Accelerated Sequen.al Probability Ra.o Test (SPRT) for Ongoing Reliability Tes.ng (ORT)

Transcription

1 cceleaed Sequen.al Pobably Ra.o Tes (SPRT) fo Ongong Relably Tes.ng (ORT) Mlena Kasch Rayheon, IDS Copygh 25 Rayheon Company. ll ghs eseved. Cusome Success Is Ou Msson s a egseed adema of Rayheon Company STR 25, Sep 9 -, Cambdge, M

2 bou SPRT and he use Common es pocedue ccepance decson cea Ovevew of he es plans Pesena.on Oulne Developmen of he es plans: Mahema.cal bacgound Envonmens o use Tes accelea.on Tes daa analyss Summay and Conclusons STR 25, Sep 9, Cambdge, M 2

3 Relably Demonsa.on Tess fo Consan Falue Rae Relably demonsa.on ess: Tme emnaed o falue emnaed Consan falue ae (nsananeous falue ae, h() f()/r()) and as a esul have consan Mean Tme o Falue (MTTF, ) f() Pobably Densy Func.on (PDF) of he.mes o falue dsbu.on R() em elably a he.me Consan falue ae (falue fequency, z() dn()/d) and heefoe he consan Mean Tme Beween Falues (MTBF, ) n() numbe of falues expeenced dung he.me.me dsbu.on of he em falues ccumulaed es.me, T s a sum of.mes accumulaed by each es em wh eplacemen of he faled ems: whou eplacemen of he faled ems: n numbe of ems n es oal numbe of faled ems In es oal es.me; T n T ( n ) accumulaed es.me a he.me of falue on faled ems STR 25, Sep 9, Cambdge, M 3 +

4 Relably Tess and Sesses ll ems ae expeced o exhb cumula.ve degada.on n lfe due o exposue o use sesses ll elably ess should have appled sesses of he magnude and use pofle expeced n use of he em Combned envonmens ae o be appled as expeced n use wheneve possble ll elably demonsa.on es plans and decson cea ae based on ehe of wo chaaces.cs, as follows: n accepable numbe of falues n a specfed es.me, o n accepable es.me fo a specfed numbe of falues STR 25, Sep 9, Cambdge, M 4

5 Wha s he SPRT? Sequen.al Pobably Ra.o Tes (SPRT) s one of he es ypes n he goup of demonsa.on ess fo consan falue aes SPRTs ae used fo elably demonsa.on and also as he elably assuance ess n poduc.on whee hey ae nown as Ongong Relably Tess (ORT) o mono poduc elably SPRT plans ae chaacezed by decson ules fo accep.ng o ejec.ng he esed lo o con.nung he es un.ll such decson can be made The specfed paamees of he ess ae: he uppe es MTBF (o he lowe es falue ae ) he lowe es MTBF (o he uppe es falue ae ) Rss: α, poduce s ha ems wh he eal MTBF hghe han uppe es MTBF ( ) wll be ejeced β, cusome s s ha ems wh he eal MTBF lowe han lowe es MTBF ( ) wll be acceped D, dscmna.on a.o, D / STR 25, Sep 9, Cambdge, M 5

6 Sequen.al Te Plans and he Common Pocedue Deemne he envonmenal and opea.onal sess cond.ons Specfy uppe es MTBF, Selec ss, α and β, and dscmna.on a.o, D, consdeng ha low values of α, β and D mae a moe poweful es, bu eque longe es.me and/o moe es ems Rss ae geneally chosen o be equal (shaed s) fo ease calcula.ons and ageemens Values of, ss and he dscmna.on a.o wll deemne he es dua.on and he es plan The es plan deemnes he cond.ons of accepance o ejec.on of esed ems as a goup o los Tes.me T a and T epesen es.mes fo accepance o ejec.on STR 25, Sep 9, Cambdge, M 6

7 : Mahema.cal Ra.onale fo SPRT Tes Plans - Fo an em wh unnown MTBF,, pobably of falng.mes n an accumulaed es.me T s: T P( ) m exp ( T )! m The es has o pove ha agans < wha s done by Wald s SPRT by es.ng he hypohess H : agans he Hypohess H : I s equed ha: The pobably of accep.ng < s less han o equal han b The pobably of ejec.ng s less han o equal a Dung he es he a.o of hese pobabl.es s: P ( ) P ( ) P ( ) STR 25, Sep 9, Cambdge, M 7

8 Mahema.cal Ra.onale fo SPRT Tes Plans - 2 Pobabl.es of havng falues n he accumulaed.me T f and ae Ra.o beween he wo s: The a.o s evaluaed beween wo consan values: je mahema.cal ansfoma.ons: Whee: he accep lne s: and he ejec s: STR 25, Sep 9, Cambdge, M 8 ( )! exp ) ( T T P ( )! exp ) ( T T P exp ) ( ) ( ) ( T D P P P ( ) P B D D α β + 2 α β B D exp < < T D B T b c T b a + < < + T b a + T b c +

9 Mahema.cal Ra.onale fo he SPRT Tes Plans- 3 The consans a, b, and c ae: a ln(b) ln( D) b ln( D) D ln( D) ccepance s when numbe of falues a a gven.me s on o below he accepance lne The lo s ejeced (o he poduc elably s lowe han equed) when he numbe of falues n gven.mes s on o above he ejec.on lne If he numbe of falues as a func.on of.me s beween he wo lnes, no decson can be made and he es con.nues 2 The es unca.on.me s: χ α; 2 χ s deemned fom he a.o: 2 χ T β ; 2 2 c 2 α ; 2 ln() ln( D) D fo : STR 25, Sep 9, Cambdge, M 9 T a, mn a b

10 Opea.ng Chaaces.c Cuve The opea.ng chaaces.c cuve (pobably of accepance cuve) s deemned fom he followng appoxma.on: h P a(h) h h B Paamee h s found fom:,9,8,7 D h h ( D ) P a,6,5,4,3,2,,3,5,7,9,,3,5,7 m/m IEC 98/6 STR 25, Sep 9, Cambdge, M

11 45 Example of a SPRT Plan 4 35 α., β. D If 5, hous 2 ems esed 9.38 yeas T/m T IEC 97/6 STR 25, Sep 9, Cambdge, M

12 SPRT ccelea.on Wh SPRT assump.on of consan em (sysem) falue ae and a.onale of physc of falue: n em fals n dffeen mannes (falue modes) Toal aveage falue ae of an em s a sum of falue aes of ndvdual falue modes, each coespondng o a sess N S Whee: s he falue ae ha he em has n s use cond.ons s he falue ae of he em coespondng o he specfc sess N S s he numbe of sesses Oveall acceleaed es falue ae s: Tes N S STR 25, Sep 9, Cambdge, M 2

13 SPRT ccelea.on - 2 Whee: s he acceleaed es falue ae Is he poduc of accelea.on facos affec.ng one falue mode, I Toal equvalen es accelea.on s hen: Smplfed by an assump.on ha equal elably can be allocaed o each of he sesses: STR 25, Sep 9, Cambdge, M 3 N S Tes ) ( ln( N S Tes R S S o S N S N cons R R R S. ) ( ) ( ) ( N S S Tes N N S S Tes N

14 Dua.on of Sess pplca.on n Tes Thee ae wo appoaches ha can be seleced:. pplca.on of sesses n vew of he poduc lfe 2. pplca.on of sesses fo he dua.on of non acceleaed ess Boh appoaches eque nowledge of he use pofle fo each sess The ndvdual sesses and lowe levels of he sess pofle ae acceleaed o one he hghes level of each sess and hen hs level s acceleaed o he sess level n es Fo ems wh shoe equed lfe (e.g. auomo.ve yeas, o lowe, e. g. sma phones), he use lfe exposue s appopae Fo ems whee he expeced lfe s consdeably longe ha he non acceleaed es dua.on, he dua.on of sess applca.on should also be shoe and mached o he dua.on of he non acceleaed es STR 25, Sep 9, Cambdge, M 4

15 Example of an cceleaes SPRT fo uomo.ve Eleconc Devce Paamee Symbol Value Requed lfe L yeas 87,6 hous Requed elably R L ( L ).8 Tme ON ON 2 hous/day 7,3 hous Tempeaue ON T ON 65 ºC Tme OFF ON 22 hous/day 8,3 hous Tempeaue OFF T OFF 35 ºC Themal cyclng ΔT Use 45 ºC, Two mes pe day Toal hemal cycles N Use 7,3 cycles Tempeaue amp ae ξ.5 ºC/mnue Vbaon, andom W Use.75 g.m.s Relave humdy RH Use 5% cvaon enegy E a.3 Ev STR 25, Sep 9, Cambdge, M 5

16 cceleaed SPRT - Example Requed lfe: yeas wh expeced elably s.8: ln ( R ( )) 392, hous α.3, β.3. D.5 8 7, ,8,7,6 P a,5,4 2,3,2, T/ T/m IEC 8/6 T/ m/m IEC 9/6 The es dua.on eques 5 2 E6 hous 4 falues; 2 uns E5 hous STR 25, Sep 9, Cambdge, M 6

17 cceleaed SPRT Mehod #- Example Fo each of fou sesses, he allocaed elably s: R [ R ( )]. 946 ( ) 4 Dua.on of applca.on of each of he sesses s deemned n egads of lfe dua.on, so ha fo he equed elably, he lfe applca.on s o be mul.pled by a faco.5 (ef. IEC 6256) Themal cyclng: N N Tes Tes ΔT NUse ΔT 452 cycles Use Tes Themal exposue: T _ Tes T _ Tes m E ON _ N exp 68. h ξ ξ a B Use Tes ON _ N ON _ N T 3 E ON + OFF exp 8,754 hous ON T Tes B T OFF T STR 25, Sep 9, Cambdge, M 7 a ON

18 cceleaed SPRT # - Example Humdy: RH Tes 95%, Tes empeaue: T RH 85 C RH _ Tes _ Tes h 2.3 RH _ Tes 3 h ON _ N RH RH Use Tes h exp E a B T ON T RH Vba.on: Requed mleage fo en yeas was 5, mles, whch anslaes no 5 hous pe axs vba.on a.7 g.m.s. W Use.7 g.m.s. W Tes 3.2 g.m.s. Vb _ Tes Wh : Vb _ Tes w Vb _ Use 4 W W Use Tes 8 hous pe axs w STR 25, Sep 9, Cambdge, M 8

19 SPRT ccelea.on Summay Fo he fou sesses he accelea.on facos ae as follows: TC TD RH Vb ΔT ΔT RH RH W W Use Tes Use Tes Use Tes Vb _ Tes Themal cyclng and vba.on affec a goup of same falue modes, and hemal exposue and humdy affec anohe goup Oveall accelea.on: SP E exp w m a B ς ς T Use Tes OFF E exp T a B Vb _ Use N N T ON Tes ON 2,6 Use 24, T TC ON _ N T _ Tes , ON _ N RH _ Tes 43,7 Fequen ndusy pac.ce: ll accelea.on facos mul.ply Should NEVER be appled TC Vb RH TD RH Vb S + N RH TD 645 STR 25, Sep 9, Cambdge, M 9

20 cceleaed SPRT Mehod #2 Sesses ae appled n vew of es dua.on ahe han he dua.on of he expeced lfe Dua.on of each sesses expeced n poduc lfe needs o be ecalculaed egadng he es dua.on In he example, he lfe dua.on was 87,6 hous whle he es dua.on equed, hous The gven dua.on of hemal exposues and humdy fo lfe, he numbe of hemal cycles and he oal numbe of mles wound need o be mul.pled no by a faco, bu by he a.o beween he needed es dua.on and lfe In he gven example he mul.ple fo use s:, 87,6.42 When he es dua.on equed fo he numbe of expeced falues ehe mehod s accepable The choce of he mehod s dffeen when he expeced lfe s consdeably longe o shoe han he equed es dua.on and he exposue should be calculaed accodngly q STR 25, Sep 9, Cambdge, M 2

21 Summay of cceleaed SPRT Requed and es falue aes and MTBF fo he es desgn: Tes ln [ R ( )] ln [ R ( )] O usng MTBF : Tes hous 68.7 hous If 5 ems esed wh a oal of 4 falues, he ems would be acceped and he uppe es MTBF would be: 2,, 4 5, hous 3 STR 25, Sep 9, Cambdge, M 2

22 cceleaed SPRT - Conclusons Sequen.al Pobably Ra.o Tess ae used fo elably demonsa.on as well as fo he Ongong Relably Tes.ng n poduc.on fo deec.on of elably vaa.on Fo eleconc componens he ORT had easonable dua.on because of he lage sample szes Fo moe complex ems, he ORT was unaffodable due o cos and he elably demonsa.ons wee deaded, avoded, and waved as cos and schedule pohb.ve s acceleaed, he SPRT can be agan undeaen In ecen.me, he use s pmaly fo he ORT Ths s because acceleaed elably gowh ess ae moe favoable snce he mpovemens of ems ae done dung he es whle n all ohe demonsa.on ess, he unaccepable ess ae epeaed hus no easly affodable STR 25, Sep 9, Cambdge, M 22

23 bou he uho Mlena Kasch Boson Pos Road Malboough M 752 mlena_asch@ayheon.com Mlena Kasch s a Seno Pncpal Sysems Engnee n Rayheon Inegaed Defense Sysems, Whole Lfe Engneeng n RM Engneeng Goup, Malboough, M. Po o jonng Rayheon, she was a Seno Techncal Lead of Relably Engneeng n Desgn Qualy Engneeng of Bose Copoa.on, uomo.ve Sysems Dvson aje he fve- yea enue a he Je Populson Laboaoy n Pasadena, Calfona. Whle n Calfona, she was a pa-.me pofesso a he Calfona Sae Unvesy Domnguez Hlls, gaduae school, and he Cal Poly Pomona, undegaduae pogams. She holds a BS and MS n Eleccal Engneeng fom he Unvesy of Belgade, Yugoslava, and s a Calfona egseed Pofessonal Eleccal Engnee. She s Techncal dvso (Cha) o he US Techncal dvsoy Goup (TG) of he IEC Techncal Commyee, TC56, Dependably. STR 25, Sep 9, Cambdge, M 23