Assignment1 IENG 4562
IENG 4562 Maintenance Engineering and Management
September 17th, 2014
Alireza Ghasemi
Assignment #1
(Chapter 1 &2)
1. Find the Laplace transform of the following functions:
a. f(t) = ? ?/2 ???(?)
b. h(t) = ? −5? + 2? 3?+1 − 9
2. A smoke detector is routinely inspected. Eighty percent of the detectors found inoperative had experienced a power surge, and twenty percent of those found in operating condition had experienced a power surge. 10 percent of the detectors inspected have failed. What is the probability of a detector failing given it experiences a power surge?
3. Having the following hazard rate for the time to failure of a component (in operating hours): λ(t) =
a.
b.
c.
d.
e.
0.4t
t≥0
Find all other three functions that characterize a failure process (i.e. The cumulative distribution function , the reliability function, the probability density function)
What is the component reliability for a 10-hr operating life?
What is the design life if a reliability of 0.975 is desired?
What is the probability of a failure occurring within 10 & 30 hour of operation?
Find the MTTF
4. The PDF for the time to failure in years of a Regional Transit bus is given by: f(t) = 0.3 – 0.04t
a.
b.
c.
d.
0 ≤ t ≤ 10 yr
Show that the hazard rate function is increasing, indicating continuous wear out over time.
Find the MTTF, the median time to failure, and the standard deviation
What is the reliability for the first year of operation?
If the bus has an 16 month burn-in period, for a desired reliability of 0.95, how much the design life will increase/decrease?
5. A new fuel injection system is experiencing high failure rates. The reliability function has been found to be
1
R(t) = (? + 1/2)−3/2
t≥0
a. What is the design life for a reliability of 0.95
b. If we want to increase the design life for a desired reliability of 0.90, what is the minimum burn-in period (if it exists)?
6. The time to failure of a typical household refrigerator has the following PDF: f(t) = 0.009? 2 −
September 17th, 2014
Alireza Ghasemi
Assignment #1
(Chapter 1 &2)
1. Find the Laplace transform of the following functions:
a. f(t) = ? ?/2 ???(?)
b. h(t) = ? −5? + 2? 3?+1 − 9
2. A smoke detector is routinely inspected. Eighty percent of the detectors found inoperative had experienced a power surge, and twenty percent of those found in operating condition had experienced a power surge. 10 percent of the detectors inspected have failed. What is the probability of a detector failing given it experiences a power surge?
3. Having the following hazard rate for the time to failure of a component (in operating hours): λ(t) =
a.
b.
c.
d.
e.
0.4t
t≥0
Find all other three functions that characterize a failure process (i.e. The cumulative distribution function , the reliability function, the probability density function)
What is the component reliability for a 10-hr operating life?
What is the design life if a reliability of 0.975 is desired?
What is the probability of a failure occurring within 10 & 30 hour of operation?
Find the MTTF
4. The PDF for the time to failure in years of a Regional Transit bus is given by: f(t) = 0.3 – 0.04t
a.
b.
c.
d.
0 ≤ t ≤ 10 yr
Show that the hazard rate function is increasing, indicating continuous wear out over time.
Find the MTTF, the median time to failure, and the standard deviation
What is the reliability for the first year of operation?
If the bus has an 16 month burn-in period, for a desired reliability of 0.95, how much the design life will increase/decrease?
5. A new fuel injection system is experiencing high failure rates. The reliability function has been found to be
1
R(t) = (? + 1/2)−3/2
t≥0
a. What is the design life for a reliability of 0.95
b. If we want to increase the design life for a desired reliability of 0.90, what is the minimum burn-in period (if it exists)?
6. The time to failure of a typical household refrigerator has the following PDF: f(t) = 0.009? 2 −