experiment. Assume that your goal is to minimize the response.

e= | 8 | d= | 8 |

a= | 9 | ade= | 10 |

be= | 35 | bd= | 32 |

ab= | 55 | abde= | 53 |

c= | 16 | cde= | 15 |

ace= | 22 | acd= | 21 |

bc= | 40 | bcde= | 41 |

abce= | 65 | abcd= | 61 |

- Determine the defining relation and alias structure for this design

- Comment on the design resolution and if need be give an alternative
- Analyze the experiment using a=0.05
- Make a recommendation to the experimenter

- You are designing an experiment for your boss. There are 8 factors and she says that you only have 32 runs to work with. Each factor has 2-levels. She has also given you the stipulation that the following interactions are most likely significant: CD, DF, CH, and FH. Create this design. Make sure that the design has the highest resolution possible keeping with the stipulations

- The design factors for an experiment in the semiconductor industry are A = laser power (9W, 13W), B = laser pulse frequency (4000 Hz, 12000 Hz), C = matrix cell size (0.07 in, 0.12 in), and D = writing speed (10 in/sec, 20 in/sec), and the response variable is the unused error correction (UEC). This is a measure of the unused portion of the redundant information embedded in the 2d matrix. A UEC of 0 represents the lowest reading that still results in a decodable matrix while a value of 1 is the highest reading. A DMX Verifier was used to measure UEC. The data from this experiment are shown below.

Standard Order | Run Order | Laser Power | Pulse Frequency | Cell Size | Writing Speed | UEC |

8 | 1 | 1 | 1 | 1 | -1 | 0.80 |

10 | 2 | 1 | -1 | -1 | 1 | 0.81 |

12 | 3 | 1 | 1 | -1 | 1 | 0.79 |

9 | 4 | -1 | -1 | -1 | 1 | 0.60 |

7 | 5 | -1 | 1 | 1 | -1 | 0.65 |

15 | 6 | -1 | 1 | 1 | 1 | 0.55 |

2 | 7 | 1 | -1 | -1 | -1 | 0.98 |

6 | 8 | 1 | -1 | 1 | -1 | 0.67 |

16 | 9 | 1 | 1 | 1 | 1 | 0.69 |

13 | 10 | -1 | -1 | 1 | 1 | 0.56 |

5 | 11 | -1 | -1 | 1 | -1 | 0.63 |

14 | 12 | 1 | -1 | 1 | 1 | 0.65 |

1 | 13 | -1 | -1 | -1 | -1 | 0.75 |

3 | 14 | -1 | 1 | -1 | -1 | 0.72 |

4 | 15 | 1 | 1 | -1 | -1 | 0.98 |

11 | 16 | -1 | 1 | -1 | 1 | 0.63 |

- Analyze the results and determine the best model
- Check model assumptions
- Determine the settings to optimize the response
- Assume that after the initial runs were created, the experimenter decided to add centerpoints. Assume that the centerpoints were: 0.98, 0.95, 0.93, and 0.96. Reanalyze the data.
- What recommendations would you make to the experimenters?