M.Sc. (Semester IV) (CBCS) Examination Nov/Dec-2018
Statistics
RELIABILITY AND SURVIVAL ANALYSIS
Time: 2½ Hours Max. Marks: 70
Instructions: Attempt five questions.
Q. No. 1 and Q. No. 2 are compulsory.
Attempt any three questions from Q. No. 3 to 7.
Figures to the right indicate full marks.
Q.1 Choose the correct alternative: 05
In type I censoring, the number of uncensored observations have
distribution.
binomial exponential
geometric normal
The log-rank test for comparing two distributions is based on data.
left censored right censored
both a and b neither a nor b
Let be the rthorder statistic in a random sample of size n taken from
exponential distribution with parameter λ. Then Var[T r is equal to
IFR class of distributions is preserved under
coherent mixture
convolution all the above
Which of the following is an example coherent system?
series system parallel system
k-out-of-n system all the above
Fill in the blanks: 05
If F is IFR then log F is function.
A series system of n components has minimal path sets.
In censored data, actuarial estimator of survival function is
A sequence of × contingency tables is used in test.
In type I censoring is a random variable.
State whether the following statement are True or False 04
Gehan's test is an extension of chi-square test of goodness of fit.
For exponential distribution failure rate is constant.
A subset of minimal cut set is also a cut set.
A single random variable is associated with itself.
Q.2 Define: 06
Reliability of a component
Reliability of system
Type I censoring
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SLR-VR-491
Write short notes on the following: 08
Pivotal decomposition of structure function
Empirical survival function
Q.3 Define minimal path vector and minimal cut vector. Prove that minimal path
vector is minimal cut vector of its dual.
07
Define k-out-of-n system. Show that it is a coherent system. 07
Q.4 Define IFR and IFRA class of life distributions. Prove that if F is IFR then F is
IFRA.
07
Suppose failure time of an item has Pareto distribution. Obtain failure rate
function and show that distribution belongs to DFR.
07
Q.5 Discuss nonparametric estimator of survival function under complete data.
Also obtain confidence band for the survival function.
07
Derive the likelihood function of observed data under type II censoring.
Obtain maximum likelihood estimate of mean of the exponential distribution
under type II censoring.
07
Q.6 Define Kaplan- Meier estimator of survival function and derive an expression
for the same.
07
Define generalized maximum likelihood estimator (GMLE). Prove that
Kaplan-Meier estimator is GMLE.
07
Q.7 Describe Gehan's test for two sample testing problem in presence of
censoring.
07