Chapter 4S – Problems 1-6 Note: This worksheet displays results only, you must copy the shaded
<Back area into the corresponding template to make additional calculations.
1a. T4-1: Reliability
1b. T4-1: Reliability
0.90 0.90
0.90 0.90
1c. T4-1: Reliability
0.90 0.90
0.9000 0.9000
0 0 2 2
System
2. T4-1: Reliability
1 1 1 1
System
3. T4-1: Reliability
0 1 1 1
System
5a. T4-1: Reliability
5b. T4-1: Reliability
0.9300
0.9300
5c. T4-1: Reliability
0.9114
0.9300
0 0 0 2
6a. T4-1: Reliability
1 1 1 1
6b. T4-1: Reliability
0.9000
1 1 1 2
6c. T4-1: Reliability
0.9200
Chapter 4S – Problems 7-13 Note: This worksheet displays results only, you must copy the shaded
<Back area into the corresponding template to make additional calculations.
0.9900 0.9600 0.9300
#1
T4-1: Reliability
0.8839
0.8839
#2
T4-1: Reliability
0.9900 0.9600 0.9300
0.9900 0.9600 0.9300
8a. T4-1: Reliability
0.8662
0.8839
0 0 0 2
System
Reliability
0.9845 0.9844684
8b. T4-1: Reliability
11. T4-1: Reliability
0.9000
0.8000
0.7000
0 0 0 3
System
Reliability
12a. MTBF – Exponential Distribution
MTBF = 30 MTBF = 30 MTBF = 30
T = 39 T = 48 T = 60
DT = 1DT = 1DT = 1
0 2 2 2
System
Reliability
MTBF = 30 MTBF = 30 MTBF = 30
T = 33 T = 15 T = 6
DT = 1DT = 1DT = 1
12c. MTBF – Exponential Distribution
MTBF = 30 MTBF = 30 MTBF = 30
T = 20.79 T = 56.92 T = 89.88
DT = 0.01 DT = 0.01 DT = 0.01
T / MTBF = 0.693 T / MTBF = 1.8973333 T / MTBF = 2.996
P(failure before T) = 0.4999264 P(failure before T) = 0.850032 P(failure before T) = 0.9500134
P(failure after T) = 0.5000736 P(failure after T) = 0.149968 P(failure after T) = 0.0499866
MTBF = 30
T = 138.16
T / MTBF = 4.6053333
P(failure before T) = 0.9900016
P(failure after T) = 0.0099984
13a. MTBF – Exponential Distribution
MTBF = 30
T = 30
DT = 1
T / MTBF = 1
P(failure before T) = 0.6321206
P(failure after T) = 0.3678794
T / MTBF = 1.1 T / MTBF = 0.5 T / MTBF = 0.2
P(failure before T) = 0.6671289 P(failure before T) = 0.3934693 P(failure before T) = 0.1812692
P(failure after T) = 0.3328711 P(failure after T) = 0.6065307 P(failure after T) = 0.8187308
DT = 1
Chapter 4S – Problems 14-22 Note: This worksheet displays results only, you must copy the shaded
<Back area into the corresponding template to make additional calculations.
14a. MTBF – Exponential Distribution
MTBF = 20000
T = 24000
DT = 1000
b. MTBF – Exponential Distribution
MTBF = 20000
T = 4000
DT = 1000
15a. MTBF – Exponential Distribution
MTBF = 6
T = 9
DT = 1
15b. MTBF – Exponential Distribution
MTBF = 6
T = 12
DT = 1
15d. MTBF – Exponential Distribution
MTBF = 6
T = 21
DT = 1
16a. Service Life – Normal Distribution
Service life mean = 41
Service life std dev = 4
T = 38
DT = 1
16b. Service Life – Normal Distribution
Service life mean = 41 Service life mean = 41
Service life std dev = 4 Service life std dev = 4
T = 40 T = 45
DT = 1DT = 1
16c. Service Life – Normal Distribution
Service life mean = 41 Service life mean = 41
Service life std dev = 4 Service life std dev = 4
T = 39 T = 43
DT = 1DT = 1
17a. Service Life – Normal Distribution
Service life mean = 6 Service life mean = 6 Service life mean = 6
Service life std dev = 0.5 Service life std dev = 0.5 Service life std dev = 0.5
T = 5 T = 6 T = 7.5
DT = 1DT = 1DT = 1
17b. Service Life – Normal Distribution
Service life mean = 6
Service life std dev = 0.5
T = 4
DT = 1
18. Service Life – Normal Distribution
Service life mean = 6 Service life mean = 6
Service life std dev = 0.5 Service life std dev = 0.5
T = 4.974 T = 5.178
DT = 0.001 DT = 0.001
19. Availability
20. Availability
MTBF = 50
MTR = 2
Availability = 0.9615385
21. Availability
MTBF = 142 MTBF = 65
MTR = 7 MTR = 2
Availability = 0.9530201 Availability = 0.9701493
22. Availability
MTBF = 100 MTBF = 105 MTBF = 100
MTR = 4 MTR = 4 MTR = 3.6
Availability = 0.9615385 Availability = 0.9633028 Availability = 0.965251
MTR = 3 MTR = 6
Availability = 0.9302326 Availability = 0.9803922