Reliability
CHAPTER 4S
RELIABILITY
PROBLEMS
P1.
A system has four components, A, B, C, D. The probability that each component will work is
P(A) =.90, P (B) = .70, P (C) =.95, and P (D) = .60; all components must operate in order for the
system to work.
Since the probabilities associated with components B and D are low, backup
components, B-B and D-D, with the same probabilities are provided:
a.
Draw the box and line diagram for this system.
b.
What is the probability that each component will not work?
c.
What is the probability that the system will work without the backup components?
d.
List the ways in which the system can work with the backup components.
e.
What is the probability that the system will work with the backup components?
f.
How much improvement in reliability do the backup components provide?
P2.
A simple system consists of three components, A. B, C, as shown below, with the probability that
each component will work.
Component A costs $20,000 each, B costs $10,000 each, and C costs
$6,000 each.
>
P (A) = .99
P (B) = .99
P (C) = .75
>
a.
What is the probability that the system will work?
b.
Management wishes to have at least a .95 probability that the system will work, and proposes
to achieve this goal by adding redundant component C’s to the system, which are identical to
the existing component C.
Each new C would switch on if the preceding C’s failed.
How
many C’s will be required?
c.
Draw the diagram of the new system.
d.
How much will it cost to achieve a .95 probability by adding C’s?
P3.
The mean operating life (MTBF) of TV picture tubes is 4,000 hours, and the failure rate of the
tubes can be modeled by a negative exponential distribution.
Use Table 4S-1 in your textbook, or
use the
e
x
function on your calculator to solve these problems.
a.
Determine the probability that a picture tube
will fail
within 3,200 hours.
b.