M.Sc. (Semester IV) (CBCS) Examination Oct/Nov-2017
Statistics
RELIABILITY AND SURVIVAL ANALYSIS
Day Date: Wednesday, 22-11-2017 Max. Marks: 70
Time: 02.30 PM to 05.00 PM
Instructions: Attempt five questions.
Question No. 1 and 2 are compulsory
Attempt any 3 questions from Q.No.3 to Q.No.7
Figures to the right indicate full marks.
Q.1 Choose the correct alternatives 05
For a parallel system of two components having reliability 0.6 each,
the reliability of system is
0.16 0.6
0.84 0.4
In a k-out-of-n system there are minimal path sets.
n 1

The scaled TTT transform for exponential distribution is
t+1
t 1-t
In type II censoring,
Duration of experiment is fixed
Number of failures is fixed
Both time and number of failures are fixed
None of these
A sequence of ×2) contingency tables is used in
Gehan's test Mantel Haenzel test
Log-rank test Mann-Whitney test
Fill in the blanks. 05
A function is star shaped if
Minimal cut sets of structure ∅ are sets for its dual.
The ith component is said to be irrelevant to structure function ∅ if

Gehan's test is an extension of
If F is IFR then its TTT transform is
State whether following statements are true or false: 04
Hazard rate is a probability.
A single random variable is associated with itself.
Random censoring is a particular case of type II censoring.
K-M estimator is nonparametric in nature.
Q.2 Define: 06
Reliability rate function
Failure rate function
Coherent structure
Page 2 of 2
SLR-MS-671
Write short notes on the following: 08
Log rank test
Random censoring
Q.3 Define dual of a structure function. Obtain the dual of k-out-of-n system. 07
Define IFR and IFRA class of distributions. If F∈ IFR then show that
F∈ IFRA.
07
Q.4 Obtain a structure function of system in terms of
minimal path
minimal cut.
07
Define mean time to failure (MTTF) and mean residual life
function. Obtain the same for exponential distribution.
07
Q.5 Describe the need of censoring experiment. Describe Type-I and Type- II
censoring with suitable examples.
07
Obtain maximum likelihood estimate of mean of the exponential
distribution under type II censoring.
07
Q.6 Describe Kaplan-Meier estimator and drive an expression for the same. 07
Discuss maximum likelihood estimation of parameters of Weibull
distribution.