NASA Technical Reports Server (NTRS) 20130009067: Bayesian Approach for Reliability Assessment of Sunshield Deployment on JWST

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Bayesian Approach for Reliability Assessment of Sunshield
Deployment on JWST
Mark Kaminskly Lui. Gallo
NASA Goddard Spate Flight Center NASA Goddard Spate Flight Center
8800 Greenbelt Ro.d '8800 Greenbelt Road
Greenbelt, MD 20771 Greenbelt, MD 20771
301-614-5900 301-286-9147
Mark.P.Kaml. .k ly@n. ... gov LulLD.Gallo@n. ...g ov
John W. Evans
NASA Goddard Spate Flight Center
8800 Greenbelt Road
Greenbelt, MD 20771
301·286-9236
John.W.EvanS@nas• • gov
AlMtrwcl-Deploy.blo s.b.ystems are ....n tlal to mlsslo. I. INTRODUCTION
....... of moot .p....,raft. ThOle .ubl)'.tem. .....b.. crltl. .1
fan_. lachodiog power, .ODlIn~nicatlolll ••d thermal Deployable subsystems are essential 10 mission success of
control Th. Iou of any of thOle function. will ,o• •r all), result most spacecraft. The .. subsyslems enable critical functions
'n losl of the mlsll •. These subsYltems and theJr cornponents including power, communications and thermal conlrol. The
oIleD oo.li,t of onIque desigIOnsU a..n..d application., for whlob loss of any of these functions will generally resull in loss or
v.rI.... standardized data are a.it applicable for
signillcant deiJ1Odation of the mission [Freeman 1993, Saleh
OItlmaliag rell.blllty and for _010, risk •• In Ibl. ltody, a
and Castet 2011, de Selding 2012]. These subsystems and
Ba),OIlan .pproaoh for reliability OIIImatioa of .p. ...r .ft
deployment was doveloped for Ibl. purpolO. Th. . approsob was their components often consist of unique dctIigns and
tlte. .pplled to the James Webb Spa.. TeI• ••o pe (JWST) applications, for which various standardized data sourc .. are
Sa. .~ leId .ublystem, • .aIqae deolp latODded for tbnnal not applicable for estimating reliability and for assessing
con.trol of tile oblervatory'. telescope and Iclence Instrumentl. risks.
I. order to oolled the prior Informatloa on deployable l)'lltem.,
detailed ltudte. of "heritage foformatlon", were conducted., From the reliability standpoint, deployable subsystelDS are
extending over 45 years of .pao. ...f t launob... The NASA beat modeled as one-shot syslelDS, for which probability of a
Goddard Sp. .. FUght Center (GSFC) Spaeeeraft Opera_al fIIilurels\1CCC88 event is governed by the binomial
Anomaly aDd ReporlinK Sy..tem (SOARS) data ..e " Iben oued distribution. The mathematically correct classical
to eltlmate lbe parameten of the eoajugadve beta prior
(1iequentist) maximum likelihood (MI.) ..l imate of the
distributfon ror anomal), and raUure occurrence, u the mOlt
probability of deployment fatlure Pr is the simple common
.......t eBt lOt of .vaUabie data aad Ibat ...I d be malobed to
sense estimate which is given by
Iluooh """'rl... Thi. allow. for an emplrlea1 B.y. ....
.J
prediction for the rllk of an anomaly occurrence of the complex
Sunsbleld deployment, with eredlblllty IImlto, u.lag prior I P, = ~ ) (1)
deployment data Ind test Information.
where N is the total iiumber..,f-lrials (deployments), n is the
TABLE OF CONTENTS number ofunsucce8sfullrials, and P, is the estimate of the
Pr·
1.INTRODUCI10N ................................................ 1
2. BAYESIAN APPROACH TO RELIABILITY As a rule, one is interested in the upper (1 - a) confid=
limit on the probability of deploymenl failure, which is
ESTIMATION DEPI,OYABLE SUBSYSTEMS ••••••••••• 2
given as a solution with respect 10 P of the followins
3. PRIOR DATA SOURCES FOR DEPLOYABLE
equation
SUBSYSTEMS RELIABILITY ESTIMATION ............ 3
4. CASE STUDY - JWST SUNSHlELD I,_p (N - n, n + 1) S; a (2)
DEPLO'YMENT ...................................................... 3
where the incomplete beta function is given by [Lawles.,
5. SUMMARy. ........................................................ !
2003]
REl'ERENCF.S •• _ ................................................... 6
BIOGRAPHY ••••••....•.•.••.••••••••.•••.••...••••••••..•••••.....••• 6
u.s. Go~ work no< prottotod by u.s. copyrigllt
·
I["(Ht) r .-, (1- ,/,., ,- In the framework of the empirical Bayesian approach, the
'L',
r(a)"b)Jo" x (3) prior information might be a set of one-shot system
J,(d,h)= 0, ift<O failure/success data based on historical perfonnance. Let's
I. ift> .. assume we have ". trialll out which Xc are failures. In this
case, the conjugate prior distnbution i. the beta di.tnbution
with parameters 0 = Xc and P - n. -Xc. At this point, it is
and r(x) is the gamma function given by: important to note that the mean of the prior beta distribution
P,,,. . is given by
rea) = f.~ X4- 1 e-xdx (4)
(6)
2. BAYESIAN APPROACH TO RELIABILITY
which coincides with classical estimate (I) of the probability
ESTIMATION DEPLOYABLE SUBSYSTEMS
of deployment failure. Thus, if there are available data on
In the given Bayesian approach, the standard bela success/failure deployment ",Iated to some similar (from
distribution is applied .. the prior distribution of the engineering stan<lpoint) subsystems, these data can be used
probability of deployment failure. Its probability density to estimate the parameters of the beta prior distnbution. Note
function (PDF) is defined over the interval [0, 1], and it is that in this case, the beta distribution parameters are integer.
given by In the general case, e.g., when the prior distribution is
estimated based on expert knowledge, the parameters can
tt-' take on any positive values
r(a+&\t<H(1 OStSI,a>O,/I>O (5)
[V;Ot,P)= r(a)" -,
{ Next, let's ..s ume that we have the test deployment results
0, otherwl3t! .
(data) ",lated to the subsystem of interest, which are x
Note that depending on its parameters, the bets distribution failures out of" deployments (trials). Based on the Bayes'
has very different shapes .. illustrated by the Figure 1, thcorem, the posterior PDF of the probability of deployment
thereby allowing flexibility in cbaJacterizing UDCCItainty. failure can be written WI
[(PIx) r(n+n,) p(n~H (1-py-.~.H
r(x+x.)r(n+ .. -x-.... )
(7)
~: -;'--·--'-'-·--"-'-/-\l-a=o.~
3.0 which is obviously the PDF of the beta distribution.
2.5 . 1- \ " . --_ . ..,--- .
" \ ."" "'" ' \:1
l- - ·,,--·;- /l=O.5 The corresponding posterior mean (which is the Bayesian
-"-- ·-1 .. - -· ,
2.0 'i'" point estimate of the failure probability) is given by
~ a=lJl=l
f"' \- FV\ 1'.- 7o\-J' --1'
1.5 X+Xo
PB=-
1.0 ' : . \ a=1.5
n+~
'-'i--~-~=--:.:~':.:~.-3 (8)
0.5 /71-'_ ......: .. .. Jl=5
;1 .,..... "a=5 Jl~ It should be noted that when" » n. and x » x., the
0.0
.~~ I - - . __ • .-&A.. Bayesian estimate (8) is getting closer to the classical
o 0.5 1 estimate (I) based on the test data. In other words, the
--.~---------' cl_ical statistical inference tends to _d ominate over the
Figure I. Probability density functions ofbela distribution Bayesian one. Likewise, if no » • and Xc » x. the
Bayesian inference tends to dominate.
It is interesting that the standard UDifonn (flat) distribution is
a particular case of the beta distribution with 0 = 1 and P= 1. Based on the posterior PDF (7), the (I - a) upper limit PB ..
of Bayes' probability interval (the Bayesian analog of the
It should be noted that the beta distribution WI a prior classical upper confidence limit) is a solution of the
distribution in binomial probability estimation is the following equation with respect to P
co'!iugatlve distribution, which means that the posterior
estimate of interest is a1sp bets distributed. This allows for I.(x+x., n + no -x-x.} =0 (9)
by-passing complex numerical integrations.
Consider the following numerical example. Let the collected
In this study, the prior distribution is estimated based on prior information be summarized WI 100 deployments with,
some appropriate data. This approach is known 8S the say, 2 failures, i.e., •• = 100 and %. = 2. The test data for a
empirical Bayesian as opposed to Bayesian estinlation based given deployable subsystem is limited to to failure·free
on elicitation of expert opinion. deployments i.e., n = 10 and x - O.
In this case, based on the test data classical point estimate
(I) of probability of deployment failure is 0, which is not
very informative. The classical upper 90% confidence limit The SOARS records reflect NASA GSFC civil spacecmft
on the failure probability calculated using Equation (2) ;. developed and launched from 1978 to 2009. The data
0.206. reflected 19 failures including both mission ending and
failures which were overcome by operatioIia1 workarounds.
Based on the prior and test data, the regpective Bayesian During this period, 123 spacecraft were successfully
upper 90% limit is 0.035, which looks consistent with the launched into orbit by NASA GSFC. This provides the most
data it is based on. consiBtent data set for the construction of a prior distnbution.
Note that data were not segregated by severity for this
3. PRIOR DATA SOURCES FOR DEPLOYABLE example. This is of course an option in applying this
SUBSYSTEMS REUABILrrY ESTIMATION methodology to test design.
In analyzing deployments, several sources of information
4. CASE STUDY - JWST SUNSHIELD
may be used for the construction of a prior distnbution. In
DEPLOYMENT
this study, source. of data analyzed, included the NASA
Glenn Rl:sesrch Center's (GRC) Spacecrsft Mechanism The James Webb Space Telescope is the next generation
Handbook [Fusaro, 1998] and the GSFC SOARS. SOARS is space telescope, which will view deep space in the infrared,
a demonstnlted consistent source of historical data for beginning with its l.unch in 2018. JWST will be one of the
NASA GSFC projects [Robertson and Stoneking 2003]. This most complex deployable structures ever launched and will
provided a look at 45 years of deployment history. The total enable NASA to peer to the epoch of the formation of the
number of litilures reviewed included 53 known failures. very first luminous objects after the primordial Big Bang.
Figures 2 and 3 show a classification of all 53 failures by The JWST is shown in Figure 4, as it will be deployed in the
suba}'5tcms and assignable causes. Failures on the same Sun-Earth L2 orbit, in which it will conduct its mission.
spacecraft, appearing in both data sets, are treated as only
one failure. 4.1 The JWST Sunshield and its Deployment
Deptoyn\Intfllklr'l. b.y. .lW..I... o.f. D eIlJovH CDmpotl-'lt Central to the success of the mission is the sunshield
scwrs_GIlc ........ sln1cture, a tenniB court size, multi-layer, gOSlllmW film
structure, which enables the telescope and science
.".
....... • • inatruments to cool to cryogenic temperatures. while
blocking light from the sun.
I
-
, ... ~~ ... ,. .•. , ..,."...'. ~. . . .... " ..." ,,,... · ..' u .......... 1
~.
Figure 2. Classification of Failures by Deployed Component
Typ,e. -
o.plo.,mliM fill'" by Ass""IIbI. c.. .....
SOAlthnd 8RC ........
"
ij ll ••.•. _-'"'
Figure 3. Classification of Failures by Aasignable Causes.
Figure 4. The
Configuration Showing the Optical Telescope Element and
Studies to support documentation of lessons learned for the
Sunshield.
Spacccmft Mechanism Handbook reflect failures occurring
on mililary and civil spacecraft launched between 1964 and
The sunshield deployment from the stowed launch
1997. These data showed 34 failures. The exact population
configuration consists of ...v eral key steps. Figure 5 shows
of spacecraft is not known for these data. However, there
how the deployment progresses from the launch to
were approximately 1262 civil and military missions
operatioIia1 configurations. The deployment steps can be
launched by the United States in this period. With a few
classified into 3 major stages. This includes deployment of
exceptions, the data reflect largely mission ending failures,
the sln1ctural supports (I), membrane release (2) and
which were not overcome by operatioIia1 workarounds and
tensioning of the 5 membrane layers (3).
'may not represent a complete anorIia1y record. The failure
records can be examined in [Fusaro, 1998].
with respect to the test results. It can be explained by the
dominance of the prior information over the test data, which
is, to an extent, typical for the deployable syatems of
interest.
It should be noted that the B.yesian estimate of
probability of deploymcot failure can be updated DOt only as
Operational Configuration. a result of additional test runs, but also through updating the
prior information, as soon as DOW empirical data become
The SOARS records from 1978 through 2009 were analyzed available.
to generate a prior diBtribution for this anaIyais. Out of these
records, 123 missions were selected as having the
deployable subsystems, which can be used 88 the prior data
for the IWST sunabicld Bayesian reliability analyais. In 19 5, CONCLUSION
of these missions, deployable subayatem anomalies
In this paper we have presented an empiricaI Bayesian
occwred, ending the mission, degrading the mission or
creating an operational contingcocy. approach to anaIyais of deployment risk and reliability. The
deployable system is modeled as a one-shot syatem
In this case study, we are considering application of the governed by the binomial distribution. This allowed for the
Bayesian approach to test desigo. Let', 88sume that a test use of conjugate beta distnbutions to explicitly treat the
sequence of 10 deploymcots has been run and the test results uncertainties in the probability of success. The application is
are fililure free. Bued on the prior data, the prior PDF is demonstrated by an example test case using 10 deployment
depicted in Figure 6. sequeuees for a deployable system. This JnCthodology can
-. also be used to establish test cycles needed to achieve a
I particular risk or reliability target. The methodoIoay uses
, 14.0 r
data explicitly. However, the historical or other prior data
12.0 ," .... , - - -IP~ dor PDf can be expected to dominate the results of the posterior
I
:' 'i \\ '\ ......- , .....' <OrPDf estimates.
10.0 :
i
I : \
•.0 I ', t- \" \ ! ACKNOWLEDGEMENT
, \ l
6.0 i ,
\.. . . The auth013 wish to acknowledge the support of the James
42..00 !I!I , , ", ,.". . ,' , . FWliegbhbt SCpcaocteer T, Meler.s cJoope eR Pardoijcehc, tM atr t.h Me aNthAeSwA S Gamodudeal radn Sdp Dacr.e
........'. -~~. ~ ~ Paul Geithuer for their commeU!s and 8Up)lOrt, and Mr. Hung
o.D
Tran for his efforts in assisting us with SOARS.
o.05D D. ... 0,150 "200 D.2S0
Figure 6. Probability Density Functions of Prior and
Posterior Dimt'butions ofProbabi1ity of Deployment Failure.
The prior mean coinciding with the classical maximum
likelihood (ML) estimate (1) is 1~3 = 0.154. Using Equation
(8), the Bayesian point estimate is evaluated as
. 19 14
(10)
PB = 123+10 O. 3
Based on the prior and test data, the respective Bayesian
upper 90% limit is 0.182. Clearly, the minimum test
sequences to run for the syatem can be targeted bued upon
the desired risk reduction using this.a pproach.
Now, we 88sume that the test result is ODC fililure out of 10
deployment sequences. In this cue, the Bayesian point
estimate is 0.154 and the Bayesian upper 90% limit is 0.191.
If our anaIyais was limited to the cl88sical approach, we
could only compare the 90"10 upper confidcoce limit on
failure probability for 0 out of 10 test result with the test
having one failure out of 10, which are 0.205 and 0.337
respectively. We can see that using the prior data in the
Bayesian approach for reliability estimation is rather robust
REFERENCES Luis D. Gallo is an Aerospace
Engineer in the ReliabiJity and Risk
[I) Lawless, 1. Statistical models and methods fur Iifctime
Analysis branch of the NASA
data. 2"" edition. New York, Wiley-intenK:ieuce, 2003.
Goddard Space F1ig/u Center. He
holds a Bachelors ofSci8nce Degree
[2) Fusaro, R.L, NASA Space Mechanisma Handbook
in Electrical Engineering from
Lesson. Learned DocumeDIed, NASA Glen Research
Florida International University and
Center, 1998.
his research interests inc/ude
http://www.grc.P8Sl,govIWWWIRTIRTI99815OOOIS9S0fu
Bayesian inference in graphical models of spacecraft
saro·html. systems, machine learning as applied to reliability and
risk analysis and reliability and risk a""lysis as applied
[3) Freeman, M.T., Spacecraft On-Orbit Deployment
to machine learning.
ADomali ••: What Can Be Done? IEEE AES Systern5
Magazine, April 1993.
John W. Evans is a Senior
[4) Saleh, 1.R and Caste!, J., Spacecraft Reliability and Multi Aerospace Engineer in the
Stall: Failures, Wiley, 201. . Reliability and Risk ASsessment
Branch of the NASA Goddard Space
[5) de Selding, P. B., Probe of1S-19 Solar AnayProb!em Flight Center. . He is an
Focuses on Sea Launch Rocket, Space News, June 7, internationally recognized expert in
2012. reliability growth and its application
to complex systems. John is the
[6) RobertsoD, B. and Stoneking, R., SATEllITE GN&C author or coau/hor of several books and numerous
ANOMALY TRENDS, AAS 03-071. conference and journal articles on electronic system
reliability, failure analysis and manrifacturlng
Biographies technology.
Mark P. Kaminskiy is a Principal
Reliability Engineer at AllES
Corporation, Providing Reliability
Analysis support to the NASA
Goddard Space Flight Center. Dr.
Kaminskiy has served as the chief
statistician at the Center of
Technology and Systems
Management, Uniwrsi~\' qfMcllyland (College Park). He
is a researcher in reliability engineering, life data
analysis, and risk analysis ofe ngineering systems and has
conducted numerous ruearch and collSldting projects
foncJed by the government and industrial companies. He
has taught .everal graduale courses on reliability
engineering at the University of Maryland and is the
author or co-author of several books and many
publications in journals, conference proceedings, and
reports.