Cost Considerations Based on Reliability of Inertial Navigation System

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```					HRA INCOSE CONFERENCE, NEWPORT NEWS, VIRGINIA

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
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)

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

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

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!

25

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