M.Sc. (Semester III) (CBCS) Examination Nov/Dec-2018
Statistics
PLANNING AND ANALYSIS OF INDUSTRIAL EXPERIMENTS
Time: 2½ Hours Max. Marks: 70
Instructions: All Questions carry equal marks.
Figures to the right indicate full marks.
Q.1 Choose the most correct alternative: 14
Smaller the experimental error efficient the design.
Less More
Not None of these
The degrees of freedom corresponding to error in single replicate design is
Zero One
At least two All of these M
Confounding is necessary to reduce
Block size No. of blocks
No. of factors All of these
Fractional factorial experiment reduces
Factors Levels of factors
Both a and b Neither a and b
In 32 factorial experiment with factors A and the interaction AB has
d. s.
8 4
1 Depending on the experiment
Preferably interactions is chosen for confounding.
Low order Middle order
Higher order None of these
For a 26−2 experiment with defining relation I=ABCD=CDEF=ABEF is a
design.
Resolution IV Resolution II
Resolution III Resolution V
RBD is orthogonal.
Always Not
Sometimes All of these
The rank of the incidence matrix in case of BIBD with v treatment in b block
is
b-1 v-1
v bv-1
10) Consider the two statements A connected design always orthogonal,
An orthogonal design is always connected. Which of the statement is true?
Only P Only Q
Both P and Q Neither P or Q
11) If there are five factors each at two levels and conducted in two replications,
then error degrees of freedom are
0 31
32 63
Page 2 of 2
SLR-VR-486
12) In resolution IV design all main effects are
Clearly estimable Strongly estimable
Estimable None of these
13) The aliased defining relation of 2k−1 design is I=ABCD, then a alias of A is

ACD BCD
ABD ABC
14) The objects which are to be compared in comparative experiment are called

Treatment Blocks
Unit None of these
Q.2 Answer the following. (Any four) 08
Define Minimum aberration Design.
Give parametric relationship of BIBD and write down the notations with
meaning of parameters of BIBD.
Define Connectedness in Design.
State the challenges in un-replicated design.
Define main effect with its graphical representation in factorial design.
Write short notes on following. (Any two) 06
Resolution in factorial design.
Partial Confounding
Balancedness
ii) Orthogonality in Design
Q.3 Answer the following. (Any two) 08
Describe a 23 factorial experiment with replications. Give a suitable
example of it.
Define a Shortest word length in defining contrast subgroup. What is
Resolution III and Resolution IV design?
Define BIBD with an example. Show that bk=vr with usual notations.
Answer the following. (Any one) 06
Discuss the Two way ANOVA without interaction model and ANOCOVA
in one way case.
Describe one way ANOVA model and obtain the least square estimates
of its parameters.
Q.4 Answer the following. (Any two) 10
Describe stepwise procedure of construction and analysis
Experiment.
Define 32 factorial experiment with 2 replications and write its layout.
What is confounding in design? What is complete and partial
confounding? Illustrate with one example of each.
Answer the following. (Any one) 04
What is alias structure? Write alias structure for 24−1 Design with ABCD
as generator.
Discuss the single replicate design. How to analyze these type of
design?
Q.5 Answer the following. (Any two) 14
Discuss the basic principles of Design of Experiments.
Explain the full analysis of 2n factorial experiment with replicate.
Write the full analysis of 32 factorial experiments with 2 replicate.