Cost Considerations Based on Reliability of Inertial Navigation System

					HRA INCOSE CONFERENCE, NEWPORT NEWS, VIRGINIA




Impact of Decisions Made to
   Systems Engineering:
 Cost vs. Reliability System
                 David A. Ekker
                 Stella B. Bondi
                 and Resit Unal

              November 4-5, 2008
                                                1
Presentation Outline

   Introduction
   Problem Statement
   Methodology
   Analysis
   Operational Impacts
   Strategies
   Conclusions


                          2
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.



                                                3
Problem Statement

   Background

   Basic System

   System requirements




                          4
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.

                                                            5
Basic System




               6
    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.

                                                   7
Solution’s Goals

   Investigate Various Strategies
   Optimize Reliability
   Evaluate Related Cost
   Minimize decision maker’s intuition
   Use a more precise cost vs. reliability
    mechanism



                                              8
    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

                                                       9
    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
                        x m
                            
      F ( x)  1  exp                       0 x
                          
                             
        Where θ is the scale and m is the shape parameter


                                                            10
Reliability vs. Time
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.

                                                        12
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.

                                                       13
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


                                             14
    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

                                                        15
Discussion Of Strategies: Option 1

    Repair When Fails (Baseline)
         Lowest reliability for both situations -
          unacceptable
         Least repair cost
         Greatest adverse operational results




                                                     16
Discussion Of Strategies: Option 2
    Carry One Spare
        Significant improvement in reliability
            42% higher cost
            Reliability still low when two operating
             systems are required (0.45)




                                                        17
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)




                                                       18
Discussion Of Strategies: Option 4
   Refurbish at 62.5% MTBF
       Compared to carrying one spare:
           Same cost
           Same reliability as for carrying one spare
           Nearly 2x reliability for 2 Units operating
           Predictability of repairs




                                                          19
Discussion Of Strategies: Option 5
   Refurbish at 58.3% MTBF
        10% increase in cost than option 4
        Best reliability
        Lines up with repair cycle
        Least operational impact




                                              20
 Planned vs. Corrective Maintenance

                                   Worst Case Reliability Experienced
                 Normalized
  Strategy                      SYSTEM-1 OR        SYSTEM-1 AND SYSTEM-
                    Cost
                              SYSTEM-2 operating        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
                    1.42            0.9900                  0.8200
62.5% MTBF

Refurbish at
                    1.56            0.9958                  0.8752
58.3% MTBF
                                                                        21
 Reliability vs. Age with Spares
                                                         Both core modules
                                                         Operating - 2 Spares
               1

              0.8
Reliability




                                                          At least one core module
              0.6
                                                          Operating - 1 Spare
              0.4
                         Both core modules                   At least one core
              0.2
                         operating                           module operating
               0
                    0   0.2    0.4      0.6   0.8    1        1.2     1.4

                                     Normalized Age, % MTBF


                                                                            22
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

                                                            23
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
THANK YOU!




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