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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

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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!