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1
Impact of Decisions Made to Systems Engineering:
Cost vs. Reliability System
David A. Ekker
Stella B. Bondi
and Resit Unal
November 4-5, 2008
HRA INCOSE CONFERENCE, NEWPORT NEWS, VIRGINIA
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Presentation Outline
Introduction Problem Statement Methodology Analysis Operational Impacts Strategies Conclusions
3
Introduction
Impact on decisions made in terms of cost and reliability
Selection of strategy for maintaining an operational system
Decisions made are faced with trade-off between cost and operational reliability.
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Problem Statement
Background
Basic System
System requirements
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Background Mission Critical Systems must assure:
Operation Safety
Critical operable subsystem in process of being replaced
Obvious reduction in its MTBF of ~80% Continuous increasing repair costs Scarcity of parts Technical repair knowledge declines Concerns that the subsystem will fail at critical
times where safety would be impacted.
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Basic System
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System Requirements
Dual, independently operation systems providing data for operations
Operating 24/7 with output verified and compared to each other
A third system checks periodically the dual system
When System–3 is not available, Systems 1 & 2 become critical which means abort of operations for safety assurance.
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Solution’s Goals
Investigate Various Strategies
Optimize Reliability
Evaluate Related Cost
Minimize decision maker’s intuition
Use a more precise cost vs. reliability mechanism
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Methodology
Data collection
Determine data distribution and equation parameters
Select strategies for analysis
Calculate system reliability using distribution equations
Compare costs of the various strategies
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Estimate Distribution Parameters
Little data available
Weibull probability distribution was the best option of approximation for reliability
The basic form of the Weibull equation is
Where θ is the scale and m is the shape parameter
x
mxxF 0exp1)(
Reliability vs. Time
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Operational Constraints
Both SYSTEM-1 and SYSTEM-2 fail and no spares are available, then all operations are aborted until both systems are replaced
Failure of either SYSTEM-1 or SYSTEM-2 will result in aborting operations. It is assumed that these situations are predictable in advance.
The overall system is expected to operate on a long term schedule and this schedule is available for planning purposes.
In certain situations, aborting operations can result in long transit times to a location where spare parts are available.
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Operational Constraints (Cont’d)
Not carrying spares adds additional expense of storage at a central facility and/or shipping costs.
Carrying spares incurs a penalty for storage and weight.
Aborting certain operations require another system to be immediately dispatched to cover operations and can result in costs on the order of 100 times the cost of a spare module – predictable situations.
The life cycle cost only involved purchase and refurbishment cost, it did not include costs of lost operations.
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Strategies
Carry no spare Carry one spare Carry two spares Refurbish equipment at a pre-determined time
equivalent to carrying one spare Refurbish equipment at a pre-scheduled time
coordinated with manufacturer and set at time between missions
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Analysis of Strategies
The life cycle cost versus reliability normalized to the least expensive strategy
Key contributing factor to the overall system reliability is infant mortality for the carrying spares
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Discussion Of Strategies: Option 1
Repair When Fails (Baseline)
Lowest reliability for both situations - unacceptable
Least repair cost
Greatest adverse operational results
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Discussion Of Strategies: Option 2 Carry One Spare
Significant improvement in reliability42% higher costReliability still low when two operating
systems are required (0.45)
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Discussion Of Strategies: Option 3 Carry Two Spares
Further reliability improvement over carrying one spare, approx. 2x reliability when 2 systems are required
Greatest cost (84.5% higher)Acceptable reliability (0.99, 0.97)
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Discussion Of Strategies: Option 4 Refurbish at 62.5% MTBF
Compared to carrying one spare:Same costSame reliability as for carrying one spare Nearly 2x reliability for 2 Units operatingPredictability of repairs
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Discussion Of Strategies: Option 5
Refurbish at 58.3% MTBF10% increase in cost than option 4Best reliabilityLines up with repair cycleLeast operational impact
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Planned vs. Corrective Maintenance
StrategyNormalized
Cost
Worst Case Reliability Experienced
SYSTEM-1 OR SYSTEM-2 operating
SYSTEM-1 AND SYSTEM-2 operating
Carry no spare 1.00 0.4500 0.0710
Carry 1 spare 1.42 0.9890 0.4530
Carry 2 spares 1.85 0.9996 0.9710
Refurbish at 62.5% MTBF
1.42 0.9900 0.8200
Refurbish at 58.3% MTBF
1.56 0.9958 0.8752
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0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
At least one coremodule operating
Both core modulesoperating
Both core modulesOperating - 2 Spares
At least one core moduleOperating - 1 Spare
Reliability vs. Age with SparesR
elia
bili
ty
Normalized Age, % MTBF
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Conclusions
Variation in key parameters can be used to check for the sensitivity of operating guidelines provided
If strategy coincides with normally scheduled maintenance periods, less operational impact will result
Selecting the proper strategy can be critical for maintaining system reliability and subsequent mission success, yet, not necessarily resulting in significant cost increases
Our analysis indicates that a reliability versus cost trade-off may be achievable
Future Work
There are many cost vs performance studies, yet few cost vs reliability.
Develop a metric that provides a cost per reliability so as to compare strategies
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THANK YOU!