Problem 1:

Consider the data in Table 1. (See attached excel spreadsheet).

1. Fit a second order model
2. What operating conditions would you recommend if the objective is to minimize the response y?
3. What operating conditions would you recommend if the objective is to operate the process at a mean response y is very close to 46?

Problem 2 :

Harry and Judy Peterson-Nedry own a vineyard and winery in Newberg, Oregon. They grow several varieties of grapes and manufacture wine. Harry and Judy have used factorial designs for process and product development in the wine- making segment of their business. This problem describes the experiment conducted for their 1985 Pinot Noir. Eight variables were originally studied

Harry and Judy decided to use 16 runs. The wine was taste-tested by a panel of experts on March 8th, 1986. Each expert ranked 16 samples of wine tasted, with rank 1 being the best.

Design an experiment with the best resolution with 16 runs:

Please see the following data:

Fractional Factorial Design

Factors: 8 Base Design: 8, 16 Resolution: IV

Runs: 16 Replicates: 1 Fraction: 1/16

Blocks: 1 Center pts (total): 0

Design Generators: E = BCD, F = ACD, G = ABC, H = ABD

1. Please fill in the Alias Structure blank
   I + ABCG + ABDH + ABEF + ACDF + ACEH + ADEG + AFGH + BCDE + BCFH + BDFG + BEGH
   + CDGH + CEFG + DEFH
   A + BCG + BDH + BEF + CDF + CEH + DEG + FGH
   B + ___________________________________
   C + ABG + ADF + AEH + BDE + BFH + DGH + EFG
   D + ABH + ACF + AEG + BCE + BFG + CGH + EFH
   E + ABF + ACH + ADG + BCD + BGH + CFG + DFH
   F + ABE + ACD + AGH + BCH + BDG + CEG + DEH
   G + ABC + ADE + AFH + BDF + BEH + CDH + CEF
   H + ABD + ACE + AFG + BCF + BEG + CDG + DEF
   AB + _______ + DH + EF + ACDE + ACFH + ADFG + AEGH + BCDF + BCEH + BDEG + BFGH
   AC + BG + DF + EH + ABDE + ABFH + ADGH + AEFG + BCDH + BCEF + CDEG + CFGH
   AD + BH + CF + EG + ABCE + ABFG + ACGH + AEFH + BCDG + BDEF + CDEH + DFGH
   AE + BF + CH + DG + ABCD + ABGH + ACFG + ADFH + BCEG + BDEH + CDEF + EFGH
   AF + BE + CD + GH + ABCH + ABDG + ACEG + ADEH + BCFG + BDFH + CEFH + DEFG
   AG + BC + DE + FH + ABDF + ABEH + ACDH + ACEF + BDGH + BEFG + CDFG + CEGH
   AH + BD + CE + FG + ABCF + ABEG + ACDG + ADEF + BCGH + BEFH + CDFH + DEGH
2. Use the average ranks as a response variable. Analyze the data and draw conclusions. You will find it helpful to examine a normal probability plot of the effect estimates.
   
   
3. Use the standard deviation of the ranks (or some appropriate transformation such as log s) as a response variable. What conclusions can you draw about the effects of the eight variables on variability in wine quality?
   
4. Suppose that just before the start of the experiment, Harry and Judy discovered that the eight new barrels they ordered from France for use in the experiment would not arrive in time, and all 16 runs would have to be made with old barrels. If have and Judy just drop column C from their design, what does this do to the alias relationships? Do they need to start over and construct a new design?
   
5. Harry and Judy know from experience that some treatment combinations are unlikely to produce good results. For example, the run with all eight variables at the high level is bad. They want to set up a new design for their 1986 Pinot Noir using these same eight variables, but they do not want to make the run with all eight factors at the high level. What design would you suggest?

Problem 3 :

Construct a 2 ^7-2 design. Show how the design may be run in four blocks of eight observations each. Are any main effects or two-factor interactions confounded with blocks?

Price: $26.89

Solution: The downloadable solution consists of 13 pages, 1389 words and 9 charts.
Deliverable: Word Document