1. LOG 211 Supportability Analysis “Reliability 101”
April 18, 2018

2. What is Reliability? Reliability Language
Mean Time Between Failure (MTBF)
Failure Rate
Other??
Formal Definition of Reliability
Reliability is the probability that a system will successfully complete a specified task under specific conditions over a specified period of time.
Four Parameters
Probability
Task
Conditions
Time

3. What is a Failure Rate?
A rate is a specific kind of ratio, in which two measurements are related to each other.
Time
Aircraft 1 failure in 6,000 flight hours
Miles
Tank 1 failure in 100 miles / 2000 operating hours
Rounds/Launches
Cruise 1 failure in 100 launches
Other
Storage 10% of the system failure rate

4. Calculating Failure Rate
For Example
TIME = HOURS FAIL
Car [ X X X ]
Car 2 [ X ]
Car 3 [ X ]
Add the total number of failures - 5
Add the total number of hours - 500
Divide the total failures by the total hours
FAILURE RATE is 5 failures/500 hours = .01 failures/hour

5. Calculating Mean Time Between Failure
For Example
TIME = HOURS FAIL
Car [ X X X ]
Car 2 [ X ]
Car 3 [ X ]
Add the total number of failures - 5
Add the total number of hours - 500
Divide the total hours by the total failures
MEAN TIME BETWEEN FAILURE = 500 hours / 5 failures = 100 hours

6. How are MTBF and Failure Rate related?
Given MTBF or Failure Rate, can I calculate the other?
Failure Rate = Total Failures / Total Hours
Failure Rate = 5 failures / 500 hours = 0.01 failures/hours
MTBF = Total Hours / Total Failures
MTBF = 500 hours / 5 failures = 100 hours/failure
MTBF = 1/ Failure Rate
Failure Rate = 1/ MTBF

7. Calculating System Level Failure Rate
Failure Rates (FR) are added to obtain a system failure rate.
System Failure Rate = Subsystem 1 FR + Subsystem 2 FR + Subsystem 3 FR
System Failure Rate =
System Failure Rate = 0.016
System
FR = ?
Subsystem 1
FR = 0.001
Subsystem 2
FR = 0.005
Subsystem 3
FR = 0.01

8. Calculating Mean Time Between Failure
Mean Time Between Failure (MTBF) is a mean (average).
MBTFs cannot be added.
System MTBF is calculated by:
Converting Subsystem MTBFs to Subsystem Failure Rates
Adding the Subsystem Failure Rates to get the System Failure Rate
Taking the reciprocal of the System Failure Rate
System MTBF = 1/Subsystem 1 MTBF + 1/Subsystem 2 MTBF + 1/Subsystem 3 MTBF
System Failure Rate = 1/ / /100
System Failure Rate =
System Failure Rate = 0.016
System Mean Time Between Failure = 1/System Failure Rate = 1/0.016 = 62.5
Subsystem 1
MTBF = 1,000
Subsystem 2
MTBF = 200
Subsystem 3
MTBF = 100
System
MTBF = ?

9. How do I calculate Mean Time To Repair (MTTR)?
System
FR = 0.016
MTBF = 62.5
MTTR = ?
Assembly A
FR = .001
MTBF = 1000
MTTR = 4.0
Assembly B
FR = .005
MTBF = 200
MTTR = 2.0
Assembly C
FR = .01
MTBF = 100
MTTR = 1.0
Calculate System MTBF
Add individual failure rates
MTBF = FR = 1/1000 = 0.001
MTBF = FR = 1/200 = 0.005
MTBF = FR = 1/100 = 0.01
System FR = = 0.016
System MTBF = 1/0.016 = 62.5
Calculate System MTTR
Multiple individual Assembly FR x MTTRs
(0.001 x 4.0) + (0.005 x 2.0) + (0.01 x 1.0) =
= 0.024
Divide Total FR x MTTR product by System Failure Rate
System MTTR = / = 1.5

10. Reliability Block Diagrams
A Reliability Block Diagram is a graphical representation of how system components are “connected” in relation to successful performance.
1. Series Configuration
3. Combination Series and Parallel Configurations
2. Parallel Configuration

11. Reliability Block Diagram Calculations
Given
A = B = C = 0.9
Then
R = A x B x C
R = 0.9 x 0.9 x 0.9 = 0.729
R = 0.729
1. Series Configuration
2. Parallel Configuration
Given
A = B = C = D = 0.9
Then
R = A x B/D x C
R(B/D) = 1- [(1-0.9) x (1-0.9)]= 0.99
R = 0.9 x 0.99 x 0.9 =
R =

12. Reliability Block Diagram Calculations
3. Combination Series and Parallel Configurations
CLASS EXERCISE

13. What is the Reliability Life Cycle?
The “Bath Tub Curve”
The Bath Tub Curve illustrates how
failure rates change over a design’s
life cycle
Three (3) distinct periods of time
Infant Mortality/Burn-In
Decreasing failure rates as
defects are eliminated
Useful Life
Constant failure rate
no ‘pattern failures”
Wear-out
Increasing failure rate
Materials fail

14. How do I calculate Reliability?
The Bath Tub Curve’s “Useful Life” identifies the design’s “Constant Failure Rate”
During this period, the exponential distribution is used to calculate reliability
Given:
MTBF = 1,000 hours
Mission time = 8 hours
R(8) = e-.001 x 8
R(8) = e = .992
R(100) = e = .904
R(500) = e = .606
R(1000) = e = .367
R(2000) = e = .135
R(t) = e-failure rate x time

15. Questions Answered Here!
Patrick M. Dallosta CPL
Defense Acquisition University
9820 Belvoir Road
Ft. Belvoir, VA 22060
(703)