In an experimental program to investigate the properties of a thin film plastic coating on...

Question

In an experimental program to investigate the properties of a thin film plastic coating on ceramic-based resistors, six factors were identified.X1 - Supplier of a basic component of the plastic (there were 2) X2 - Viscosity of the coating at time of application X3 - Thickness of coating X4 - Temperature of the first bake (dry) cycle X5 - Temperature of the second bake (cure) cycle X6 - Speed of the conveyer(a) List the experiments and a random list of run orders for a full factorial design with these six factors using symbolic - and + signs for the levels. Show the complete confounding table.(b) List the experiments and random run orders if we are to run a ih fractional design .(c) Describe how you would analyse the data in each of the situations defined in (a) and (b) above.Question 2You are trying to help an ice cream vendor to be able to predict how many ice cream cones he will sell in a given afternoon (so that he knows how much ice cream to buy). He decides, with your help, to run a half fraction of a 25 to study the influence of several factors on sales. The data are given on the next page.  From the data given, is a prediction equation justified? If so, what is the equation? Justify your answers.Question 3Consider the 25-2 fractional factorial design with generators: 4 = 12 and 5 = 123. Specify the factor level combinations for this design and determine the complete confounding pattern.  
	
Document Preview: Macquarie	  University	  
Faculty	  of	  Science	  
Department	  of	  Chemistry	  and	  Biomolecular	  Sciences	  
Analytical	  Measurement	  Uncertainty	  and	  Method	  Validation	  
CBMS760	  /	  CBMS860	  
	   2013	  
2010	  
	  
Tutorial	  Set	  4	  /	  Assignment	  4	  
	  
Hand	  in	  complete	  solutions	  /	  working	  for	  all	  three	  questions	  below	  by	  6	  pm	  on	  
Wednesday,	  May	  8,	  2013.	  
	  
Question	  1	  
	  
In	  an	  experimental	  program	  to	  investigate	  the	  properties	  of	  a	  thin	  film	  plastic	  coating	  on	  
ceramic–based	  resistors,	  six	  factors	  were	  identified.	  
	  
X 	  –	  Supplier	  of	  a	  basic	  component	  of	  the	  plastic	  (there	  were	  2)	  
1
X 	  –	  Viscosity	  of	  the	  coating	  at	  time	  of	  application	  
2
X 	  –	  Thickness	  of	  coating	  
3
X 	  –	  Temperature	  of	  the	  first	  bake	  (dry)	  cycle	  
4
X 	  –	  Temperature	  of	  the	  second	  bake	  (cure)	  cycle	  
5
X 	  –	  Speed	  of	  the	  conveyer	  
6
	  
(a)	   List	  the	  experiments	  and	  a	  random	  list	  of	  run	  orders	  for	  a	  full	  factorial	  design	  with	  
these	  six	  factors	  using	  symbolic	  –	  and	  +	  signs	  for	  the	  levels.	  	  Show	  the	  complete	  
confounding	  table.	  
	  
(b)	   	  List	  the	  experiments	  and	  random	  run	  orders	  if	  we	  are	  to	  run	  a	  ½	  fractional	  design	  .	  
	  
(c)	   	  Describe	  how	  you	  would	  analyse	  the	  data	  in	  each	  of	  the	  situations	  defined	  in	  (a)	  
and	  (b)	  above.	  
	  
Question	  2	  
	  
You	  are	  trying	  to	  help	  an	  ice	  cream	  vendor	  to	  be	  able	  to	  predict	  how	  many	  ice	  cream	  
cones	  he	  will	  sell	  in	  a	...

Robert · Accepted Answer

1
Q1. 
a) Table of the experiments and random list of run orders for level 2
RUN
X1
X2
X3
X4
X5
X6
1
-
-
-
-
-
-
2
+
-
-
-
-
-
3
-
+
-
-
-
-
4
+
+
-
-
-
-
5
-
-
+
-
-
-
6
+
-
+
-
-
-
7
-
+
+
-
-
-
8
+
+
+
-
-
-
9
-
-
-
+
-
-
10
+
-
-
+
-
-
11
-
+
-
+
-
-
12
+
+
-
+
-
-
13
-
-
+
+
-
-
14
+
-
+
+
-
-
15
-
+
+
+
-
-
16
+
+
+
+
-
-
17
-
-
-
-
+
-
18
+
-
-
-
+
-
19
-
+
-
-
+
-
20
+
+
-
-
+
-
21
-
-
+
-
+
-
22
+
-
+
-
+
-
23
-
+
+
-
+
-
24
+
+
+
-
+
-
25
-
-
-
+
+
-
26
+
-
-
+
+
-
27
-
+
-
+
+
-
28
+
+
-
+
+
-
29
-
-
+
+
+
-
30
+
-
+
+
+
-
31
-
+
+
+
+
-
32
+
+
+
+
+
-
33
-
-
-
-
-
+
34
+
-
-
-
-
+
35
-
+
-
-
-
+
36
+
+
-
-
-
+
37
-
-
+
-
-
+
38
+
-
+
-
-
+
39
-
+
+
-
-
+
40
+
+
+
-
-
+
41
-
-
-
+
-
+
42
+
-
-
+
-
+
43
-
+
-
+
-
+
44
+
+
-
+
-
+
45
-
-
+
+
-
+
46
+
-
+
+
-
+
47
-
+
+
+
-
+
48
+
+
+
+
-
+
49
-
-
-
-
+
+
50
+
-
-
-
+
+
51
-
+
-
-
+
+
52
+
+
-
-
+
+
53
-
-
+
-
+
+
54
+
-
+
-
+
+
55
-
+
+
-
+
+
56
+
+
+
-
+
+
57
-
-
-
+
+
+
58
+
-
-
+
+
+
59
-
+
-
+
+
+
60
+
+
-
+
+
+
61
-
-
+
+
+
+
62
+
-
+
+
+
+
63
-
+
+
+
+
+
64
+
+
+
+
+
+
There is No Confounding rule present for level 2
 b) For ½ fractional design
RUN
X1
X2
X3
X4
X5
X6
1
-
-
-
-
-
-
2
+
-
-
-
-
+
3
-
+
-
-
-
+
4
+
+
-
-
-
-
5
-
-
+
-
-
+
6
+
-
+
-
-
-
7
-
+
+
-
-
-
8
+
+
+
-
-
+
9
-
-
-
+
-
+
10
+
-
-
+
-
-
11
-
+
-
+
-
-
12
+
+
-
+
-
+
13
-
-
+
+
-
-
14
+
-
+
+
-
+
15
-
+
+
+
-
+
16
+
+
+
+
-
-
17
-
-
-
-
+
+
18
+
-
-
-
+
-
19
-
+
-
-
+
-
20
+
+
-
-
+
+
21
-
-
+
-
+
-
22
+
-
+
-
+
+
23
-
+
+
-
+
+
24
+
+
+
-
+
-
25
-
-
-
+
+
-
26
+
-
-
+
+
+
27
-
+
-
+
+
+
28
+
+
-
+
+
-
29
-
-
+
+
+
+
30
+
-
+
+
+
-
31
-
+
+
+
+
-
32
+
+
+
+
+
+
Confounding rule-
X6 = X1* X2*X3*X4*X5
c) We can analyze the data after getting the response variable in both the cases, however the complexity in analysis will be lesser in second case as number of runs are lesser as well as number of factor can be reduced. Also confounding rules are available in the case.
In first case data will be analyzed using Leaf Spring experiment. After looking on the result and applying effect hierarchy principle, we can reduced the number of runs by eliminating the 6, 5 and even 4 factor interaction based on values.
Further model can be frames based on response variable. The model in both the cases should not be significant different if we had eliminated less effect factor interaction.
Further the impact of each factor on the model can be determine by seeing the p value for each of the cases. The significance of overall model can be determine by looking the overall p and F value of model. 
Q2 Below is the given data-
RUN
X1
X2
X3
X4
X5
Response
1
1
24
cloudy
5
regular
happy
105
2
1
25
cloudy
5
regular
surly
122
3
1
24
sunny
10
regular
happy
92
4
1
25
sunny
10
regular
surly
149
5
1
24
sunny
5
waffle
happy
106
6
1
25
sunny
5
waffle
surly
153
7
1
24
cloudy
10
waffle
happy
111
8
1
25
cloudy
10
waffle
surly
113
9
2
24
sunny
5
regular
surly
100
10
2
25
sunny
5
regular
happy
146
11
2
24
cloudy
10
regular
surly
105
12
2
25
cloudy
10
regular
happy
125
13
2
24
cloudy
5
waffle
surly
105
14
2
25
cloudy
5
waffle
happy
126
15
2
24
sunny
10
waffle
surly
94
16
2
25
sunny
10
waffle
happy
156
Main Effect Plot
Interaction plot
Numerical optimizer result
Results- 
DESIGN DETAILS                                                                                                                                                                                      
      Design type:                  Two-level                                                                                                                                                          
      Design description:           1/2 Fraction                                                                                                                                                       
      Number of factors:            5                                                                                                                                                                  
      Number of runs:               16                                                                                                                                                                 
      Resolution:                   4                                                                                                                                                                  
      Number of blocks:             2                                                                                                                                                                  
   FACTORS                                                                                                                                                                                             
      Factors and Levels:                                                                                                                                                                              
      __________________________________________________                                                                                                                                               
      Factor     Label           Low      Center  High                                                                                                                                                 
      __________________________________________________                                                                                                                                               
      X1         temperature     24       24.

In an experimental program to investigate the properties of a thin film plastic coating on ceramic-based resistors, six factors were identified. X1 - Supplier of a basic component of the plastic...

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