Acceleraed Sress Tesng and Relably Tools for Analyss of Acceleraed Lfe and Degradaon Tes Daa Presened by: Reuel Smh Unversy of Maryland College Park smhrc@umd.edu Sepember-5-6 Sepember 28-30 206, Pensacola Beach, Florda
Acceleraed Sress Tesng and Relably Tools and Educaon of Acceleraed Tesng Rsk and relably ools and educaon are becomng more effecve and realsc due o relance upon he Physcs of Falure (PoF) approach PoF modelng uses acceleraed lfe or acceleraed degradaon esng o assess model parameers based on he relaons of sress, damage, and lfe Sandards of Acceleraed Tesng Educaon Concepual defnons and mehodologes Supplemenary example problems Algorhms and codes www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 2
Acceleraed Sress Tesng and Relably Overvew of ALT/ADT Tools and Educaon Par I Probablsc physcs of falure (PPoF) Mechansc models of falure mechansms Sress-srengh Damage endurance Performance-requremen Model examples Fague Wear Corroson Creep www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 3
Acceleraed Sress Tesng and Relably Overvew of ALT/ADT Tools and Educaon Par II Lfe-Sress Models Acceleraed Lfe Tesng (ALT) [2,3] Analyss: Plong Mehod MLE Bayesan Esmaon Acceleraed Degradaon Tesng (ADT) Sep-Sress and Sress Varyng Tes Types of ALT and Pfalls Tes plannng, Performance, Daa Sorng, and Evaluaon www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 4
Acceleraed Sress Tesng and Relably Overvew of ALT/ADT Tools and Educaon Par III Applcaons of Physcs-Based Models for: Relably Engneerng Prognoss Healh Managemen (PHM) Comprehensve Case sudes Feld Examples www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 5
Acceleraed Sress Tesng and Relably MLE ALT Example [] Consder he followng mes-o-falure a hree dfferen sress levels Sress (Temperaure) 406 K 436 K 466 K Recorded Falure Tmes (Hours) 248 64 92 456 76 05 528 289 55 73 39 84 83 386 29 965 459 235 972 - - 528 - - www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 6
Acceleraed Sress Tesng and Relably MLE ALT Example (Con.) If he daa s bes represened by a Webull dsrbuon and he Lfe (L)-Sress (T) model s bes modeled as an Arrhenus model, L = Aexp A Consan o be deermned E a Acvaon energy (ev) T emperaure n Kelvn K Bolzmann consan (/K=605 ev) Esmae produc lfe a gven use-lfe 353 K usng he plong mehod and he MLE mehod and compare Ea KT www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 7
Acceleraed Sress Tesng and Relably Plong Mehod MLE ALT Example (Con.) STEP : Plo he lfe dsrbuon a each sress level STEP 2: Fnd he Webull parameers of he dsrbuon α=899, β=.9 @ 406 K α=342, β=2.5 @ 436 K α=88, β=2.7 @ 466 K www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 8
Acceleraed Sress Tesng and Relably MLE ALT Example (Con.) Plong Mehod (Con.) STEP 3: Plo he lfesress a 63.2% falure and solve for Arrhenus parameers Ea 63.2% L63.2% = A63.2% exp KT L = 0.0043exp 4959 T ˆ β = (.9 + 2.5 + 2.7) / 3 = 2.5 Aˆ 0.0043; ˆ / 4959 ; ˆ 63.2% = Ea K = K Ea = 0.43( ev ) 63.2% 63.2% L use = 5, 404hours www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 9
Acceleraed Sress Tesng and Relably MLE Mehod MLE ALT Example (Con.) STEP : Oban he Webull-Arrhenus lkelhood expresson Λ = STEP 2: Se he frs dervaves of he lkelhood w.r.. he parameers o zero and solve smulaneously ˆ β = 2.7; Aˆ = 0.0024; Eˆ / K = 520 K; Eˆ M = a a = N β ln Ea Aexp KT 0.45( ev ) Ea Aexp KT β exp Λ Λ Λ = 0 ; = 0; = 0 β A E a Ea Aexp KT β 520 L = 0.0024exp T L use =, 272hours www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 0
Acceleraed Sress Tesng and Relably Bayesan ADT Example [, 4] Consder he followng ADT where 25 LED uns each are esed a emperaures 25 C, 65 C, and 05 C [4] www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda
Acceleraed Sress Tesng and Relably LED degradaon s modeled, Bayesan ADT Example (Con.) Y jk = + β jk exp β 3605 T u + 273.5 T + 273.5 β 2 + ε jk jk he k h me of he j h LED a he h emperaure level ε jk normal dsrbuon NOR(0, σ ε ) If pror knowledge of he parameers β, β 2, β 3, and σ ε s lmed o a unform dsrbuon UNIF(0,00) for each, and an Arrhenus relaonshp s assumed for he ADT, fnd he poseror dsrbuon and mean-me-o-falure for he LED a use emperaure (T u ) 20 C. NOTE: Falure occurs a 50% lumnosy www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 2
Acceleraed Sress Tesng and Relably Bayes Rule Mahemacs π Bayesan ADT Example (Con.) The model parameers vecor, θ ( ) ( DATA θ ) ( ) π 0 θ pror dsrbuon of parameers l lkelhood l ( ) ( DATA θ ) π 0( θ ) θ DATA = l( DATA θ ) π ( θ ) d π DATA poseror dsrbuon of parameers θ 0 θ [ θ θ ] 2 θ n www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 3
Acceleraed Sress Tesng and Relably Bayesan ADT Example (Con.) The poseror dsrbuon s usually esmaed usng advanced numercal smulaons. For example by usng MCMC (Markov Chan Mone Carlo) smulaon made n he MATLAB sofware we ge: Poseror Parameer Lower Bound Mean Upper Bound β 9.7 x 0-6 0.027 0.062 Β 2 0.29 0.6.0 β 3 0.0047 0.57.3 σ ε 0.007 0.09 0.20 www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 4
Acceleraed Sress Tesng and Relably Bayesan ADT Example (Con.) The MTTF esmae s aken from he Bayesan poseror of each un Recall falure occurs a 50% lumnosy MTTF use =2, 975hours www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 5
Acceleraed Sress Tesng and Relably Sep-Sress Example [, 5] Consder a sep-sress es of cable nsulaon ype : Faled + Censored Noe: Sress s defned as volage/cable hckness where nomnal sress s 400 V/mm www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 6
Acceleraed Sress Tesng and Relably Sep-Sress Example (Con.) If he pror daa s obaned from hs es of cable nsulaon ype 2, 40 45 Volage (klovols) 35 30 Volage (klovols) 40 35 30 25 0 20 40 60 80 00 20 40 25 0 00 200 300 400 500 Tme (mnues) Tme (mnues) 40 34 Volage (klovols) 35 30 Volage (klovols) 32 30 28 25 0 500 000 500 26 0 000 2000 3000 4000 Tme (mnues) Tme (mnues) Updae he model parameers usng Bayesan esmaon www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 7
Acceleraed Sress Tesng and Relably Sep-Sress Example (Con.) Ths me he lfe-sress model s represened by he nverse power law (IPL) L = AV p A and p are consans o be deermned V s he sress n vols/mm www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 8
Acceleraed Sress Tesng and Relably Sep-Sress Example (Con.) www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 9
Acceleraed Sress Tesng and Relably Sep-Sress Example (Con.) The lkelhood for an n-sep-sress model s, number of falure daa pons a sep me of j-h falure daa pon a sep number of rgh censored daa pons a sep me of k-h rgh censored daa pon a sep, and www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 20 ( ) ( ) [ ] = = = = k k j j r k r r r n c j c c c F f l * * * * * *,,,,,, 2 2 ( ) ( ) [ ] ( ) ( ) [ ] ( ) [ ] ( ) n p c p c p c p c c V V AV AV AV V f AV V F j j j j j + = + + = + = 2 2 * * * * * exp, exp, τ τ τ τ β τ β β β c j * cj r k * ck
Acceleraed Sress Tesng and Relably Sep-Sress Example (Con.) 000 Prors 000 Poserors freq 500 0 0 0.5.5 2 freq 500 0 0 0.5.5 2 freq A 0-4 000 500 0 0 0.5.5 2 Sep-sress es daa freq A 0-4 500 0 0 0.5.5 2 000 p Bayesan Updang 000 p freq 500 0 0 5 0 5 freq 500 0 0 5 0 5 Parameer Lower Bound Upper Bound A 4.38 x 0-0 5.69 x 0-5 p.37 x 0-4 2.78 β.74 x 0-4 2.0 Parameer Lower Bound Upper Bound A 3.70 x 0-9 5.68 x 0-5 p.2 x 0-3.82 β 4.68 x 0-3 2.0 www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 2
Acceleraed Sress Tesng and Relably Closng Remarks Relably engneers should be cognzan and aware of he mporance of acceleraed esng pracces Necessary componens for undersandng acceleraed esng Theory Mehods and models Tools and applcaons www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 22
Acceleraed Sress Tesng and Relably Abou Reuel Smh Reuel Smh s a PhD level Relably Engneerng graduae suden a he A.J. Clark School of Engneerng a he Unversy of Maryland College Park. Hs curren research s n he area of fague crack propagaon, deecon, and modelng. Reuel Smh receved hs M.S. degree n boh Aerospace Engneerng and Mechancal Engneerng from he Unversy of Maryland College Park. www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 23
Acceleraed Sress Tesng and Relably Abou Dr. Mohammad Modarres Mohammad Modarres s he Ncole Y. Km Emnen Professor of Engneerng and Drecor Cener for Rsk and Relably, A.J. Clark School of Engneerng, Unversy of Maryland, College Park. Hs research areas are probablsc rsk assessmen and managemen, uncerany analyss and physcs of falure degradaon modelng. Professor Modarres has over 350 papers n archval journals and proceedngs of conferences, ncludng several books n varous areas of rsk and relably engneerng. He s a Unversy of Maryland Dsngushed Scholar. Professor Modarres receved hs M.S. and PhD n Nuclear Engneerng from MIT and M.S. n Mechancal Engneerng also from MIT. www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 24
Acceleraed Sress Tesng and Relably References. M. Modarres, M. Amr and C. Jackson, Probablsc Physcs of Falure Approach o Relably: Modelng, Acceleraed Tesng, Prognoss and Relably Assessmen, College Park, MD: Cener for Rsk and Relably A.J. Clark School of Engneerng, 205. (PDF verson s avalable for download from hp://crr.umd.edu/node/56) 2. W. Nelson, Acceleraed Tesng - Sascal Models, Tes Plans, and Daa Analyss, Hoboken, NJ: John Wley and Sons, 990. 3. W. Nelson, Acceleraed Tesng - Sascal Models, Tes Plans, and Daa Analyss, New York: John Wley and Sons, 2004. 4. M. S. Hamada, A. Wlson, S. Reese and H. Marz, "Chaper 8: Usng Degradaon Daa o Assess Relably," n Bayesan Relably, New York, Sprnger Scence+Busness Meda, 2008, pp. 27-37. 5. W. Nelson, "Acceleraed Lfe Tesng Sep-Sress Models and Daa Analyses," IEEE Transacons of Relably, Vols. R-29, no. 2, pp. 03-08, 980. www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 25
Acceleraed Sress Tesng and Relably Conac Informaon: Quesons? Mohammad Modarres Professor of Relably Engneerng modarres@umd.edu Tel: 30-405-5226 Fax: 30-34-960 www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 26
Acceleraed Sress Tesng and Relably Thank You THE END! www.eee-asr.org Sepember 28-30 206, Pensacola Beach, Florda 27