Question

X1 X2 X3 X4 X5 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1 -1 -1 1 -1 -1 1 -1 -1 1 - 1 1 -1 1 - 1 1 1 1 1 1 1 1 -1 -1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 1 1 -1 -1 1 1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 1 1 --- 1. Consider the above design with 5 factors. It is known that the design is a regular fractional factorial design of N=16 runs. Answer the following questions. (a) Please identify the defining relation of this design and write down the alias structure, and the resolution of this design. Please explain how you find your answers. (b) Suppose we only need to select 4 columns from this design for fitting a model with an overall average, 4 main effects, and the interactions up to 4 factors (i.e. the most complicated model for 4 factors). Please suggest which column you would delete from the above design to generate such a 4- factor design, and (ii) provide your reason for your selection. Would it make a difference if you replace a column of your selected design with the column that you chose to delete? Discuss.

Answer 1

This qution is solve by using minitab ,here input and out put is given in photo,for more understanding go through it.explanation is also attach with it.

MINITAB - Untitled Session S File Edit ManipCalc Stat Graph Editor Window Help Fractional Factorial Design 5, 16 Resolution: V Fraction: 1/2 Factors: Runs: Blocks: 5 16 none Base Design: Replicates: Center pte (total): 0 Design Generators: E = ABCD Alias Structure I + ABCDE A + BCDE B + ACDE C + ABDE D + ABCE E + ABCD AB + CDE AC + BDE AD + BCE AE + BCD BC + ADE BD + ACE BE + ACD CD + ABE CE + ABD DE + ABC

This example can be easly solve by using Minitab software The procedure is discribe below Open Minitals → Stat → DOE → Factorials (mate factoriel Type of Design 2-level factorial is No of factors [5] 3 besigns 1/2 fraction No. of replicate a Then click on ok. You get (10 fraction required design. The out put is a given as: Answers Here Resolution is Resolution I design lalias structure is also given Ansa Resolution I design b. Alias Structure is given in minital window) (6 suppose we only need to select 4 columns I from this design for fitting a model with an overall average, 4 main effect of the interaction effect apto 4 factor, you can delete & xg factor because here gesign generator is E= ABCD we can delete the column of E I because the information of t is already I in A B C D ( As the generator is EZABOD so we can confound the effect E. (11) If we you use only four factor X X2 X3 X4 we definitly get the better result column)