LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION – STATISTICS
SECOND SEMESTER – APRIL 2012
ST 2957 – RELIABILITY THEORY
Date : 24-04-2012 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION – A
Answer all the questions (10×2=20)
- Define Reliability R(t) of a system
- Define Hazard function r(t)
3.
RA=0.87, RB=0.85, RC=0.89. Determine system reliability
- Define Parallel-Series system
- Define MTBF
- Define a (k,n) system
- Define Standby system
- R(t) = e– 0.2t determine the warranty period for a reliability of 0.9
- An equipment has a hazard function r(t) = 6×10-8t2. The equipment is required to operate a 100
hours. What is the reliability at 100 hours?
- Define a) DFRD b)IFRD
SECTION-B
Answer any five questions (5X8=40)
- Obtain the system reliability function R(t) and hazard function r(t) when the system failure time distribution follows Weibull distribution
- Establish the following (3+3+2)
- i) ii) If R*(s) = LT{R(t)} then MTBF = R*(0) iii)If T~Exponential distribution then MTBF=1/λ
- Obtain system failure time density function for a (k,n) system
- Define Series-Parallel system. Obtain system hazard function r(t) and MTBF for a
Series-Parallel System
- Consider a series system consisting of two components with first component following a
exponential failure time distribution with λ=1/10,000 and second component following a
weibull with parameters β=6 and η=10,000. i)Obtain system reliability ii)Obtain system’s cdf
and pdf iii) Given that the system has performed 500 hrs what is the reliability of the system
for an additional 1000hr mission iv)Obtain the system failure rate v)What should be the
warranty period for a system reliability of 90%
- Explain the methods of obtaining the reliability of a Complex system
17 Establish the following
- F is IFR ó on [0,∞)
- F is IFR ó
- i) Establish: r(t) is a conditional probability function but not a conditional pdf
- ii) Establish: r(t)↓t ó F is DFRD
SECTION-C
Answer any two questions (2X20=40)
- Obtain the reliability function R(t) and hazard function r(t) for the following failure time
distributions i) Exponential ii) Gamma
- Obtain MTBF for the case when failure time(T) of a system is distributed as i) Exponential
ii)Weibull iii) Gamma
- Consider a Standby system of order 3 with Ti ~ Exponential(λi), i=1,2,3 . obtain the system
failure time density function and hence obtain the reliability function R(t) for the case when
λ1= λ2= λ3 and λ1≠ λ2≠ λ3(20)
- Obtain system mean time between failure (MTBF) for a (k,n) system