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Copyright 2016 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE342.html

Product AssuranceSpace System Design, MAE 342, Princeton University

Robert Stengel

• Assembly, Integration, and Verification

• Dependability• Reliability• Task Planning• Quality Assurance

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Failure Analysis of Cygnus CRS Orb-3Orbital Sciences Antares 130

• Possible causes– Manufacturing defect in

turbopump AerojetRocketdyne AJ-130 motor

• Refurbished EnergomashNK-33 motor from stockpile

• Built in 1970s– Design flaw in hydraulic

balance assembly and thrust bearings

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Assemble, Integrate, and Verify

• Verify– Demonstrate compliance with goals

• Qualification of design• Acceptance of hardware

– Methods• Test• Analysis• Inspection• Design Review

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– System Level• Spacecraft• Module or sub-system• Unit• Equipment or component

Fortescue, Ch. 17

• Integrate– Make it function

• Assemble– Build spacecraft

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Manage Risk

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Classify Risk

5http://www.riskbusinessamericas.com/Public.IndustryRiskProfiles.aspx

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6http://www.riskbusinessamericas.com/Public.IndustryRiskProfiles.aspx

Assess Risk

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Spacecraft Product Assurance• Origins

– Industrial Revolution– Formal quality assurance during WWII

• Evolution– Standards and certification methods borrowed

from USAF, ABMA– See Lecture 24 Course Materials on Blackboard

• Special problems– Extremes of operating conditions– Length of unattended operation– Inaccessibility for maintenance

7Fortescue, Ch. 19

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Saturn V Second StageIntegral serial tanks, with

common bulkhead

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Principles and Definitions for Product Assurance

• Quality• Basis for quality assessment• Proof of quality

10Fortescue, Ch. 19

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Objectives and Project Phases

11Fortescue, Ch. 19

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Overlapping Issues

12Fortescue, Ch. 19

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Task Planning

Situation awarenessDecomposition and identification of communities

Development of strategy and tacticsPhaseProcess Outcome

Objective Tactical (short-term)

Situation Assessment

Situation Awareness

Strategic (long-term)

Comprehension Understanding

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Boyd’s “OODA Loop”for Combat Operations

Derived from air-combat maneuvering strategy

General application to learning processes other than military

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Endsley, 1995

Elements of Situation Awareness

• Perception• Comprehension• Projection

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Important Dichotomies in Planning

Strength, Weakness, Opportunity, and Threat (SWOT) Analysis “Knok-Knoks” and “Unk-

Unks”

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Program Management: Gantt ChartProject schedule

Task breakdown and dependencyStart, interim, and finish elements

Time elapsed, time to go

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Program Evaluation and Review Technique (PERT) Chart

MilestonesPath descriptors

Activities, precursors, and successorsTiming and coordination

Identification of critical pathOptimization and constraint

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-ilities• Dependability

– Availability– Maintainability– Security

• Reliability– Qualitative– Quantitative– Design or predicted– Operational

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Parts Procurement• Vendors’ track record• Standardization• Procurement systems

– Organization– Documentation

• Substitution of less reliable equivalents

• Out-of-date/specification parts20

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Materials and Processes

21Fortescue, Ch. 19

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Materials to Avoid

22Fortescue, Ch. 19

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Material Problems in Orbit

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Materials Problems within Parts

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Product Assurance in Manufacturing

• Controls and Records• Training and certification• Traceability• Measurement and calibration• Non-conformance control• Alerts, handling, … margins• Audits

25Fortescue, Ch. 19

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Non-Conformance Control

26Fortescue, Ch. 19

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Technology Readiness Levels

27Fortescue, Ch. 19

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Product Assurance and Safety in Operations

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Reliability of a Component

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R = e−λtIf failure rate is constant,

Also see Lecture 17 slides for reliability assessment

where failure rate is estimated as

λ =1 MTBF (repairable system)

1 MTTF (non-repairable system)

⎧⎨⎪

⎩⎪

MTBF : Mean time between failuresMTTF : Mean time to failure

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Failure Rate, λ

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Expected number of failures per unit time

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Reliability Enhancement• Use of redundancy• Design diversity• Limitation of failure effects• De-rating of parts• Radiation screening• Handling/assembly controls• Inspection/testing

31Fortescue, Ch. 19

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Reliability Analysis Techniques• Failure state probabilities• Worst-case analysis

– https://en.wikipedia.org/wiki/Worst-case_circuit_analysis• Failure modes and effects analysis

– https://en.wikipedia.org/wiki/Failure_mode_and_effects_analysis• Fault tree analysis

– https://en.wikipedia.org/wiki/Fault_tree_analysis• Contingency analysis

– What to do when failure occurs

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Probability Distributions

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Relative Frequency of Discrete, Mutually Exclusive Events

• N = total number of events• ni = number of events with value xi

• I = number of different values• xi = ordered set of hypotheses or values

Pr xi( ) = niN

in [0,1]; i = 1 to I

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Pr xi( )i=1

I

∑ = 1N

nii=1

I

∑ = 1

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Cumulative Probability, Pr(x ≥/≤ a), and Discrete Measurements of a

Continuous Variable

Suppose x represents a continuum of colorsxi is the center of a band in x

00.10.20.30.40.50.60.70.80.9

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1 2 3 4 5

Pr(x)Cum Pr(x) ≥ aCum Pr(x) ≤ a

Pr xi ± Δx / 2( ) = ni / N

Pr xi ± Δx / 2( ) = 1i=1

I

∑35

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Probability Density Function, pr(x)Cumulative Distribution Function,

Pr(x <X)Probability density function

Pr x < X( ) = pr x( ) dx−∞

X

∫

Cumulative distribution function

pr xi( ) = Pr xi ± Δx / 2( )Δx

Pr xi ± Δx / 2( ) = pr xi( ) Δxi=1

I

∑ Δx→0I→∞

⎯ →⎯⎯ pr x( ) dx−∞

∞

∫ = 1i=1

I

∑

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Probability Density Function, pr(x) Cumulative Distribution Function,

Pr(x <X)

Pr x < X( ) = pr x( ) dx−∞

X

∫

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Properties of Random Variables

• Mode– Value of x for which pr(x) is maximum

x = E(x) = x pr x( ) dx−∞

∞

∫

• Median– Value of x corresponding to 50th percentile– Pr(x < median) = Pr(x ≥ median) = 0.5

• Mean– Value of x corresponding to statistical average

• First moment of x = Expected value of x

“Moment arm”

“Force”

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Expected Values

• Second central moment of x = Variance– Variance from the mean value rather than from zero– Smaller value indicates less uncertainty in the value

of x

σ x2 = E x − x( )2⎡⎣ ⎤⎦ = x − x( )2 pr x( ) dx

−∞

∞

∫

x = E(x) = x pr x( ) dx−∞

∞

∫

• Mean Value is the first moment of x

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Mean Value and Variance of a Uniform Distribution

Variance

If xmin = −xmax ! a

σ x2 = 1

2ax2 dx

−a

a

∫ = x3

6a −a

a

= a2

3 40

pr(x) =

01

xmax − xmin0

;x < xmin

xmin < x < xmaxx > xmax

⎧

⎨⎪⎪

⎩⎪⎪

x = xxmax − xmin( ) dxxmin

xmax∫ = 12xmax + xmin( )

Mean

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Gaussian (Normal) Random Distribution

pr(x) = 12π σ x

e−x− x( )2

2σ x2

E(x) = x pr x( ) dx−∞

∞

∫ = x

Variance

Units of x and σx are the same

Unbounded, symmetric distributionDefined entirely by its mean and standard

deviation

E x − x( )2⎡⎣ ⎤⎦ = x − x( )2 pr x( ) dx−∞

∞

∫ = σ x2

Mean value; from symmetry

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Probability of Being Close to the Mean

(Gaussian Distribution)

• Probability of being within

Pr x < x +σ x( )⎡⎣ ⎤⎦ − Pr x < x − σ x( )⎡⎣ ⎤⎦ ≈ 68%

• Probability of being within

• Probability of being within

Pr x < x + 2σ x( )⎡⎣ ⎤⎦ − Pr x < x − 2σ x( )⎡⎣ ⎤⎦ ≈ 95%

Pr x < x + 3σ x( )⎡⎣ ⎤⎦ − Pr x < x − 3σ x( )⎡⎣ ⎤⎦ ≈ 99%

±1σ x

±2σ x

±3σ x

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Experimental Determination of Mean and Variance

Divisor is (N – 1) rather than N to produce an unbiased estimate

x =xi

i=1

N

∑N

Sample variance for same data set

σ x2 =

xi − x( )2i=1

N

∑N −1( )

Sample mean for N data points, x1, x2, ..., xN

Histogram

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Log-Normal Distribution

xl ! log x

pr(xl ) =1

σ l 2πe−xl−xl( )2σ l

2

• Variation in large ensembles for which x > 0

• The logarithm of x is Gaussian

• Replace x by xl in previous equations

Pr(xl ) =121+ erf xl − xl

σ l 2⎛⎝⎜

⎞⎠⎟

Probability Density Function

Cumulative Probability Function

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Weibull Distribution

pr(x) = bθ − xo

⎡

⎣⎢

⎤

⎦⎥x − xoθ − xo

⎡

⎣⎢

⎤

⎦⎥

b−1⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪e−x−xo( )bθ−xo( )b

Pr(x) = 1− e−x−xo( )bθ−xo( )b

• Variation in life characteristics of parts or components

• Variation in large ensembles for which x > 0

Probability Density Function

Cumulative Probability Function

xo : expected minimum valueb : shape or slope parameter (k in figure)

θ : characteristic life or scale parameter (λ in figure)45

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Exponential Distribution

pr(t) = 1θe−

tθ

Pr(t) = 1− e−tθ

λ = 1θ : failure rate

• Special case of Weibulldistribution, with b = 1, xo = 0, and x = t

• Time to failure of systems or parts

• Modeling of independent events that occur at a constant average rate

Probability Density Function

Cumulative Probability Function

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Poisson Distribution

pr(r = ri ) =e−λyri

ri !

• Occurrence of isolated, independent events whose average rate is known– Number of events can be

observed– Number of non-events cannot be

observed• Examples:

– Number of machine breakdowns in a plant

– Number of errors in a drawing

Probability Mass Function

Cumulative Probability Function

λ : average number of occurrences47

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Binomial Distribution

�

pr(r) =nr

⎛

⎝ ⎜ ⎞

⎠ ⎟ prqn−r =

nr

⎛

⎝ ⎜ ⎞

⎠ ⎟ pr 1− p( )n−r

wherenr

⎛

⎝ ⎜ ⎞

⎠ ⎟ = n!

r! n − r( )!n = number of trialsp = probability of successq = probability of failure

• The probability of rsuccessful outcomes in ntrials

• Examples: inspection of parts, probability that a system will operate correctly

Probability Mass Function

Cumulative Probability Function

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Confidence Level• The probability that a probability

estimate is correct, e.g.,

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“The likelihood of failure is 90%, with a confidence level of 95%”

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Trials Required to Estimate Probability Depend on Confidence Interval

1e+01

1e+03

1e+05

1e+07

1e+09

1e-06 1e-05 1e-04 0.001 0.01 0.1 1

2%5%10%20%

100%

Num

ber o

f Eva

luat

ions

0.5

IntervalWidth

Probability or (1 - Probability)Binomial Distribution

Required number of trials depends on outcome probability and desired confidence interval 50

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How Will You Estimate the Likelihood of Success for Project

2020 UA?

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MAE 342, Space System Design

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