What would be the defining relationship and generator in this design?

ISE 135 In-class exercise (Groups of max. 3 students)

Fractional Factorial Design

You need to answer the following questions and submit a word document to CANVAS with your answers (include ANOVA table and required plots)

Consider a 2^5-1 design below. Note that Basic design is already created using 2⁴ runs.

1. Create the 5^th column (column of factor E –look at the rule to create it on slide 14 pf Fractional Factorial Design lecture slides)
2. What would be the defining relationship and generator in this design? (i.e. Defining relationship when I=?, generator is when a factor is generated by using other factor columns). Minitab will also tell you what the generator of this /1/2 fractional design of 2⁵ experiment once you create the design.
3. Calculate the main effect of A manually (using contrast)
4. Enter the data to Minitab and analyze the data and make conclusions. Be careful- this is a single replicate, so you need to do some extra steps to create an ANOVA table.
5. If your aim was to find the best combination of factor levels that maximize your response, what would they be? (look at the effects plots to see how response is affected when factor levels were changed from low to high, and determine, which levels for each factor should be selected to get the highest response)

 

 

	Basic Design					Treatment Combination	Yield
Run	A	B	C	D	E
1	–	–	–	–		e	8
2	+	–	–	–		a	9
3	–	+	–	–		b	34
4	+	+	–	–		abe	52
5	–	–	+	–		c	16
6	+	–	+	–		ace	22
7	–	+	+	–		bce	45
8	+	+	+	–		abc	60
9	–	–	–	+		d	6
10	+	–	–	+		ade	10
11	–	+	–	+		bde	30
12	+	+	–	+		abd	50
13	–	–	+	+		cde	15
14	+	–	+	+		acd	21
15	–	+	+	+		bcd	44
16	+	+	+	+		abcde	63