Assignment 5
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University of North Texas *
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Course
5130
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
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Uploaded by MajorOryxPerson702
MSET 5130.002
Assignment 5
Spring 2024
1.
A system consists of three identical components. For the system to perform as intended, all the
components must perform. Each component has the same probability of performance. If the system
is to have .92 probability of performing, what probability of performance is needed by each of the
individual components?
2.
The following data shows the number of failures of 1,000 units of an electronic component in time
intervals of 100 hours. a. Compute the failure rate during each time interval as a proportion of numbers that survived until the
beginning of that interval. What can you conclude about the failure rates? b. Calculate the MTTF for this component. 3.
A product is composed of four parts. For the product to function properly, each of the parts must
function. Two of the parts each have 0.96 probability of functioning, and the other two each have
probability of 0.99. What is the overall probability that the product will function properly?
4.
One of the industrial robots designed by a leading producer has four major components.
Components’ reliability is 0.98, 0.95, 0.94, and 0.90. All the components must function for the robot to
operate effectively. If one backup with a reliability of .92 can be added to any one of the main components, which
component should get it to achieve the highest overall reliability?
5.
A type of light bulb has a life that is Exponentially distributed with a mean of 5,000 hours. Determine
the probability that one of these light bulbs will last: a.
At least 6,000 hours. b.
No longer than 1,000 hours. c.
Between 1,000 hours and 6,000 hours.
MSET 5130.002
Assignment 5
Spring 2024
6.
A machine can operate for an average of 50 days before it needs to be overhauled, a process that
takes two days. Calculate the availability of this machine.
7.
A car has four independent and identical tires. The reliability of a tire is .99. If any tire is flat, the car
cannot be driven. Calculate the reliability of a car with respect to its tires.
8.
A designer estimates that she can (1) increase the average time to failure of a product by 5 percent at
a cost of $450, or (2) reduce the average repair time by 10 percent at a cost of $200. Which option
would be more cost-effective? Currently, the average time to failure is 100 hours and the average
repair time is 4 hours.
9.
Five units of an electronic component were subjected to stress testing until they failed. 4 The
observed failure times (in days) were 550, 680, 820, 910, and 1,110. Calculate the MTTF and the
failure rate for this component.
10.
A weather satellite has expected life of 10 years from the time it is placed into Earth’s orbit. Determine
its reliability for each of the following lengths of service (assume that Exponential distribution is
appropriate.) a. 5 years b. 12 years c. 20 years d. 30 years
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