1. 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, The cause was the failure of a single eyebar in the suspension chain, due to a defect 0.1 inch deep.
Week 9 - Systems Engineering
System Wide Requirements – The ‘Ilities’
Reliability
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2. Worst case reliability - Engineering disasters…
AT&T Network Crash story (See )
Kansas City Hotel story (See for example )
Challenger (discussed here)
AT&T network map

3. The Ilities Reliability – Quality Interoperability Usability
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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4. 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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5. 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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6. 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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7. 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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8. 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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12. 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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16. Three Aspects of Reliability
Analysis – how to quantify, equations
Testing – how to test
Prediction – how do I know in advance
We’ll look at analysis first 
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17. Measures of Reliability (B&F 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) = At t = ∞, F(t) = 1.0.
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18. R(t) for Exponential distn.
Integral from t to infinity is “the rest of the probability” beyond t, i.e., the probability it didn’t 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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19. Resulting R(t) function
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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20. Failure rate and MTBF R(t) = = l = 1/q = 1/MTBF
l is “instantaneous failure rate”
M or q are MTBF.
l = 1/q = 1/MTBF
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21. Wasson MTTF
Light bulb failures
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22. 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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23. 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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24. 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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25. Exponential Distn f(t) = e-t See figure 12.1 errors
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26. Failure and Hazard Rates
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27. 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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28. 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 =
MTBF= ?? (This is a prediction for all.)
MTBF = 1/ = 836 hours. (See slide 20.)
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29. Reliability Nomograph - Fig 12.3
For exponential distribution.
Relationship between MTBF, l, R(t).
Example : MTBF is 200 hrs (l=0.005) and operating time is 2 hrs – then R(t) =0.99
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30. l = 1/q = 1/MTBF
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31. Failure Rates vs. Life
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32. Wasson – Bathtub Curve
‘Burn-in’ of electronics devices
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33. Wasson – Electronic Equip
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34. 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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35. Series Networks Series components – all must function.
R = (RA ) (RB ) (RC) (multiply R’s)
R = (add l’s)
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36. 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 )
What is MTBF for the series system ??
Total lambda is 1/ / / /3200.
Then do 1000 * that to get the value for 1000 hours.
See next slide!
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37. Solution A B C D
MTBF
6000
4500
10500
3200 λ
9.52E-05 R
Prod Rs
Sum the λ’s
e– 1000 *
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38. Parallel Networks R = RA + RB – (RARB)
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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39. Reliability and Redundancy
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40. Series and Parallel Networks
Figure Reduce parallel blocks to equivalent series element.
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41. 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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42. 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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43. A Common Service Shop Finding – NTF, no trouble found
Figure 12.11
How to calculate MTBF, MTBM ??
MTBF – 58 failed ?
MTBM – 100 ‘failed’ ?
A Common Service Shop Finding – NTF, no trouble found 43
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44. Service Life Extension
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45. 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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46. 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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47. MTBFs have to get larger
Reliability Flow Down
Series : Add lambdas
Series : Add lambdas
MTBFs have to get larger
- See slide 33
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48. Boeing Flowdown Example
KPP = Key Performance Parameter
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49. 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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50. Redundant Subsystems
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51. 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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52. UA232
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53. 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 for one standby.
R(standby) > R(operating)
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54. Sample Problem - Standby
One operating, one standby (identical)
200 hrs operating period, l = per hr.
Calculate R (standby)
Calculate R (operating) assuming both operating.
Switch R = ? (100% ?)
Why Standby > Operating ??
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55. 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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56. Cause and Effect Chart
Graphical document of possible causes for an effect (problem, error, fault).
Usually consider ‘5M’s + E’ as main branches.
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57. FMEA Steps – Review Team activity
Select component, system, process step, etc.
Identify possible failure modes.
Identify causes of failure modes.
Identify effects of failures.
Estimate (1-10 ranking):
Occurrence – how often (1=not, 10=often)
Severity – how bad (1=not, 10=severe)
Detection – how easy (1=easy, 10=difficult)
Calculate RPN – risk priority number
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58. Reliability Prediction
Predict based on similar equipment – easy but inaccurate.
Predict from Parts Count
Predict from Life/Stress Analysis
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59. Example – Parts Count where: n = Number of part categories
Ni  = Quantity of ith part
λ= Failure rate of ith part
π= Quality Factor of ith part(handbook)
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60. MTBF = 1/l where: n = Number of part categories
Ni  = Quantity of ith part
λ= Failure rate of ith part
π= Quality Factor of ith part(handbook)

61. Reliability Testing - 12.6 Part of test and qualification.
Assure that MTBF requirements are met.
Testing :
Either accept, reject, continue test (Fig )
Test under simulated mission profile (Fig 12.31)
‘Run some tests’ – how confident are we in the results ??
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62. Sequential Test Plan
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63. Simulated Mission Profile
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64. Reliability Testing-2
Establish criteria for accept, reject, and risks of false decisions.
Equations 12.29, Determine regions for accept, reject, continue, with defined acceptance risks.
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65. Example MIL-STD Fig
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66. Actual Test Conditions – Fig. 12-33
MTBF=400
Max time = 4000
Failures noted and fixed.
Accept at 3200 hrs.
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67. Test Results
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