Reducing Test Cost of Infrared Detectors: A Machine Learning Approach to Failure Prediction of Infrared Detectors

) 8 1 0 2 S M S M C ( s c it s it a t S l a c it a m e h t a M d n a n o it a l u m i S , g n il e d o M ,l a n o it a t u p m o C n o e c n e r e f n o C l a n o it a n r e t n I 8 1 0 2 8 7 9 : N B S

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1_{AcademyofMathemaitcsandSystemScience,ChineseAcademyofSciences,Beiijng,China}

2_{Schoo lofMathemaitca lSciences,UniverstiyofChineseAcademyofSciences,Beiijng,China}

3_{BeiijngInsttiuteofControl Engineer,Beiijng,China}

g n i d n o p s e r r o C

* author

: s d r o w y e

K Infrareddetector, Logisitcregressionmodel, Two-stageprediciton, Reducingtestcost.

t c a r t s b

A . Iti simportantt oensuretheinfrareddetectorswil lworkproperlyinpractica lapplication, o

s aseriesoftests mus tbecarriedoutbeforeputting themintoapplication .In orderto reducetest t

s o

c ,this paper proposed a two-stage failure prediction mode lf or infrared detectors during tests d

e s a

b on the logistic regression model .Thesoluiton has shown significan tbusinessvalues .With t s r i f e h t y l n

o three tes tstages’ data ,under the condition tha t99% of the norma ldetectors are 5 5 . 4 5 t u o n e e r c s n a c e w , s t c u d o r p l a m r o n s a d e i f i s s a l

c %ofthedetectorswhich wil lfai lbeforethe t s e t m u u c a v t s a

l .Furthermore ,in thesecond stage prediction ,we can screen ou t80% ofthe fina l . s r o t c e t e d e r u l i a f n o it c u d o r t n I . n o i t a i d a r d e r a r f n i o t s t c a e r t a h t r o t c e t e d a s i r o t c e t e d d e r a r f n i n

A Mos toftheinfrared detectors

a

h ev been provided tofulfil lmilitaryneeds ,bu tpeacefu lapplicationshaveincreasedcontinuously . [ s n o i t a c i l p p a n o i t a v r e s n o c y g r e n e d n a , s e c r u o s e r h t r a e , y r t s u d n i , l a c i d e m e d u l c n i e s e h

T 1-3 .] The

r i e h t n i s e g n a h c r o s t n e v e t c e t e d o t d e e n s r o t c e t e d d e r a r f n

i environmentsand send theinformaiton

. s c i n o r t c e l e r e h t o o

t Iti si mportantt oensuret hei nfrareddetectorswil lworkproperly ,especiallyfor . ) s e l c i h e V l a i r e A d e n n a m n U ( s V A U s a h c u s s e l c i h e v d e n n a m n u o t s n o it a c i l p p a e t e d d e r a r f n i n i s t r o f f e , t n e s e r p t

A ctorresearch aredirected towardsimproving theperformance e r u t a r e p m e t g n i t a r e p o r e h g i h d n a s y a r r a d e n n a c s y l l a c i n o r t c e l e e g r a l , s e c i v e d t n e m e l e e l g n i s f o

[4-5] .Another importan taim is to make IR detectors cheaper and more convenien tto use [6 .] e

r e f e

R nce[7]studied theLW MCT IRFPA cos topitmization and [8] pointed ou ttha tthecos tof l a u q e t u o b a f o s t r a p e e r h t o t n i n w o d n e k o r b e b n a c s t n e n o p m o c d e l o o c e c n a m r o f r e p h g i h g n i k a m . s t s e t d n a n o i t a r g e t n i , r a w e d e h t , ) C I O R d n a r o t c e t e d ( p i h c e h t : t h g i e w o

T ensure tha tthe infrared detectors used in pracitce are as reilable as possible, a variety of . n o it a r e p o o t n i t u p e r a y e h t e r o f e b d e r i u q e r e r a s t s e t g n i n e e r c

s However ,thetes ttimeisvery long

. h g i h e t i u q s i t s o c e h t d n

a Thetests stepsusually contain sealing tube ,thermalcycling test ,aging ,

t s e

t aging tes t under therma l vacuum environmen t and under norma l temperature vacuum ,t n e m n o r i v n

e electrifiedatambien ttemperaturefor9 monthsandaging tes tundertherma lvacuum t n e m n o r i v n

e for4months ,wherecos tofvacuumt esti squtiehigh. , r e v e w o

H tothebes tofourknowledge ,wehaven’ tfound researchesonthefaliureprediction of s r o t c e t e d d e r a r f n

i . The main focus of this paper is to predic tequipmen tfailures in advance, to v

o r p m

i e the efficiency of screening and to reduce the cos tof tests. W e proposed a two-stage n o it c i d e r

p method .Firstly ,we predicted the faliure of the infrared detector only based on the t s e t m u u c a v t s r i f e h t e r o f e b n o i t a m r o f n

i .Sincethere aremany testscould beapplied to verify the o , s r o t c e t e d d e r a r f n i f o s e i t i l a u

q nly i f detectors’ failure probabiilties are quite high ,they wil lbe s

s a l

c ified sa failuredetectors. Secondly ,wepredicted thefailure oftheinfrareddetectorbeforethe t

s a

l vacuum test which lasts for 4 months. To reduce the high cos to f vacuum test ,we need to e l b i s s o p s a h c u m s a s r o t c e t e d d e r a r f n i e r u l i a f l a i t n e t o p e h t t u o n e e r c

Therearevarioustypesofmethodstha tcan beused to predic tthefailureofinfrared detectors . a

t a

D -driven methodsareindependen tofphysical/exper tknowledgeandcanbedeveloped basedon s

l e d o m l a c i t s i t a t

s 9[ ] tha tdescribe the failure behavior of the infrared detectors. Models can be e

t a e r c o t d e p o l e v e

d “learning rules” automatically from historica ldata to better predic twhich r

o t c e t e

d i smorel ikelyt ohaveproblem .Thescreeningofi nfrareddetectorsi sabinaryclassificaiton .l

a i t n e s s e n

i Inorder togenerateprobabilisticresults ,thelogisticregressionmodel si selected. r

e h

T emainder of the paper is organized as follows. Section 2 proposes the method to failure d

n a g n it s a c e r o f y t i l i b a b o r

p crtieria for threshold selection .Section 3 demonstrates the prediction S

. s r o t c e t e d d e r a r f n i f o s t l u s e

r ection4providesconcludingremarks.

g n i n e e r c

S Model

k a e p , r o t c a f e s i o n , t n a t s n o c e m i t , h t d i w d n a

B voltage (major and auxiliary) and resistance (major t

a , y r a il i x u a d n

a 25° rCo 03 C° ) areobservedi ntests ,wheret hevaluesofnoisefactoraremeasured s

e g a t s t s e t e m o s n i y l n o d e d r o c e r e r a s r o t c a f r e h t o d n a , e g a t s t s e t h c a e n i d e d r o c e r d n

a .

T heFirst-stagePredicitonModel

a s i r o t c a f e s i o

N crucia lfactorin the screening of detectors .I tis found tha ttheinfrared detectors l

i a f s y a w l

a when thenoisefiguresare higher than 1.6 orthechange rate of noisefactorishigher %

0 2 n a h

t .

f , n o i t i d d a n

I ailuremodesfordifferen tbatchesofdetectorsmay bedifferen .tAssuming tha twe M

e v a

h batches fo detectors ,we firstly need to classify M batches’ detectors into k clusters by k-meansclusteringmethodaccordingt othegapofnoisefactorbetweent hefollowingt es tstageand

e g a t s t n e r r u c e h

t .

, n o it c i d e r p e g a t s t s r i f e h t n i e c n i

S only information o n the firs tthree stages of t est is used to t

c e t e d e h t t c i d e r

p ors’ states after electrified tes ta ta room temperature for 9 months ,where the a

c n o i s s e r g e r e s i w p e t s e h t , w e f e r a s r o t c a f d e v r e s b

o nbeappliedt oselec tsignificantfactors . t

f o s l e b a l e h

T hedetectorswhichfai lafterelectrifiedtes ta tnorma ltemperaturefor9monthsare o

t t e

s ,1 andothersaresett o0 .Thent hefailureprobabilityofadetectori sshowni nEq .1.

)( 1 Where Y istheclasslabel; x denotestheselected factorvector; b istheintercep tofthemodel ,

r o t c e v t n e i c i f f e o c e p o l s e h t s i w d n

a .Theprobability variesfrom 0 to 1 on anS-shaped curve. By 2

. q E g n i z i m i n i

m on the training set ,the esitmator of (b ,w) can be obtained. Then failure i

c e p s a f o y t i l i b a b o r

p f icinfrareddetectorwil lbepredictedgivenx.

)( 2

e h

T Second-stagePredicitonModel

, p e t s s i h t n

I wepredic tthefailureprobabiiltyinthelas tvacuumtes tbased onexperimenta ldataof .

s e g a t s s u o i v e r

p A tthismoment ,thefeaturedimension observed i squitehigh. In ordertoenhance ,

l e d o m e h t f o y t i l i b a t e r p r e t n i d n a y c a r u c c a n o i t c i d e r p e h

t we appiled lasso [ 01 ] (leas tabsolute

o t ) r o t a r e p o n o i t c e l e s d n a e g a k n i r h

s variable seleciton and dimension reduction .Then the objec t o

t n i d e g n a h c s i n o i t c n u

f Eq .3, where isatuning parameterwhich balancesthe goodnessof fi t .

y ti x e l p m o c l e d o m d n a

r o f a i r e ti r

C ThresholdValueSeleciton

e r u li a f s ti t c i d e r p n a c e w , r o t c e t e d d e r a r f n i w e n a r o

F probabiilty according to Eq .1 .However,the t

l u s e r l a n i f e t i s i u q e

r is1(failure)or0(normal) .Anoptimumt hreshold isneededt oconverset he o

t n i y t i l i b a b o r p e r u l i a

f t he classificaiton resul.t In addiiton ,since the classification problem is f

n i l a m r o n f o n o i t r o p o r p e g r a l a , d e c n a l a b m

i rared detectors dominate the learning accuracy .To p

e h t f o e c n a m r o f r e p e h t e t a u l a v

e rediction modelsand selec ttheopitmum threshold ,we usetwo y

t i c i f i c e p s d n a ) e t a r e v i ti s o p e u r t ( y t i v i ti s n e s , s e r u s a e

m (truenegativerate) ,whichnaturallyprovide e

d a r t

a -offt ha tneedst obebalancedi npractice . n

o i t r o p o r p e h t s e r u s a e m y t i c i f i c e p

S of negatives tha tare correclty identified as such (e.g .the )

s t c u d o r p l a m r o n s a d e i f i t n e d i y l t c e r r o c e r a h c i h w s r o t c e t e d l a m r o n f o e g a t n e c r e

p ,which isshown

n

i Eq .4. Sensitivity measurestheproportion of positivestha tare correctly idenitfied assuch (e.g . )

t l u a f e h t g n i v a h s a d e i f i t n e d i y l t c e r r o c e r a h c i h w s r o t c e t e d e r u l i a f f o e g a t n e c r e p e h

t ,tha tis

5 . q E n i d e t a r t s n o m e

d . InEq .4andEq .5 , istheDiracdeltafunction.

)( 4

)( 5

s tl u s e R

h c a e n i d e t s e t e b n a c t a h t s r o t c e t e d f o r e b m u n e h t , t n e m p i u q e m u u c a v f o e m u l o v d e t i m il e h t e c n i S

e W . d e t i m i l s i h c t a

b obtained274 infrareddetectorstesteddividedintosixbatches ,wheretes tdata t

s r i f e h t n i s r o t c e t e d e h t l l a f

o -stageare obtained ,however ,only 44 detectorsare selected for the .

s h t n o m r u o f s t s a l h c i h w t s e t m u u c a v

e h

T First-stageFaliurePrediciton

e w , y l t s r i

F clusteredt hebatchesbyapplyingk-meansalgorithm .Becausethereareonlysixbatches ,

k is se tto 2 ,which means 6 batches wli lbe clustered into 2 groups. Theresultssuggesttha tthe 5

h c t a

b is clustered into a group and the other batches are clustered into a group . Fig. 1 e h t t a h t e e s n a c e W . t s e t m u u c a v t s r i f e h t e r o f e b h c t a b h c a e n i r o t c a f e s i o n e g a r e v a e h t s e t a r t s n o m e d

h c t a b n i r o t c a f e s i o n f o m r o f e g n a h

c 5i squitedifferen tfromt ha tint heotherbatches.

g i

F u 1. re Noisefactorchangesbeforet hefirs tvacuumt est.

0 2 . 1

2 2 . 1

4 2 . 1

6 2 . 1

8 2 . 1

0 3 . 1

2 3 . 1

4 3 . 1

6 3 . 1

8 3 . 1

e b u t g n il a e s r e tf

a therma lcycilng secondagingt est

N F

f d e h s i l b a t s e e r a s l e d o m o w

T or detectors in batch 5 and in other batches respective yl .By e

s i w p e t

s covariatesselection ,noisefactoraftersealingtube ,noisefactoraftertherma lcyclingand t

s e t g n i g a e h t r e t f a e s i o

n are selected for both models .In addiiton ,the major peak voltage a nd e

c n a t s i s e

r a t25° C aftersealingtubeareselectedintothemode lforbatch5 ,andstandarddeviation s

r o t c a f e s i o n f

o isselectedformodeilngt heotherbatches. n

e h

W we predic ta new detector ,firstly a mode lisnecessari ly to be chosen b y calculaitng the Mahalanobis distances between the sample and the two groups respectively. Then the failure

1 . q E y b d e n i a g e b n a c n o it c i d e r

p .Sincetherearemanychancest oscreenoutt heabnormali nfrared s

r o t c e t e

d afterfirst-stage predic ntio .So when wecarry ou tpredictionsin thefirst-stage ,high true a

g e

n tiverateismoresignificant. Table 1 showsthe results foreach batch .Wecan see tha tifthe e

r h

t shold is0.45 ,thenegativerateareal lhigherthan 95% ,andtheaveragerateis98.96% ,which s

n a e

m only abou t1% norma ldetectors wil lbe predicted as abnorma ldetectors. The average s

r o t c e t e d % 5 5 . 4 5 t a h t s e t a c i d n i h c i h w , % 5 5 . 4 5 s i e t a r e v i t i s o

p , which w ill f ail after tes tstage of

g n i e

b electrified a tnorma ltemperature for 9 months ,can be screened ou tonly based on the t

s e t m u u c a v t s r i f e h t e r o f e b n o i t a m r o f n

i .

1 e l b a

T . Predictionresultsforeachbatch. h

c t a

B SPC TPR Positivesamples 1 0.45 0.9706 0.6250 8 2 0.45 1.0000 0.0000 1

3 0.45 1.0000 - 0

4 0.45 1.0000 0.0000 1 5 0.45 0.9655 0.4167 1 2 6 0.45 1.0000 0.6364 1 1

l a t o

t 0.45 0.9896 0.5455 3 3

, n o it a u t i s l a c it c a r p n

I i ftheabnorma lproportion ofabatch ishigh ,forexamplehigherthan 20% s

i h t n

i issue, thewholedetectorsin abatchusuallywil lbediscarde . d Table2 showstheprediciton f

o abnorma lproportion ofeach batch .Thewholebatch detectorswli lbediscarded ifprediction of l

a m r o n b

a proportionishighert han20% .Wecanseet ha tonlyonebatchwil lbemissclassified ,and e

v i t a v r e s n o c e r a s tl u s e r n o it c i d e r p e h

t ,whichavoidswasteofdiscardingthenorma ldetectors.

2 e l b a

T . Theabnorma lproportionpredictionofeachbatch.

h c t a

B Abnorma lproportionprediction Prediction Real

1 20.00% N o Y es

2 2.32% N o N o

3 14.29% N o N o

4 10.64% N o N o

5 23.40% Y es Y es

6 44.44% Y es Y es

e h

T Second-stageFaliurePrediciton

o s s a l h g u o r h

T variableselection ,noisefactoraftertherma lcycling ,noisefactorin thefirs tmonth t

n e r r u

c -carrying test ,B-value ,noise factor under 5-100Hz bias voltage and noise factor under 1-30Hzbiasvoltageareselectedi ntot hemode.l

d n o c e s e h t n i t e s a t a d e h t e s u a c e

B -stagepredictionisquitesmal,lt omakeful luseoftheexisting ,

n o i t a m r o f n

i we perform afivefold crossvalidation using thedataset .In each trial ,we randomly n

a t s e t o t d e s u s i e n O . s p u o r g e v i f o t n i a t a d e h t e d i v i

d d the other four are used for training .We

. p u o r g g n i t s e t e h t g n i t a t o r y b s s e c o r p s i h t t a e p e

r O ntrainingset ,wefound ou tthethresholdwhich e

i f s i t a

s d thelower ilmi tofspecificity and maximized thesenstiivity ,and verifiedtheperformance t

s e t e h t n

o s e.t Table 3 reveals the average resutls for severa lSPC lower limits. We can see tha t e

h t h t i

w condition of negative ratebeing around 70% ,abou t80% ofthefailureinfrared detectors .t

3 e l b a

T . Predictionresultsint hesecond-stage. g

n i t t i

F Prediction

P

S Cl owerl imit S C P TPR Prediction ofabnorma lproportion S C P TPR 4

7 .

0 0.90 0.73 24% 0.74 0.75

2 7 .

0 0.72 0.87 33% 0.70 0.78

0 7 .

0 0.72 0.87 33% 0.71 0.77

8 6 .

0 0.72 0.87 33% 0.66 0.80

6 6 .

0 0.72 0.87 33% 0.69 0.80

4 6 .

0 0.72 0.87 33% 0.63 0.83

2 6 .

0 0.72 0.87 33% 0.64 0.83

0 6 .

0 0.72 0.87 33% 0.58 0.87

n o is u l c n o

C s

, y d u t s s i h t n

I we have explored a two-stage failure prediction of infrared detectors during the .t

n e m i r e p x

e The soluiton we provide has shown significan tbusiness values .Wtih only the firs t e

e r h

t stages’ data ,under the condition tha t99% of the norma ldetectors are classified as norma l ,

s t c u d o r

p we can screen ou t54.55% of the failure detectors. Furthermore ,in the second stage t

u o n e e r c s n a c e w , n o it c i d e r

p 80%oft hefailuredetectors. d

o h t e m d e s o p o r p e h t , n o i ti d d a n

I canprovidefailureprobabilityforecast ,onwhichbasedwecan e

u l a v t r o s h t l a e h e h t y l p p u

s s ofthedetectors. f

o n o i t a r e d i s n o c n

I manufacturing cos tand tes tcos tforeach step ,theoptimizationobjec tofthe l

e d o

m canbesett ocos tsaving.Thisi swha tcanbefurtherstudied .

e r e f e

R n ces

[1]A .Rogalski, Infrareddetectors .CRCPress ,2000.

[2] .B .B Lahiri ,S . Bagavathiappan, .T Jayakumar ,& J . Philip, Medica lapplications of infrared w

e i v e r a : y h p a r g o m r e h

t ,InfraredPhys. Techn., 55 (2012) ,221-235.

[3]E .Sousa ,R .Vardasca ,S .Teixeira ,A .Seixas ,J .Mendes& A .Costa-Ferreira, A reviewon the .

s d n a h n i g n i g a m i l a m r e h t d e r a r f n i l a c i d e m f o n o it a c i l p p

a Infrared Phys. Techn., 58 (2017),

5 1 3 -323.

[4]A .Rogalski, Infrareddetectors :anoverview.InfraredPhys .Techn., 43(3- )5 (2002) ,187-210. [5] .A Rogalski ,Recen tprogressininfrareddetectort echnologies.InfraredPhys. Techn., 45 (2011),

6 3 1 -154.

[6]A .Rogalski ."Infrareddetectors :statusandt rends."Prog. Q nua .t Electron. ,27(2003) :59-210. [7] .J .P Chatard, LW MCT IRFPA cos toptimization .In Infrared Technology and Applicaitons

V X

X (3698(1999) ,407-420) .Internationa lSocietyforOpitcsandPhotonics.

[8] .F Bertrand, .J .L Tissot ,& G .Destefanis, Second generaiton cooled infrared detectorsstateof n

I . s t c e p s o r p d n a t r a e h

t PhysicsofSemiconductorDevices(Vol .3316 ,1998 ,713). 9

[ ] M .Mishra , .J Martinsson ,M .Rantatalo ,& K .Goebel, Bayesian hierarchica lmodel-based m

u i h t il r o f s c i t s o n g o r

p -ionbatteries.Reilab. E . ng Syst. Safe., 27 (2018) , - .25 35 ]

0 1

[ R .Tibshirani .Regression shrinkage and seleciton via the lasso, J. R. S . tat S . ,oc B (1996), 7