Prof. Edwin Romeijn
ESI 6321 Applied Probability Methods For Engineers
Homework 7
Spring 2008
ESI 6321 APPLIED PROBABILITY METHODS FOR ENGINEERS
Homework 7 – Spring 2008
Reading material:
Sections 17.1 and 17.2 from
Hayter (Coursepack II), as well as the course
slides.
Note
: the material in the slides goes beyond the material in Hayter!
Problems:
17.1.4, 17.1.5, 17.2.2, as well as the following 3 problems:
Problem 1:
Consider the system of problem 17.1.2. However, now suppose that the
components have the following constant failure rates (where
λ
i
denotes the
failure rate of component
i
):
λ
1
= 0.01,
λ
2
= 0.10,
λ
3
= 0.01,
λ
4
= 0.05, and
λ
5
=
0.08. Moreover, suppose that components 4 and 5 are configured as standby
parallel, with component 4 the primary unit. Provide an expression for the
overall system reliability as a function of time.
Problem 2:
•
Consider Problem 17.2.7.
Note
: the parameterization of the Weibull
distribution in the coursepack is different from that in the slides: parameters
(
a
,
λ
) in the coursepack correspond to m=a and
θ
=1/
λ
in the slides.
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 Spring '07
 JosephGeunes
 Failure rate, Weibull distribution, HAYTER, applied probability methods, Prof. Edwin Romeijn, Edwin Romeijn Homework

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