Reliability Prediction

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Reliability Prediction

• A Quest for Reliable Parameters

By Yair Shai
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Goals

• Compare the MTBCF MTTCF parameters in view of
  complex systems engineering.
• Failure repair policy as the backbone for
  realistic MTBCF calculation.
• Motivation for modification of the technical
  specification requirements.

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Promo Description of Parameters
time
t1
t2
t3
t4
t5
.......
r Number of Failures
? Failure Event of an Item
Repairable Items Mean Time Between Failures
Semantics ?
Non Repairable Items Mean Time To Failure

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MTBF MTTF ??
An assumption Failed item returns to As
Good As New status after repair or renewal.
note Time To Repair is not considered.
UP
TIME
DOWN
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Critical FailuresMoving towards System Design

• A System Failure resulting in (temporary or
  permanent) Mission Termination.

X
COMPUTER
A simple configuration of parallel hot
Redundancy.
SUBSYSTEM
X
COMPUTER
A Failure any computer failure A Critical
Failure two computers failed
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Critical Failures
A clue for Design Architecture
MTBCF Mean Time Between Critical Failures
MTTCF Mean Time To Critical Failure
SAME? Remember the assumptions
Determining the failure repair policy COLD
REPAIR No time for repair actions during the
mission
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Functional System Design
Operational Demand At least two receiver units
and one antenna should work to operate the
system.
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From System Design to Reliability Model
A
ANT
CPU
PS1
INDEPENDENT BLOCKS
B
ANT
CONT
PS2
sw
x
C
ANT
CPU
PS1
x
x
D
ANT
2 / 4
Is this a Critical Failure ?
Serial model Rs R1x R2
Parallel model Rs 1- (1-R1)x(1-R2)
K out of N model Rs Binomial Solution
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From RBD Logic Diagram to Reliability Function
Simple mathematical manipulation
Rsys(t) f( serial / parallel / K out of N)
Classic parameter evaluation
WARNING !!!
Is this realistic ?
MTTCF
MTBCF
After each repair of a critical failure - The
whole system returns to status As Good As New.
S.Zacks, Springer-Verlag 1991, Introduction To
Reliability Analysis, Par 3.5
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MTBCF vs. MTTCFA New Interpretation
First
Common practice interpretation MTBCF MTTCF
MTTCFF Each repair Resets the time count to
idle status (or) Each failure is the first
failure.
Realistic interpretation MTBCF MTTCF Only
failed Items which cause the failure are repaired
to idle. All other components keep on aging.
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Presentation I
Simple 3 aging components serial system model
HAD WE KNOWN THE FUTURE
A
B
C
A
3
2
1
2
B
3
2
2
3
1
C
3
2
1
1
1
TTCF
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Presentation II
Simple 3 aging components serial system model
HAD WE KNOWN THE FUTURE
A
B
C
A
4
3
2
1
B
2
1
3
C
1
3
2
4
TBCF
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Presentation III
Simple 3 aging components serial system model
HAD WE KNOWN THE FUTURE
A
B
C
A
4
3
2
1
B
2
1
3
C
1
3
2
4
TBCF
MTBCF lt MTTCF
A
3
2
1
2
B
3
2
2
3
1
C
3
2
1
1
1
TTCF
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Simulation Method
MONTE CARLO
MATHCAD
MIN (X1,1 X2,1 X3,1)
MIN (X1,1 X2,1 X3,1)
MIN (X1,2 X2,2 X3,2)
MIN (X1,2 ?1,2 ?2,2)
N100,000 SETS
N100,000 SETS
.
.
MIN (X1,N X2,N X3,N)
MIN (X1,N ?1,N ?2,N)
_________________
_________________
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How BIG is the Difference ?
1. Depends on the System Architecture.
2. Depends on the Time-To-Failure
distribution of each component.
3. The difference in a specific complex
electronic system was found to be 40
Note True in redundant systems even when all
components have constant failure rates.
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Why Does It Matter ?
Suppose a specification demand for a systems
reliability MTBCF 600 hour
Suppose the manufacturer prediction of the
parameter MTBCF 780 hour
-40
X
ATTENTION !!! How was it CALCULATED ????
Is this MTBCF or MTTCF ????
Real MTBCF 480 lt 600 (spec)
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Example 1
Aging serial system each component is weibull
distributed
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??????? ??????? ??? ??? ???????
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??????? ??????? ??? ??? ???????
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??????? ??????? ??? ??? ???????
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Example 2
Two redundant subsystems in series each
component is exponentially distributed
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Constant failure rate
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Constant failure rate
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A Comment about Asymptotic Availability
()
() S.Zacks, Springer-Verlag 1991, Introduction
To Reliability Analysis, Par 4.3
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Repair policies

• Hot repair is allowed for redundant components.
• All components are renewed on every failure
  event.
• All failed components are renewed on every
  failure event.
• Failed components are renewed only in blocks
  which caused the system failure.
• Failed subsystems are only partially renewed.

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Conclusions

• System configuration and distribution of
  components determine the gap.
• Repair policy should be specified in advance to
  determine calculation method.
• Flexible software solutions are needed to
  simulate real MTBCF for a given RBD.
• Predict MTBCF not MTTCF