ME 776.01
Homework 2
1. The probability of a jet fighter surviving an intense combat mission is 0.8, and three
fighters are needed for the success of the mission. How many fighters must be sent on the
mission in order to achieve a 95% probability of succe
ME 776.01 Homework 1
Due September 13, 2011
1. , , ,
(1) Please calculate .
(2) Are events A and B independent?
2. A, B and C are three events. , , . What is the probability that at least one of the three events
will occur?
3. Simplify the following event
ME 776.01
Homework 3
1. Failure times for a randomly failing component are 3.3, 14.1, 26.9, 41.0 and 91.6 hours.
i) Using the median rank tables, plot the Cdf for failure F(t).
ii)
Using the results of Part (i) and curve fitting by the least-squares appro
ME 776.01
Homework 2
1. The probability of a jet fighter surviving an intense combat mission is 0.8, and three
fighters are needed for the success of the mission. How many fighters must be sent on the
mission in order to achieve a 95% probability of succe
Homework 4 Solution
ME 776.01
1.
Find the reliability function for the electric circuit shown below. You can assume that all the
components are identical with constant failure rate. Also, find the MTTF if there is no crosslink from Component C to F. Compa
ME/ECE.IE 776.01
Exam 1
Due October 27th , 2009 in class
1. The failure times for a device are uniformly distributed between 1,000 and
1,500 hours:
a) (10)Find the probability that the device will: i) survive for 1000 hours, ii)fail within
1,200 hours, an
Homework 4
1.
Find the reliability function for the electric circuit shown below. You can assume that all the
components are identical with constant failure rate. Also, find the MTTF if there is no crosslink from Component C to F. Compare the result to th
Supplementary Notes for Homework 2
For question 4 in Homework 2, please note that we are using an alternative expression of
the Logarithmic distribution. In this expression:
where and are the parameters used in the class notes and and are the parameters u
SOLUTIONS
ME/EE/ISE 776.01
Exam 1
October 28, 2008
1.
We are concerned with the reliability level of a new and yet untested launch vehicle. Eighty
percent of the design team believes that the vehicle reliability is R1=95% during the launch and
20% of the
Final Exam
ECE 776.01
December 7, 2009- 3:30pm to 5:18pm
1.
Consider the electric circuit shown below. You can assume that all the components are
identical with constant failure rate.
a) Find the reliability function for the circuit in terms of the compon
Problems discussed in class (September 20)
Problem 1 Assume two random variables X and Y are independent. X follows the
uniform distribution at 0 X 2 and Y follows the uniform distribution at 0 Y 1.
Z is another random variable and Z = XY. Please calculat
ME 776.01
Homework #3
Solutions
1. Failure times for a randomly failing component are 3.3, 14.1, 26.9, 41.0 and 91.6 hours.
Using the median rank tables, plot the Cdf for failure F(t).
ii)
Using the results of Part (i) and curve fitting by the least-squar
ME 776.01 Homework 1 Solution (Total marks are 85)
1. , , ,
(1) Please calculate . (5 points)
A: ;
Where
And
Thus
(2) Are events A and B independent? (5 pints)
A: From problem (1) we know that ,
On the other hand, ,
Thus A and B are not independent.
2. A,
Algebra of Events
A, B two events
null event (set)
universal event (set)
The algebra of events is fully dened by the following 5 laws
or axioms:
(1) CommutaCve Laws
A B = B A
A B = B A