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.
Week 9 - Systems Engineering
and Analysis
System Wide Requirements – The ‘Ilities’
Reliability
1
Engineering disasters…
• AT&T Network Crash story (last week’s links)
• Kansas City Hotel story (ditto)
• Challenger (tonight’s slides)
AT&T network map
2
The Ilities
• Quality
• Reliability –
•
•
•
•
•
– Blanchard and Fabrycky – Ch 12
– Wasson – Ch 50
Interoperability
Usability
Maintainability
Serviceability
Producibility and Disposability
3
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 ?
4
The Second ‘Ility’ - Reliability
•
Our focus –
1.
2.
3.
4.
5.
Reliability Definitions.
Series and Parallel Systems.
Reliability Improvement Methods.
Reliability Prediction and Testing.
Risk (Ch. 19)
5
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.
6
Reliability vs. Quality
• Reliability :
• Quality :
includes passage of time.
static descriptor.
• 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.
7
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’.
•Launch ‘reliability’ calculated as 0.87 at 31 deg F. (0.98 at 60 deg F).
8
9
10
11
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 as 0.87 at 31
deg F. (0.98 at 60 deg F).
12
13
14
15
Three Aspects of Reliability
• Analysis – how to quantify, equations
• Testing – how to test
• Prediction – how do I know in advance
16
Measures of Reliability (12.2)
• 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.
17
R(t) for Exponential distn.

• R(t) = 1 – F(t) =
 f (t )dt
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.
t
• If ‘time to failure’ is (assumed to be)
defined by Exponential Function (Constant
Failure Rate) then –
f(t) =
1

e (  t / )
18
Resulting R(t) function
• R(t) =
t /
e
• Mean life () is average lifetime of all
items considered.
• For exponential distribution, MTBF is .
19
Failure rate and MTBF
• R(t) =
e
 lt
t / M
=
e
 l is instantaneous failure rate
• M or  are MTBF.
 l = 1/ = 1/MTBF
20
Wasson MTTF
Light bulb failures
21
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
22
The Failure Rate
• Failure Rate is:
• Number of Failures/Total Operating Hrs
• Failure rate expressed as failures per
hour, failures per million hours, etc.
27
Failure Rate Example
• 10 Components tested for 600 hrs.
Component Failure (hrs)
1
75
2
125
3
130
4
325
5
525
• Failure Rate per hr, l = 5/4180 = 0.001196
• MTBF= ??
28
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
29
l = 1/ = 1/MTBF
R=e
 lt
30
Failure Rates vs. Life
31
Wasson – Bathtub Curve
‘Burn-in’ of electronics devices
32
Wasson – Electronic Equip
33
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.
34
Series Networks
• Series components – all must function.
• R = (RA ) (RB ) (RC)
(multiply R’s)
• R=
 ( l A  l B ... l n ) t
e
A
B
(add l’s)
C
35
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 ??
36
Parallel Networks
• Parallel components – all must fail for
system to fail.
A
B
• R = RA + RB – (RARB)
C
• R = 1 – (1 – RA) (1 – RB) (1 – RC)…
– (n components)
38
Reliability and Redundancy
39
Series and Parallel Networks
• Figure 12.10Reduce parallel
blocks to
equivalent series
element.
40
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
41
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
42
Figure 12.11
• How to calculate
MTBF, MTBM ??
• MTBF – 58 failed ?
• MTBM – 100 ‘failed’ ?
A Common Service
Shop Finding – NTF,
no trouble found
43
Service Life Extension
44
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.
45
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.
46
Reliability
Flow
Down
Series : Add lambdas
Series : Add lambdas
MTBFs have to
get larger
- See slide 33
47
Reliability Prediction
1. Predict based on similar equipment – easy
but inaccurate.
2. Predict from Parts Count
3. Predict from Life/Stress Analysis
58
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)
59
where:
n = Number of part categories
Ni = Quantity of ith part
λ= Failure rate of ith part
π= Quality Factor of ith part(handbook)
MTBF = 1/l
60
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 ??
61
Sequential Test Plan
62
Simulated
Mission
Profile
63
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.
64
Example
MIL-STD-781
Fig. 12.32
65
Actual Test Conditions –
•
•
•
•
Fig. 12-33
MTBF=400
Max time = 4000
Failures noted and fixed.
Accept at 3200 hrs.
66
Test
Results
67