QUAL8115 Advanced Design of Experiments

Topics:Process Robustness, Nested designs & Split Plot Designs

Exercise

Question 1

Which of the following statements are true regarding crossed array designs (select all that apply)?

1. Crossed array designs have the advantage that they ignore potential noise factories.
2. The goal is to minimize variation in the process output irrespective of output levels.
3. Crossed array designs are often created as multiple response optimization experiments.
4. They allow trade-offs to be made between the output level of the process and variation in the process output.

Question 2

Large response measurements will always dictate the use of split-plot design.

1. True
2. False

Question 3

Which of the following statements are true regarding robust process design (select all that apply)?

1. Crossed array designs divide variables into 2 categories of controllable and uncontrollable variables.
2. Robust design techniques are a special class of mixture designs.
3. The goal of a robust design experiment is to determine how to produce predictable, consistent results from a process.
4. The results of 2k designs may be used to optimize the robustness of a process.

Question 4

A company buys raw materials in batches from four different suppliers. The purity of this raw material varies considerably, which causes problems in manufacturing the finished product. We wish to determine whether the variability in purity is attributable to differences between the suppliers. Four batches of raw material are selected at random from each supplier, and three determinations of purity are made on each batch. The data is in the attached Excel file. Note that the purity data is in coded values where 92 has been subtracted from the actual measurement.

Data File (Batches)

Supplier	Batch	Y
1	1	1
1	1	-1
1	1	2
1	2	-4
1	2	-3
1	2	-1
1	3	-2
1	3	2
1	3	3
1	4	1
1	4	4
1	4	0
2	1	1
2	1	-2
2	1	-3
2	2	0
2	2	5
2	2	2
2	3	-2
2	3	0
2	3	-2
2	4	0
2	4	3
2	4	2
3	1	1
3	1	4
3	1	0
3	2	-2
3	2	0
3	2	2
3	3	1
3	3	-1
3	3	2
3	4	3
3	4	2
3	4	3

Using the data above, use Minitab or other software & answer the following 4 questions.

1. What is the F Statistics for Supplier to Two & Three decimal places?
2. What is the DF for batch (Supplier)?
3. Is there significant variations between Suppliers (Yes or No)?
4. What is the Actual Measured value for the First data point in the spreadsheet?

Question 5

A company buys raw materials in batches from four different suppliers. The purity of this raw material varies considerably, which causes problems in manufacturing the finished product. We wish to determine whether the variability in purity is attributable to differences between the suppliers. Four batches of raw material are selected at random from each supplier, and three determinations of purity are made on each batch. The data is in the attached Excel file. Note that the purity data is in coded values where 94 has been subtracted from the actual recorded value.

Data File (Batches)

Supplier	Batch	Y
1	1	1
1	1	-1
1	1	2
1	2	-4
1	2	-3
1	2	-1
1	3	-2
1	3	2
1	3	3
1	4	1
1	4	4
1	4	0
2	1	1
2	1	-2
2	1	-3
2	2	0
2	2	5
2	2	2
2	3	-2
2	3	0
2	3	-2
2	4	0
2	4	3
2	4	2
3	1	1
3	1	4
3	1	0
3	2	-2
3	2	0
3	2	2
3	3	1
3	3	-1
3	3	2
3	4	3
3	4	2
3	4	3

Using the data above, use Minitab or other software & answer the following 4 questions.

1. What is the F Statistics for Supplier to Two & Three decimal places?
2. What is the DF for the Error Term?
3. State if there is a significant variation between Suppliers (Yes or No).
4. What is the Actual Measured value for the First data point??

Question 6

The surface finish of metal parts made on four machines is being studied. An experiment is conducted in which each machine is run by three different operators and two specimens from each operator are collected and tested. Because of the location of the machines, operators used on each machine is not controlled. Use the data below to perform the analysis.

Data

Finish	Machine	Operator
80	1	1
61	1	1
90	2	1
97	2	1
88	3	1
75	3	1
36	4	1
53	4	1
95	1	2
71	1	2
86	2	2
84	2	2
53	3	2
56	3	2
40	4	2
56	4	2
42	1	3
59	1	3
76	2	3
68	2	3
46	3	3
57	3	3
62	4	3
47	4	3

You can use the above data plot, and please make an analysis in Minitab or other software to answer the following 4 questions.

1. What is the F statistic for the machine to Two & Three decimal places?
2. What is the DF for the Error Term?
3. At an alpha of 0.1, is the machine effect significant (Enter Yes or No)
4. Based on graphical analysis, which machine appears to show the most variation in surface finish? (Enter a numeric character).

Question 7

Split plot designs are often used when it is easy or cheap to change the levels of the whole-plot factor.

1. True
2. False

Question 8

Which of the following statements are true regarding crossed array designs (select all that apply).

1. Crossed array designs are often created as multiple response optimization experiments.
2. Crossed array designs have the advantage that they ignore potential noise factors.
3. The goal is to minimize variation in the process output irrespective of output level.
4. They allow trade-offs to be made between the output level of the process & variation in the process output.