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

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

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

Calculating Failure Rate For Example TIME = 0 50 100 150 200 HOURS FAIL Car 1 [----------X-----------X----------X-------------] 200 3 Car 2 [---------------X---------------------------------] 200 1 Car 3 [----------X-----------] 100 1 500 5 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

Calculating Mean Time Between Failure For Example TIME = 0 50 100 150 200 HOURS FAIL Car 1 [----------X-----------X----------X-------------] 200 3 Car 2 [---------------X---------------------------------] 200 1 Car 3 [----------X-----------] 100 1 500 5 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

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

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 = 0.001 + 0.005 + 0.01 System Failure Rate = 0.016 System FR = ? Subsystem 1 FR = 0.001 Subsystem 2 FR = 0.005 Subsystem 3 FR = 0.01

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 = 1/1000 + 1/200 + 1/100 System Failure Rate = 0.001 + 0.005 +0.01 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 = ?

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 = 1000 FR = 1/1000 = 0.001 MTBF = 200 FR = 1/200 = 0.005 MTBF = 100 FR = 1/100 = 0.01 System FR = 0.001 + 0.005 + 0.01 = 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) = 0.004 + 0.01 + 0.01 = 0.024 Divide Total FR x MTTR product by System Failure Rate System MTTR = 0.024 / 0.016 = 1.5

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

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 = 0.8019 R = 0.8019

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

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

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-.008 = .992 R(100) = e-.01 = .904 R(500) = e-.5 = .606 R(1000) = e-1 = .367 R(2000) = e-2 = .135 R(t) = e-failure rate x time

Questions Answered Here! Patrick M. Dallosta CPL Defense Acquisition University 9820 Belvoir Road Ft. Belvoir, VA 22060 patrick.dallosta@dau.mil (703) 805-3119