components. Components’ reliabilities are .97, .95, .94, and .91. All of the components must
function in order for the robot to operate effectively.
a. Compute the reliability of the robot. (Round your answer to 4 decimal places.)
Reliability
b1.
Designers want to improve the reliability by adding a backup component. Due to space
limitations, only one backup can be added. The backup for any component will have the
same reliability as the unit for which it is the backup. Compute the reliability of the
robot. Which component should get the backup in order to achieve the highest reliability?
(Round your answers to 4 decimal places.)
Reliability
Component 1
Component 2
.
Component 3
.
Component 4
.
Planetary Communications, Inc., intends to launch a satellite that will enhance reception of
television programs in Alaska. According to its designers, the satellite will have an expected
life of six years. Assume the exponential distribution applies.
T / MTBF
0.10
0.20
0.30
0.40
0.50
0.60
0.70
e-T / MTBF
.9048
.8187
.7408
.6703
.6065
.5488
.4966
T / MTBF
2.60
2.70
2.80
2.90
3.00
3.10
3.20
e-T / MTBF
.0743
.0672
.0608
.0550
.0498
.0450
.0408
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
.4493
.4066
.3679
.3329
.3012
.2725
.2466
.2231
.2019
.1827
.1653
.1496
.1353
.1255
.1108
.1003
.0907
.0821
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
5.00
.0369
.0334
.0302
.0273
.0247
.0224
.0202
.0183
.0166
.0150
.0136
.0123
.0111
.0101
.0091
.0082
.0074
.0067
Determine the probability that it will function for each of the following time periods:
your intermediate calculations to 2 decimal places and final answers to 4 decimal
places.)
a.
More than 9 years.
T
>9
e-T/MTBF
.2231
b.
Less than 11 years.
T
e-T/MTBF
<11
c.
More than 9 years but less than 11 years.
T
e-T/MTBF
9<T<11
d.
At least 25 years.
T
>25
e-T/MTBF
