Week 9 - Systems Engineering

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Week 9 - Systems Engineering
How bad can a weakest link problem be? This is
the Silver Bridge at Point Pleasant, WV, which
collapsed into the Ohio River during rush hour on
Dec 15, 1967. The cause was the failure of a
single eyebar in the suspension chain, due to a
defect 0.1 inch deep.

• System Wide Requirements The Ilities
• Reliability

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Worst case reliability - Engineering disasters

• ATT Network Crash story (See http//users.csc.cal
  poly.edu/jdalbey/SWE/Papers/att_collapse.html. )
• Kansas City Hotel story (See for example
  http//ethics.tamu.edu/Portals/3/Case20Studies/Hy
  attRegency.pdf. )
• Challenger (discussed here)

ATT network map
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The Ilities

• Quality
• Reliability
• Blanchard and Fabrycky, Systems Engineering and
  Analysis, 4th Ed. Ch 12
• Wasson Ch 50
• Interoperability
• Usability
• Maintainability
• Serviceability
• Producibility and Disposability

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The Ilities-2

• All are System Wide in Scope.
• All are desirable system outcomes.
• Technical, engineering, mathematical definitions
  behind each one.
• Included as Technology and System-Wide
  requirements when critical enough.
• How to measure and quantify ?

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The Second Ility - Reliability

• Our focus
• Reliability Definitions.
• Series and Parallel Systems.
• Reliability Improvement Methods.
• Reliability Prediction and Testing.
• Risk (Ch. 19)

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Definition of Reliability

• The reliability of an item is the probability
  that it will adequately perform its function for
  a specified period of time.
• Time is involved
• specify units hrs, miles, etc.
• specify time duration.

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Reliability vs. Quality

• Reliability includes passage of time.
• Quality a static descriptor.
• Or, may include Reliability as one component
• High reliability implies high quality converse
  not true.
• Tire example
• Ones made in 1960 and 2000.
• Both high quality wrt current standards
• New ones last longer more reliable.
• Microsoft example
• Quality means three dimensions Reliability,
  Feature Set, and Schedule!

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Reliability Example

• Space Shuttle Challenger accident on January 28,
  1986.
• O-Rings sealed the joints in the solid rocket
  motors.
• Engineers used two O-rings one for backup.

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Launch Details

• During flight, the rocket casing bulges which
  widens the gap between sections.
• Due to low temperature and bulging effect both
  O-rings failed resulting in accident. (not
  independent systems).
• Launch reliability calculated (after the
  accident) as 0.87 at 31 deg F. (but 0.98 at 60
  deg F).

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Three Aspects of Reliability

• Analysis how to quantify, equations
• Testing how to test
• Prediction how do I know in advance
• Well look at analysis first ?

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Measures of Reliability (BF 12.2, Wasson Ch 50)

• Reliability Function, R(t) probability that
  system will be successful for some time period t.
• R(t) 1 F(t)
• F(t) is the failure distribution or
  unreliability function.
• Like, what are the odds of the system staying
  up for a year?
• At t 0, R(t) 1.0. At t 8, F(t) 1.0.

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R(t) for Exponential distn.
Integral from t to infinity is the rest of the
probability beyond t, i.e., the probability it
didnt fail up to time t.

• R(t) 1 F(t)
• If time to failure is (assumed to be) defined
  by Exponential Function (Constant Failure Rate)
  then
• f(t)

Like, if half fail in year 1, then half of the
remaining ones will fail in year 2, etc.
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Resulting R(t) function

• R(t)
• Mean life (q) is average lifetime of all items
  considered.
• For exponential distribution, MTBF is q.

This is the accumulated value, what you get doing
the integration.
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Failure rate and MTBF

• R(t)
• l is instantaneous failure rate
• M or q are MTBF.
• l 1/q 1/MTBF

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Wasson MTTF
Light bulb failures
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Wasson MTBF

• Wasson suggests
• MTBF MTTF MTTR
• Mean Time Between Failures
• Mean Time To Failure
• Mean Time To Repair
• Since MTTR is small, MTBF approx MTTF

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Systems Perspective of Failures

• A failure is any event where system is not
  functioning properly.
• Failures may be classified as primary, secondary,
  etc. (Table 12.1).
• Wasson suggest MIL-HBDK-470A failure of
  mission critical items.
• Systems engineers must consider all failure modes
  and types.

Failure distributions consider many modes of
failure therefore are often difficult to
characterize
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Useful fact

• If a system has a constant failure rate, the
  reliability of that item at its mean life is 37.
• 37 probability that it will survive to its mean
  life without failure.

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Exponential Distn f(t) e-tSee figure 12.1
errors
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Failure and Hazard Rates
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The Failure Rate

• Failure Rate is
• Number of Failures/Total Operating Hrs
• Failure rate expressed as failures per hour,
  failures per million hours, etc.

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Failure Rate Example

• 10 Components tested for 600 hrs.
• So the other 5 lasted the full 600 hours.
• Total of 4180 hours in the test, for all 10.
• Failure Rate per hr, l 5/4180 0.001196
• MTBF ?? (This is a prediction for all.)

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Reliability Nomograph - Fig 12.3

• For exponential distribution.
• Relationship between MTBF, l, R(t).
• Example MTBF is 200 hrs (l0.005) and operating
  time is 2 hrs then R(t) 0.99

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l 1/q 1/MTBF
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Failure Rates vs. Life
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Wasson Bathtub Curve
Burn-in of electronics devices
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Wasson Electronic Equip
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Reliability of Component Relationships

• Engineers assemble systems from components and
  sub-systems.
• How to analyze the reliability of the whole
  based on structure and component reliabilities.
• Two simple structures series and parallel.

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Series Networks

• Series components all must function.
• R (RA ) (RB ) (RC) (multiply Rs)
• R (add ls)

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Sample Problem Series

• Series system of four components, expected to
  operate to 1000 hrs.
• MTBFs
• A (6000 hrs), B(4500), C(10500), D(3200)
• What is R for the series system ??
• (Ans. 0.4507)
• What is MTBF for the series system ??

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Solution
  A B C D
MTBF 6000 4500 10500 3200
? 0.000167 0.000222 9.52E-05 0.000313 0.000797 0.450847
R 0.846482 0.800737 0.909156 0.731616
Prod Rs 0.450847
Sum the ?s
e 1000 0.000797
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Parallel Networks

• Parallel components all must fail for system to
  fail.
• R RA RB (RARB)
• R 1 (1 RA) (1 RB) (1 RC)
• (n components)

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Reliability and Redundancy
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Series and Parallel Networks

• Figure 12.10- Reduce parallel blocks to
  equivalent series element.

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Sample Problems

• Figure 12.10 a and c.
• RA 0.99
• RB 0.96
• RC 0.98
• RD 0.92
• RE 0.8
• RF 0.8

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Related Figures of Merit (FOM)

• Mean Time Between Maintenance MTBM
• Scheduled
• Unscheduled
• Availability A
• Probability that system when used under stated
  conditions in ideal/actual operational
  environment will operate satisfactorily.
• Wasson RAM
• Reliability
• Availability
• Maintenance

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Figure 12.11

• How to calculate MTBF, MTBM ??
• MTBF 58 failed ?
• MTBM 100 failed ?

A Common Service Shop Finding NTF, no trouble
found
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Service Life Extension
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Reliability and System Life Cycles section 12.3

• What Reliability should the System have to
  accomplish mission, over life cycle, under
  expected environment.
• Requirements that affect reliability
• System performance factors,
• Mission profile,
• Use conditions, duty cycle, etc.
• Environment temp, vibration, etc.

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Review of Key Concepts

• Ilities are System Wide Requirements.
• Specify Reliability as MTBF, MTBM, R(t),..
• Flow down/allocate top level requirements to
  functional blocks (Fig 12.16,17)
• We have functional architecture.
• We have series/parallel tools to do this.

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Reliability Flow Down
Series Add lambdas
Series Add lambdas
MTBFs have to get larger - See slide 33
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Boeing Flowdown Example
KPP Key Performance Parameter
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Ways to Manage/Improve Reliability

• Failure Analysis
• Component Selection
• Pick standardized components.
• Evaluate prior to acceptance.
• Custom parts/testing takes time money.
• Part Derating
• Electrical part concept.
• Operate at lower conditions, longer life.
• Redundancy

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Redundant Subsystems
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Ways to Manage/Improve Reliability-2

• Redundancy
• Parallel paths higher reliability.
• But- penalties of weight, space, cost, etc.
• Must truly be independent systems.
• (Buede pg. 242, Sioux City Plane crash)
• Genesis spacecraft
• Often cannot be applied, or on limited basis.

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UA232
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Ways to Manage/Improve Reliability-3

• To now have considered Operating Redundancy
  all subsystems working.
• Standby redundancy if A fails, switch to and
  operate B. B not operating while A operates.
• Equation 12.27 for one standby.
• R(standby) gt R(operating)

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Sample Problem - Standby

• One operating, one standby (identical)
• 200 hrs operating period, l 0.002 per hr.
• Calculate R (standby)
• Calculate R (operating) assuming both operating.
• Switch R ? (100 ?)
• Why Standby gt Operating ??

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Reliability Analysis Methods Section 12.4

• FMECA failure mode, causes, effects, and
  criticality analysis.
• Identify failure modes early.
• Focus on high risk/problem items.
• Stress/strength analysis
• Operate at critical/maximum stress conditions.
• Identify weak, critical components.

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Cause and Effect Chart

• Graphical document of possible causes for an
  effect (problem, error, fault).
• Usually consider 5Ms E as main branches.

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FMEA Steps Review

1. Team activity
2. Select component, system, process step, etc.
3. Identify possible failure modes.
4. Identify causes of failure modes.
5. Identify effects of failures.
6. Estimate (1-10 ranking)
7. Occurrence how often (1not, 10often)
8. Severity how bad (1not, 10severe)
9. Detection how easy (1easy, 10difficult)
10. Calculate RPN risk priority number

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Reliability Prediction

1. Predict based on similar equipment easy but
   inaccurate.
2. Predict from Parts Count
3. Predict from Life/Stress Analysis

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Example Parts Count
where  n Number of part categories  Ni 
Quantity of ith part ? Failure rate of ith part
p Quality Factor of ith part(handbook)
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MTBF 1/l
where  n Number of part categories  Ni 
Quantity of ith part ? Failure rate of ith part
p Quality Factor of ith part(handbook)
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Reliability Testing - 12.6

• Part of test and qualification.
• Assure that MTBF requirements are met.
• Testing
• Either accept, reject, continue test (Fig. 12.30)
• Test under simulated mission profile (Fig 12.31)

Run some tests how confident are we in the
results ??
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Sequential Test Plan
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Simulated Mission Profile
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Reliability Testing-2

• Establish criteria for accept, reject, and risks
  of false decisions.
• Equations 12.29, 12.30. Determine regions for
  accept, reject, continue, with defined acceptance
  risks.

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Example MIL-STD-781 Fig. 12.32
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Actual Test Conditions Fig. 12-33

• MTBF400
• Max time 4000
• Failures noted and fixed.
• Accept at 3200 hrs.

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Test Results