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Problems:
1. Consider the following system:
Determine the probability that the system will perform correctly under the following
scenarios:
a. The system as shown above.
b. Each system component has a backup with a probability of .90 and a switch
that is 100 percent reliable
c. Each system component has a backup with .90 reliability and a switch that is
.98 reliable
2. UNCW’s admissions department has experienced quality problems lately. An
investigation shows that each freshman application must pass through four
separate and distinct offices. Two of the offices have recorded reliability levels of
.96 and the other two offices have recorded reliability levels of .99.
a. What is the overall reliability that an application will be reviewed
successfully?
b. If step 1 which currently has .96 reliability, was given a backup with .96
reliability, what would be the resulting overall reliability of reviewing a
freshman application?
c. How else could the overall reliability be improved?
3. The Romba floor cleaning system is controlled by a computer that has three
major modules. In order for the product to work all three modules function
properly. Two of the modules have reliabilities of .97; the other module has a
reliability of .99.
a. What is the reliability of the floor cleaning system?
b. A backup computer identical to the one in place will be installed in
premium models to improve overall reliability. Assuming the backup
will function automatically if the main one fails, what would be the
resulting reliability?
c. If the backup computer requires a switch to activate it when the main
computer fails, and the switch has reliability of .98, what is the overall
reliability of the system?
4. A service has four major components required for completion and delivery to the
consumer. The component reliabilities are, .90, .94, .95, and .98. All four
components must be preformed for the service to take place.
a. What is the reliability of the current service offering?
b. The boss wants to improve reliability by providing a backup. Because
he/she is cheap they have informed you that they will only backup one of
the four components with a identical component. (The backup will have
the same reliability as the component it is replacing). Which component
should get the backup in order to achieve the highest reliability?
c. If one backup that has a reliability of .93 can be added to any of the
main components, which one should get it to achieve the highest overall
reliability?
.90
.90
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