MTBF: Understanding Its Role in Reliability

Transcription

1 Modul MTBF: Undrsanding Is Rol in Rliabiliy By David C. Wilson Foundr / CEO March 4, Wilson Consuling Srvics, LLC dav@wilsonconsulingsrvics.n Wilson Consuling Srvics, LLC Pag of 47 MTBF: Undrsanding Is Rol in Rliabiliy

2 Tabl of Conns Scion Pag.: Inroducion : Rliabiliy Mahmaics : Bahub Curv : Failur Ra : MTBF : MTTF : MTTR : Rlaionships Summary & Rliabiliy Modls : Summary Wilson Consuling Srvics, LLC Pag of 47 MTBF: Undrsanding Is Rol in Rliabiliy

3 Inroducion.: Inroducion Th objciv is o nabl an individual who is unfamiliar wih h us of h Man Tim Bwn Failurs MTBF rliabiliy paramr o undrsand is rlaionship in produc prdicions, failur ras, fild prformanc, c. Afr compling his uorial, h paricipan will know and undrsand how MTBF rlas o produc prformanc ovr im. In ordr for h praciionr o spak inllignly and auhoriaivly on h paramr, MTBF, i imporan a a minimum ha a cursory undrsanding of h mahmaical concps involvd wih Rliabiliy b masrd. Thrfor, mahmaical and pracical ramns rlaiv o MTBF ar includd in his uorial using h xponnial disribuion modl. Addiionally, o achiv a horough undrsanding of saisics and rliabiliy, many saisical xprs lis four kinds of undrsanding as shown blow.*. Compuaional/Numrical Visual/Graphical 3. Vrbal/Inrpriv *For addiional informaion on h ims abov, plas conac h auhor of his uorial. Wilson Consuling Srvics, LLC Pag 3 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

4 Inroducion con d Wha is MTBF? Masur of ra of failur wihin h dsign lif. Wha is dsign lif? Inndd priod of us which is xpcd o b failur fr. Wha do hs rms man? Rliabiliy? Failur? Failur Ra? Hazard Ra? MTBF/MTTF? Wilson Consuling Srvics, LLC Pag 4 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

5 Inroducion con d Assumpion of a consan failur ra Whn using Man Tim Bwn Failur MTBF or Man Tim o Failur MTTF, a consan failur ra is assumd and h xponnial disribuion modl prvails. Th xponnial disribuion is among on of h mos common and usful lif disribuion modls. Th xponnial P.D.F occurs frqunly in rliabiliy nginring. Dscribs h siuaion whrin h hazard ra is consan. I is h disribuion of im o failur for a gra numbr of lcronic sysm pars. Wilson Consuling Srvics, LLC Pag 5 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

6 Inroducion con d Rliabiliy Dfiniions RELIABILITY [R] - Th probabiliy ha an im will prform is inndd funcion wihou failur undr sad condiions for a spcifid priod of im. FAILURE - Th rminaion of h abiliy of an im o prform is rquird funcion as spcifid. FAILURE RATE FR - Th raio of h numbr of failurs wihin a sampl o h cumulaiv opraing im. HAZARD RATE [, h] - Th "insananous" probabiliy of failur of an im givn ha i has survivd up unil ha im. Somims calld h insananous failur ra. Wilson Consuling Srvics, LLC Pag 6 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

7 Rliabiliy Mahmaics. Rliabiliy Mahmaics Wha is h Probabiliy Dnsiy Funcion P.D.F.? Dscripion of is maning Frquncy disribuion and cumulaiv disribuion ar calculad from sampl masurmns. Sinc sampls ar drawn from a populaion, h qusion is wha can b said abou h populaion? Th ypical procdur suggs a mahmaical formula, which provids a horical modl p.d.f. for dscribing h way h populaion valus ar disribud. A hisogram and cumulaiv frquncy funcions ar hn simas of hs populaion modls. Wilson Consuling Srvics, LLC Pag 7 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

8 Rliabiliy Mahmaics con d P.D.F. con d A posiiv coninuous random variabl follows an xponnial disribuion if h probabiliy dnsiy funcion is as shown: Thus h P.D.F. f x a ax For For x x I is imporan in rliabiliy work bcaus i has h sam Cnral Limi Thorm rlaionship o Lif Saisics as h Normal disribuion has o Non-Lif Saisics. Wilson Consuling Srvics, LLC Pag 8 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

9 Rliabiliy Mahmaics con d P.D.F. con d I is a probabiliy dnsiy funcion P.D.F. f Lambda is a consan and is calld h failur ra f Figur Wilson Consuling Srvics, LLC Pag 9 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

10 Rliabiliy Mahmaics con d Wha is h Cumulaiv Disribuion Funcion C.D.F.? Th cumulaiv disribuion corrsponds o a populaion modl calld cumulaiv disribuion funcion C.D.F. and is donad by F. I is rlad o h P.D.F. via h following rlaionship. F. P T f d Us as a dummy variabl; L =, hn d =d C.D.F., F Figur A Wilson Consuling Srvics, LLC Pag of 47 MTBF: Undrsanding Is Rol in Rliabiliy

11 Rliabiliy Mahmaics con d C.D.F. Rlaionship o P.D.F. Rliabiliy dals wih failur ims,, which ar nonngaiv valus. C.D.F. for populaion failurs im is rlad o P.D.F. Th P.D.F., which f can b ingrad o obain h cumulaiv disribuion funcion F, and h hazard funcion h can b ingrad o obain h cumulaiv hazard funcion H. Th P.D.F. for h xponnial disribuion f Th C.D.F for h xponnial disribuion F Wilson Consuling Srvics, LLC Pag of 47 MTBF: Undrsanding Is Rol in Rliabiliy

12 Wilson Consuling Srvics, LLC MTBF: Undrsanding Is Rol in Rliabiliy Pag of 47 f. Probabiliy dnsiy funcion p.d.f. C.D.F. mahmaical drivaion Rliabiliy Mahmaics con d Th probabiliy ha a componn fails in h inrval F is. C.D.F. is drivd by ingraing p.d.f. QED R F F F d F d f T P F

13 Wilson Consuling Srvics, LLC MTBF: Undrsanding Is Rol in Rliabiliy Pag 3 of 47. Hazard funcion R f F f h. Cumulaiv hazard funcion: Ingraing h hazard funcion o obain h cum hazard funcion. Us dummy variabl of ingraion ln R H d d d R f d h H ln ln xp ln ln : log R as rssd b can R R sids boh of naural h Taking Rliabiliy Mahmaics con d QED

14 Hazard Ra Th xponnial P.D.F. is a valid usful lif im o failur modl for many dbuggd lcronic componns. P.D.F. f Whr rprsns a consan failur ra ha dos no vary wih im. For rliabiliy purposs, h C.D.F. is dsignad F rahr han Fx and F is dfind as h probabiliy of failur in h inrval < T <. h Rliabiliy Mahmaics con d Usful Lif h f R Figur Wilson Consuling Srvics, LLC Pag 4 of 47 MTBF: Undrsanding Is Rol in Rliabiliy im

15 Rliabiliy Mahmaics con d. R Illusraions: Exponnial Rliabiliy Curv R im Figur 3 Dnsiy f Probabiliy Dnsiy Funcion Curv f im Figur 4 Wilson Consuling Srvics, LLC Pag 5 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

16 Rliabiliy Aras of Probabiliis Illusraion. R Rliabiliy Mahmaics con d Unrliabiliy ara F F f d P T Rliabiliy xponnial disribuion plo Rliabiliy ara R R f d F 3 4 Figur 5 F R R Wilson Consuling Srvics, LLC Pag 6 of 47 MTBF: Undrsanding Is Rol in Rliabiliy F

17 Wilson Consuling Srvics, LLC MTBF: Undrsanding Is Rol in Rliabiliy Pag 7 of 47 d f F Exampl : For xponnial disribuion, ak h ingral of f, whr f = -, whr = d F d F Rliabiliy Mahmaics con d Soluion

18 Rliabiliy Mahmaics con d Exampl : An lcronic dvic conains discr ransisors. Each ransisor has a consan failur ra of = 5 failur ra/hour. Wha is h probabiliy ha a singl ransisor will surviv a mission of 4 hours? R F Soluion R R R F R Wilson Consuling Srvics, LLC Pag 8 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

19 Exampl 3: Wha is h probabiliy ha i will surviv a mission of 3 hours? Soluion Rliabiliy Mahmaics con d R 5 3 R. R.99 F R.99. Wilson Consuling Srvics, LLC Pag 9 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

20 Bahub Curv 3. Bahub Curv Rliabiliy Bahub curv for consan failur ra Failurs infan moraliy consan failur ra warou Figur 6 Tim Infan moraliy- ofn du o manufacuring dfcs In lcronics sysms, hr ar modls o prdic MTBF for h consan failur ra priod Bllcor Modl, MIL-HDBK-7F, ohrs Undrsanding warou rquirs daa on h paricular dvic - Smiconducor dvics should no show warou xcp a long ims - Elcrical dvics which warou: rlays, EL caps, fans, conncors, soldr Wilson Consuling Srvics, LLC Pag of 47 MTBF: Undrsanding Is Rol in Rliabiliy

21 Bahub Curv con d Infan Moraliy Usful Lif Warou Rliabiliy: Bahub Curv Bah Tub Curv composi Hazard Ra Manufacuring Dfcs Exrnal Srss Failurs Warou Failurs Snsors & Firwalls Analyzing shor rm warrany/rma daa Tying dsigns o mfg. capabiliis Insiuing procss CTQ chckpoins Improving nvironmn knowldg Rliabiliy Mrics on Dashboards Figur 7 Tim Rliabiliy Prdicion & Validaion Bginning us of: Fild & indusry daa Prdicion ools Acclrad Lif Tsing Warou Mchanism Analysis Marials characrizaion Long-rm daa mining ALT s o failur Sysm Lif Modling Wilson Consuling Srvics, LLC Pag of 47 MTBF: Undrsanding Is Rol in Rliabiliy

22 4. Failur Ra Graph: Cumulaiv disribuion funcion c.d.f. for h xponnial disribuion funcion. Failur Ra Hazard Ra - Consan wih rspc o im - A funcion of im - An avrag - Insananous % Failur Ra Probabiliy of Failur..95 Avrag Failur Ra Insananous Hazard Ra.9 Figur Tim Rliabiliy: Avrag Failur Ra vs. Hazard Ra Wilson Consuling Srvics, LLC Pag of 47 MTBF: Undrsanding Is Rol in Rliabiliy

23 Wilson Consuling Srvics, LLC MTBF: Undrsanding Is Rol in Rliabiliy Pag 3 of 47 R R H H d h AFR ln ln Avrag Failur Ra AFR for, AFR Pr oof : QED ln ln ln ln : ln : Pr R R AFR R R AFR Thn R H If H H AFR oof QED ln ln ln ln : ln : Pr R R AFR R R AFR Thn R H If H H AFR oof Failur Ra - con d

24 Exampl..98 R Failur Ra - con d Exponnial Disribuion.95 T x AFR AFR AFR ln R im in hours ln R ln.98 ln Figur E Wilson Consuling Srvics, LLC Pag 4 of 47 MTBF: Undrsanding Is Rol in Rliabiliy 6

25 AFR can b rprsnd by lambda Failur Ra - con d Exampl coninud Illusraion - Exponnial Disribuion Thrfor: = 3.55E-6, which is h hazard funcion h h 3.55E-6 hours Figur Wilson Consuling Srvics, LLC Pag 5 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

26 Esimaing Failur Ra Failur Ra - con d Lambda can b obaind as an sima -ha of h ru populaion for all opraing hours for all unis sd including faild and hos ha compld h s wihou failing. I is h bs sima for compl or cnsord sampl: ˆ numbr of failurs oal uni s im Th dnominaor is obaind by adding up all opraing hours on s of all unis sd, including hos ha faild and hos ha compling h s wihou failing. Wilson Consuling Srvics, LLC Pag 6 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

27 Exampl : Fiv lcronics Sub-sysms faild from a sampl of which wr usd consanly for 9 days. Wha is h Failur Ra? Esima of failur ra for λ Failur Ra - con d ^ λ 5 failurs 5 = Failur ra = = *4*9,59, failurs / hour =.93E-6 failurs/hour Ohr xprssions Failurs pr million hours Fpmh Fpmh *E 6.93E 6E 6.93 Prcn pr housand hours This ra ra can b xprssd by muliplying E+5 rsuling in h avrag failur ra = AFR =.93%/ hours Wilson Consuling Srvics, LLC Pag 7 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

28 Failur Ra - con d Sysm failur ra Sysm failur funcion h s is h sum of n componn failur ra funcions h, h,,h n. Whn h componns hav xponnial lifims wih paramrs,,, n, hn h sysm has a consan failur ra qual s n i i Wilson Consuling Srvics, LLC Pag 8 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

29 Failur Ra - con d Facors o convr h and h AFR PPM or FIT whn priod is in hours. Failur ra in %/K = [E+5][h] AFR in %/K = [E+5][AFRT,T ] Failur ra in FITS = [E+4][failur ra in %/K] AFR in FITS = [E-9][AFRT,T ] Wilson Consuling Srvics, LLC Pag 9 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

30 MTBF 5. MTBF Dsign Lif: MTBF: MTBF is no Lif Inndd priod of us which is xpcd o b failur fr. Masur of ra of failur wihin h dsign lif. EXAMPLES: Im Dsign Lif MTBF Conacor 5, cycls 55, cycls Pushbuon 3 million op s million op s CPU-Panl 5 yars 37 yars Do no confus MTBF wih Dsign Lif of an im Wilson Consuling Srvics, LLC Pag 3 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

31 MTBF By l : y MTBF MTBF MTBF subsiui y d dy Ingrain g on y by d y pars dy y QED MTBF con d y Mahmaical Proof Wilson Consuling Srvics, LLC Pag 3 of 47 MTBF: Undrsanding Is Rol in Rliabiliy l u by udv y v y y Rcall: - = Ingraing by pars soluion: & y y y uv dv du & dv facoring y y y y vdu dy y y dv y dy

32 MTBF con d Man Tim Bwn Failurs [MTBF] - For a rpairabl im, h raio of h cumulaiv opraing im o h numbr of failurs for ha im. Exampl AFR can b rprsnd by lambda Thrfor: = 3.55E-6, which is h hazard funcion h h 3.55E-6 MTBF MTBF Figur 3.55E hours d 6 8,757hours Wilson Consuling Srvics, LLC Pag 3 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

33 MTBF con d Man Tim Bwn Failurs MTBF Exampl : If a moor is rpaird and rurnd o srvic six ims during is lif and provids 45, hours of srvic. Also MTBF failurs im 6 45, ,5 hours Toal opraing im 45, MTBF 7, 5 # of failurs 6 hours Wilson Consuling Srvics, LLC Pag 33 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

34 Exampl 3 MTBF con d Using Chi-squar modl o find MTBF MTBF Uppr and lowr bound is calculad such as 5%, 8% 9%, 95%, c. Daa from xampl, prvious pag. MTBF MTBF lowr uppr T, n T, n n Numbr of dfcs T Toal opraing im Dgrs f frdom = n Significanc lvl Wilson Consuling Srvics, LLC Pag 34 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

35 Chi-squar modl - con d Daa from xampl 3, us 9% confidnc or % lvl of significanc. Soluion lowr bound MTBF MTBF MTBF MTBF lowr lowr Uppr bound luppr luppr T, n MTBF con d * 45,., ν 6 T, n * 45,.,ν6 9,., 9,.9, 9, 8.5 9, 6.3 4,865 hours Can b found in any Chisquar disribuion abl 4,86 hours Wilson Consuling Srvics, LLC Pag 35 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

36 MTBF con d Exampl 4 An lcronics assmbly has a goal of.99 rliabiliy for on yar. Wha is h MTBF ha h dsignr should work owards o m h goal? Rliabiliy quaion: R = - and MTBF = / Solv for MTBF Soluion: ln R = = M TBF* ln R - MTBF Hnc : R MTBF MTBF = = ln R 876 -ln.99 = 87, hours Wilson Consuling Srvics, LLC Pag 36 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

37 MTBF con d Exampl 5: If MTBF for an auomobil is, mils... Rliabiliy as a Funcion of Mission Tim Mission Lngh, mils Rliabiliy*, 99.%, 9.5% 5, 6.7%, 36.8%, 3.5% *Consan hazard ra Thr is only a 36.8% chanc of surviving pas h priod of on MTBF i.. whn = MTBF Wilson Consuling Srvics, LLC Pag 37 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

38 6. MTTF MTTF Man Tim To Failur [MTTF] - For non-rpairabl ims, h raio of h cumulaiv opraing im o h numbr of failurs for a group of ims. Exampl : monioring dvics ar oprad for 9 days. During ha im, fiv failurs occur. Also, failurs 5 5 λ 9. 9E im * 4* 9, 59, MTTF 58, 43 hours λ 9. 9E 7 7 Toal Opraing Tim * 4* 9 MTTF 58, 43 Toal Failurs 5 hours Wilson Consuling Srvics, LLC Pag 38 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

39 Exampl MTBF con d An lcronics assmbly has a goal of.99 rliabiliy for on yar. Wha is h MTTF ha h dsignr should work owards o m h goal? Rliabiliy quaion: R = - and MTTF = / Solving for MTTF MTTF ln R MTTF MTTF 876 ln R ,64 hours Wilson Consuling Srvics, LLC Pag 39 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

40 7.: MTTR Man Tim To Rpair MTTR - his is corrciv mainnanc, which includs all acions o rurn a sysm from a faild o an opraing or availabl sa. I is difficul o plan. I nails, for xampl:. Prparaion im: finding a prson for h job, ravl, obaining ools and s quipmn, c.. Aciv mainnanc im, i.., doing h job 3. Dlay im logisic im: waiing for spar pars., onc h job has bn sard. Availabiliy MTTR MTTR r Summaion of xpcd ims of individual failurs mods Summaion of individual failur ras MTBF MTBF MTTR man prvniv main nanc im Wilson Consuling Srvics, LLC Pag 4 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

41 8. Rlaionships Summary Rliabiliy Paramrs Dscripion Hours Rliabiliy C.D.F. Unrliabiliy Rlaionships Summary Hazard ra failur ra/hour P.D.F. Avg. failur ra AFR Failur ra in PPM Fails in im Failurs pr million hours Produc MTBF R F h f % / K hrs. PPM / K hrs. FIT Fpmh AMPS E E CPU E-6.988E CPU E E NCM-W E-6.443E NCA E-6.585E Wilson Consuling Srvics, LLC Pag 4 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

42 Rlaionships con d. Dfiniions: Rlaionships Summary - con d Failur ra Th raio of h numbr of failurs wihin a sampl o h cumulaiv opraing im. Exampl: PPM / K hrs. MTBF Man im bwn failur, which mans ha 63.% of h produc would hav faild by his im. Exampl: MTBF o f d o d Rliabiliy R Th probabiliy ha an im will prform is inndd funcion wihou failur undr sad condiions for a spcifid priod of im. Exampl: R f d Unrliabiliy F - Commonly rfrrd o as cumulaiv disribuion funcion CDF Th probabiliy ha an im will no prform is inndd funcion wihou failur undr sad condiions for a spcifid priod of im. Also, commonly rfrrd o as cumulaiv dnsiy funcion. Exampl: Hazard ra h Th "insananous" probabiliy of failur of an im givn ha i has survivd up unil ha im. Somims calld h insananous failur ra. I is h failur ra pr uni im. Exampl:.8E-6 / hour, F f d o h f R Wilson Consuling Srvics, LLC Pag 4 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

43 Rlaionships Summary - con d Rlaionships con d Hazard ra h Th "insananous" probabiliy of failur of an im givn ha i has survivd up unil ha im. Somims calld h insananous failur ra. I is h failur ra pr uni im. Exampl:.8E-6 / hour, h f R Probabiliy Dnsiy Funcion PDF Commonly rfrrd o as f I is dnod by f whr is a h variabl of inrsd whr fd is h fracion of failur ims of h populaion occurring in h inrval d. Basically, i assums a mahmaical formula ha provids a horical modl dscribing h way h populaion valus ar disribud. Th dfini ingral of is domain mus qual. Exampl: f, Exampls. % / hrs. On prcn pr housand hours would man an xpcd ra of fail for ach unis opraing hours. Exampl:.8%/ hours mans ha 8 failurs ach million unis opraing for hours.. PPM / hrs. On pr million pr housand hours mans fail is xpcd ou of million componns opraing for hours. Exampl: 8 pars pr million pr housand hours mans ha 8 failurs ar xpcd ou of million componns opraing 3. Failur in im FIT: FIT = Failur in On Billion Hours Exampl: 8 FITS = 8 failurs in on billion hours Wilson Consuling Srvics, LLC Pag 43 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

44 Rliabiliy Modls Typ of Disribuion Paramrs Probabiliy dnsiy funcion, f Rliabiliy funcion, R = - F Hazard funcion insananous failur ra, h = f / R Normal Man,.4 4 Sandard dviaion, Numrous applicaions. Usful whn i is qually likly ha radings will fall abov or blow h avrag. f. f 3 3 R R f d 3 h 3 3 f h R Exponnial Failur ra, MTBF, = - Dscribs consan Failur ra condiions. Applis for h usful Lif cycl of many Producs. Frqunly, im Is usd for x. Wibull Usd for many rliabiliy applicaions. Can s for h nd infan moraliy priod. Can also dscrib h normal and xponnial disribuions. f Shap, Scal characrisic lif, f Locaion m inim um lif, Curvs shown for = f 3 f.5 =3 = =.5 3 R R xp R.5 =.5 =3 = 3 R xp h 4 h 3 h =3 = =.5 3 h Wilson Consuling Srvics, LLC Pag 44 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

45 Rliabiliy Modls - con d Typ of Disribuion Gamma Dscribs a siuaion whn parial failurs can xis. Usd o dscrib random variabls boundd a on nd. Th parial failurs can b dscribd as sub failurs. Is an appropria modl for h im rquird for a oal of xacly? indpndn vns o ak plac if vns occur a a consan ra Probabiliy dnsiy Paramrs funcion, f Failur ra, =.5 Evns pr failur, or Tim o ah f a = failur.5 a = No: whn a is an ingr I 4 f Rliabiliy funcion, R = - F R.5 a = a = a =.5 4 R Hazard funcion insananous failur ra, h = f / R h d a =.5 a = a = 4 h f R Lognormal Man,.8 Th Lognormal disribuion is ofn a good modl for ims o failur whn failurs ar causd by faigu cracks. L T b a random variabl wih a Lognormal disribuion. By dfiniion h nw random variabl X = ln T will hav a normal disribuion. Sandard dviaion, f f xp ln R.5 3 R f d h 3 h f R Wilson Consuling Srvics, LLC Pag 45 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

46 9. Summary Summary This papr did labora on h valu of using h MTBF paramr. Howvr, hr hav bn rmndous improvmns in solid-sa dvics ovr h yars. In arlir ims, lcronic componns wr fragil, usd glass ubs, filamns, c., had inhrn war ou mchanisms. By h sam okn, arlir solid-sa dvics had mchanisms ha would caus failurs in im, such as chmical conaminaion, mallizaion dfcs, and packaging dfcs, which rsuld in corrosion and dlaminaing. Many of hs dfcs wr acclrad by high mpraur, which rsuld in succssful us of h burn-in procss o wd ou infan moraliy." Saisical prdicion during ha priod was valid and accpd bcaus dsigns a ha im consis mosly of discr componns; hrfor, rliabiliy saisical simas of h lif of a nw dsign had for h mos par, a rasonabl corrlaion o h acual MTBF. Today hundrds of nw componns ar inroducd o h mark almos vry wk and hundrds ar probably akn off h mark vry wk; hrfor, i is impossibl o mak an accura prdicion basd on a summaion of pars rliabiliy. Exampl: Mil-Sd-7 Today s componns do no hav war-ou mods ha ar wihin mos lcronics chnologically usful lif. Thrfor, h vas majoriy of failurs is du o dfcs in dsign or inroducd in manufacuring. Unplannd vns in manufacuring such as ECN, chang in machin opraors, or chang in vndor s capabiliis of dsign, inroducion of cos rducd pars, c.; any of hs or combinaions can inroduc a dcras in dsign margins. Hnc: his affcs rliabiliy and incras fild rurns. Many xprs fl ha i is bs o spnd im, no on saisical prdicions rahr on discovring h ral capabiliis and idnifying h wak links in h dsign or manufacuring procss, and improving hm. This approach will hlp raliz significan improvmn in rliabiliy. Th nd usr nvironmn is vn mor unconrolld. Th nd-usr will always push h limis; hrfor, a robus dsign will hav a highr survivor ra for hs xrms. Wilson Consuling Srvics, LLC Pag 46 of 47 MTBF: Undrsanding Is Rol in Rliabiliy

47 Rfrncs Rfrncs. Parick D.T. O Connor, Pracical rliabiliy Enginring, hird diion John Wily & Sons 99. Paul A. Tobias & David C. Trindad, Applid Rliabiliy, scond diion Chapman & Hall/CRC 995 Wilson Consuling Srvics, LLC Pag 47 of 47 MTBF: Undrsanding Is Rol in Rliabiliy