M.Sc. Statistics (Semester IV) (CBCS) Examination, 2017
RELIABILITY AND SURVIVAL ANALYSIS
Day Date: Monday,24-04-2017 Marks: 70
Time: 02.30 PM to 05.00 PM
Instruction. Attempt five questions.
Q. No. and Q .No. are compulsory.
Attempt any three from Q.NO.(3) to Q. No.(7).
Figures to the right indicate full marks.
Q.1 Choose the correct alternative: 05
Series system of n components has __minimal path sets.
n 1 2n 2n-1
Reliability of a system always lies between
0 an 1 and 1 o and and
For which of the following family each member has non
Monotone Failure rate?
Exponential Weibull Log normal Gamma
The TTT transform of an IFRA distribution is
Concave Convex
Linear Neither concave nor convex
The rejection criterion to reject H0: F1=F2 against F1< F2 by
using Gehan's statistics U is
U c U c c1 or U c2 c1 c2
Fill in the blanks: 05
A state vector X is called a cut vector if
A parallel system is a special case of k-out-of-n system when

If F IFRA then its cumulative hazard function is
In type censoring, the time of experiment is
Under type-I censoring, the MLE of mean of exponential
distribution is
State whether the following statements are TRUE or FALSE. 04
A subset of associated random variables is not always
associates
IFR class is preserved under convolution.
Hazard rate is probability rate
Actuarial method cannot be used when data consists of
censored observations.
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Q.2 Answer the following: 06
Define minimal path sets and minimal cut sets. Illustrate the
same by example.
Explain the concept of random censoring giving one example.
Write short notes on the following: 08
Type II censoring
Cumulative hazard function
Q.3 Define Poly function of order 2 (PF2). Prove that if f PF2 then
F IFR
If failure time of an item has gamma distribution obtain the failure
rate function
Q.4 Define NBU and NBUE class of distribution. Prove that if f IFRA
then F NBU.

State and prove IFRA closure theorem
Q.5 Develop a test for exponentiality against NBU.
Define type-I censoring and obtain the likelihood corresponding to
a parametric model for lifetime distribution.
Q.6 Derive Greenwood's formula for variance of estimate of survival
function.

Discuss maximum likelihood estimation of parameters of gamma
distribution under no censoring.
Q.7 For a coherent system with n components prove that:
0 and
Describe Mantel- Haenzel test. Indicate the null distribution of test
statistic