HDBK-781.pdf

MIL-HDBK-781

14 July 1987

Ml LITARY

Reliability Test

HANDBOOK

Methods, Plans, and Environments for

Engineering Development, Qualification, and Production

No deliverable data required by thk document.

AREA RELI

DISTRIBUTION STATEMENT A:

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Department OF DEFENSE Washington. Or 20363 .s100

Reliability Tesl Methods Plan% And Environments For Engineering

Oevelopmenl, Qualification, And Production

I Thi$ Military Handbook is approved for use by all Departments and Agencie$ of the DeparImenl of

Oefen$e

2. Beneficial commen!s [recommendations. addmom, deletions) and any perlinenl data which may be of use in improving thi$ document should be addressed 10: Commander, Space and Naval Warfare Sptem$ Command, AlTN: SPAWAR 003-121. Wa$hmglon, DC 20363-5100. by u~ing the self -addressed Standardization Document Improvement Propmal (OD Form 1426) appearing al the ●nd of lhIS document or by letter t!

1!

L . . . ..___-_._../_.

FOREWORD

1. MIL. HDBK.7B1 ii designed to be u$ed with MIL.STD-781. The test methods, te!l plan!, and environmental profile data are presented ,n a manner which facilitates their use with the ta,lor able ta~k$ of

MI L-STD.781.

2. The testing of electronic equipment procured for new military $yslem$ is an increasingly complex process Reliability engineers and ma~er$ must select test methods. test plans, and t.?$t ●nv!ronmenl$ which will enwre that cont,accually required reliability Ievel$ are attained in the field and early defect failures are removed prtor to field deployment MIL-HD8K-781 provides reliability ●ngineers and managers with a menu of test plans, test methods, and environmental profiles. The mo$t appropriate material maybe selected for each program and incorporated into lhe tailored reliability test program derived from

MIL-STD-781.

3. This handbook IS wr, tten for use by the reliability engineer and manager. The sections on rel, abil, ty Ie$t methods and lest plan$ presenl melhods for growth monitoring. environmental stress screen, ng, mean. ume. between. failufe a$wrance testing, sequential tests. fixed-durat!on Ies:s, and all-equtpmen! tests The wctmns on Ies! enwronmemal profiles provide test environments for f,xed-grou~d equ, pment. momte ground vehicle, shipboard. jet aircraft, turboprop and helicopter. and m,ss,les and assembled ealerna! stores eau, pment The references provided will expand the u$er’> knowledge and ?mdIn the destgn and implementation of re)!ab!l,ly Ie%l programs through more delailed data

Ill

CONTENTS

I

Paragraph

1.2 1,2 I

1.2 :

1.3 1.4

2. i

2.1 “.

2., :

3. a

3:?

3.!3

3.1.4

3.1.5 3.1.6

3.1.7

3.1.8 3.1.9

4.

4.1 4.!.1 4.1.2

4.1.3 4.1,4 4.2

&2. i 4.2.2 4.3 4.3.1 4.3,2 4.4

4.4. !

4.4.2 4.4.3 4.5

4.5.1

4.s.2 4.5

SCOPE .,,

Purpose

Applicability Application of handbook.

Taiioring.

h~e;h,cdci!refe:eeoce

Equipmentcategori=

REFERENCE DOCUMENTS

Government documents specificaliGns, Siafidard$, and %m%ak.$ Olher Government documents

DEFINITIONS

Term%

Contractor Corrective maintenance (repair) Decision risk~ Failures Independent chargeable failure categories

Measures oirei!abiiity

Mis$ion profile Life-cycle profile

Procuring activity

RELIABILITY TEST METIIODSANDTEST P@NS

Purpos e c.. ---p Applicatiomm atria Te%t methods

Te\t plans Test method and test plan selection factors

Test melhti and test pliir, $ekder, Tes! method and%! plan pararnew$ebc!icm Reliability DevelopmenVGrowth Evaluation Methods

The Duane Method The AMSAAMethod E.SmOnilOringm etho6s

Ccmpti:ed CA time irotewa! m.et%d Graphical me!h~

Standard EMS . . . . . . . . .;;;;;;.~;

MTBFaswrance test

Derivation of equation.

Procedure

Sequen:ia! :enp!an:

iv

Page i

Q

A s

;5 Is

Paragraph cONTENTS(Continued)

Page

4.6.1 4.6.2

4.6.3 4.6.4 4.6.5 4.6.6

4.6.7 4.6.8

4.7 4.7.1 4.7.2 4.7.3

4,7.4 4.7.5 4.7.6 4.7.7 47.8

4.7.9 4.7.10 A8

4.8.1 4.8.2

4.8.3 4.84

4.9 4.9,1 4.9.2

4.9.3 4.9.4 4.9.5 4.9.6 4.9.7 4.9.8

5.

s 1

5.1.1 5.2

5.2.1 5.2.2 5.3

5.31 5.3.2

5.3.3

Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . j:

Application Theoretical background 21

Test truncation . . . . . . . . . . . . . . . . . . . . . . . .?3

Sequential testexamP1e 23

Standard PRST accepl-rejecl criteria and OC curves 2s

Confidence limits for sequential test$ . 25

Sequential tetts: Program Manager’$ as$e$$ment. . 2-I

Fjxed-duralion leS1s

Symbols

Example problem

Standard fixed.durat,on test plans and OC curves 29

Alternative fixed-duration te$t plans 30

MTBF est, mat, on from observed lest data 30

Exclusion of hypothesm lesivalue$ 30

Specified con f,denceinlerval 30

MTBF est$matton from f,xed-duralion test plans 30

Projecuonof erper,ed field MTBF 32

Fixed-duration tesls. Program Manager’s a%%es%ment 32

All-equipment Production Reliability Acceptance Test Plan 33

Tesldurauon

Evaluation

Accepl. re)ect criteria for the ail-equipment IeSl 33

Add, uonal al!-equ, pmenl production reliability acceptance lest plans

Reloabll,ty estimate% from unit.level results 34

Calculawmm ethos

Numertical esample$

The ca%eolonlyone failure Insomesubsyslem(s) 38

An estimator of the failure rate upper bound AO

Depaflure$ from AO method requirements 40

Noobsecved failures

Typelcemoring

Compmerp rogram

COMBINEO ENVIRONMENTAL TEST CONDITIONS 44

Purpose

Scope

M#ss,on and Ii fe.cycle en.lronmental PrOfile$ and ~e~t conditions . . . . . . . . . . . . . . . . . . . A4

Mission and life-cycle environmental Profiles 44

Environmental testcond,tlons. 44

Combined environments for fixed-ground equipmenl 44

Electrmwc stress and duly cycle 44

Vbbralion stress

Thermal stress v

CONTENTS (ContinueO)

Paragrapt, 5.3.4

5.4 5.4.1 5.4.2

5.4.3 5.4.4 5.5

5.5.2 5.53 5.54

56!

56.2 5.63 5.6.4 56.5

5.7

5.7.1 5.7.2

5.7.3 5.7.4

57.5 5.7.6 5.7.7

5.8

5.8.1 S.8 2

5.9

S.9 1 S.9.2

5.9.3 S.lo 5.10.1

6.

6.1 6.1.1 6.2

6.2.1

6.2.3

Hum, d,ty

Combbned environments for mobile ground equipment

Electrical $Iressanddutycycle Vibration Stre$s

Thermal stress . .

Moisture .

Combined environment% for shipboard and underwater vehicle equipment$

Naval surface crall .,.

Naval wbmanne Mar$ne crab (Army) .,. .

Underwalervehicle$ Combined environments for [et aircraft equipment Mission profiles Env, ronmemal test profde~ Comtrucbon of anenv,ronmenlal profile Test proftle development .,.

COmpOslle enwronmental Iesl profile for multlm, sslonappl, cattons

Comb, ned environments f,>, VfiTOL equtpmeni M,s%ion de$cr, pl, on

Thermal \tress

V, bralion $Iress Electr!ca~ %uess Hum!d81~

Equipment operation Test pro fnle~

Comb, ned environments for wrbopropeller atrcratl and hel, coplerequipmenl Turbopropeller alrcrah environments

Heljcopler environments

Comb,ned environments for a,r-launched weapons and a$!embled external stores M,won’proftle%, Environmental lest profile%

Example of construction of environmental profile W$sile transponauon, handl!ng, and storage Rail transpon condluom

TEST INSTRUMENTATION AND FACILITIES.

Purp05e

Scope Te$I Iacilltie$and apparatus.

Te$l chambers, Equipment cooling Test in%trumenlat!on .

Page

4s 4s

4s so so S& S4

S9

VI

6,2.4

6.2.5 6.2.6

6.2.7

7.

TABLE

9A

10A lB

MIL-HDBK-781

CONTENTS IContinuedl

Cdibrmiona nd. ccumcv Tes!ing the:est focilky Installation oftietest tiamintk test facilii

Sub;ect WJm{Keywordlfk iW

REFERENCES

TA6LES

Apdicntion mmri x Summarv olvariables forthe AMSAA model

Summarv ofeauations, AMSAA model Equalion 6election guide, AMSAA model Critical va!ues of C: mvamettic form of the

Cramm.Von M,sesstatintic Confidence intervals for MTOF. Iailure.terminmed test

Confidence intervals for MTBF, time.terminated tesl AMSAAmodel eaamole

( 1 .>1 100 oercem standard confidence limits on MTBF atiet

Bccenldecision llowet. OL”l>.i)l

(1 II 100 oe.rcent acertdare Canf idence limits on MTBF aher,, accepldec,s#on luvper.0u17,all

(1 .>1 1Od percent standard Conf idnnce limits on MTBF after reiectdecicion llowe, -R,”l>.1))

11 .,1 100 percent mnndard confidence Iimim on MTeF after rejec!decision (upper .O~lv.111 Summarv oftixed4wntion te.l plans Summary of high risk freed-duration test plans Demonstrnled MTBF confidence limit multipliers. for failure calculatmn

Dnmonstcnted MT9F confidence limit mu ftipliefs, for time cnlculalion Accept times of fixedduralion test plans, Proeram Manager’s

Assessment !

Compari80n of risks. standard fixed. duration tests versus PrOQ,Bm Mamwer’sAs sessmant

Test times, .Wmdafd fixad-dumtion tes! plans versus Program ManaQer.a Assessmanl

Failure times fofthe numerical example

Example of correct ordering in the AO bound calculation

Example of incorrect ordering in the AO bound calculation

Example data for computer program Exnmple computer run fordatain TA8LE 21 vii

I—.

Page

MIL-HDBK-7B1

CONTENTS (Continued)

I TASLE Page

I 25

I 29

E

4.9 so

Thermal stress environments for marine crab Environmental profile data (example)

Test profile data (example) HOI day temperatures ~C) for Cla$s I equipment in air-conditioned compartments HOI day ambient temperature (“C) for Class II equipment inair<ond, tioned companments Hot day ambient temperatures ~C) for ●quipment in ram air-cooled companmems Cold day arnb, enl temperatures ~C) for equipment ir?

ram air-cooled compartments Temperatures ~C) for Clasi I and Class II equipmenl ,n air-conditioned companments

Jet aircrafi random vibration lest.

Tabulation of temperature values Summary of temperature values Tabula; ,onof wbrallon Ievel$

Summary of vi brat$on levels Composite test prof,le t,mel, ne Temperature level Iab”lat, on hot day(example) Temperature summary - hot day (example) Temperature level labulation - cold day (e,ample)

Temperature summary cold day (example) V, bral,on level Iabulal,on (e,ample) V, bral, on level wmmary (example) Temperaw,e rate of change (example)

Composite test prof,le timeli,>e (example) Random vibration test for Vf5TOLaircratl Env8r0nmenlal pro f,lesequence

Stores hosl a,rcrati m,ssion utlllzat, on ratei for enwronmental testing

Random wbratmn. 9,-, [OVL), level adluslmenl fanors for the max, mum predicted environment (951h percentile with 50 percent confidence based on one+ide tolerance limO1) lt7

Method of calculating the acceleration power spectral den!ily u spectrum to produce ~ A, ●qual 10a unit - g,m, (OVL) 132

,.1 Preliminary operational des,gn requirements (expected lifeof5years)

Life cycle environments 140

Assumed typ!cal a!tack mission profiles 158

A method for calculating test profde ttmes for a specific number of test cycles 159

Attack a!rcran caplive-carriage mission profole data (e~ample) 161

VIII

TAELE

4a so

S1 cONTENTS (Continued)

Thermal stress environments for marine crafl

Environmental profile data (example) Ten orofile data (example)

Hot day temperatures rC) for Class I equipment in air-conditioned companments Hot day ambient temperature ~C) for Clas\ II equipment in air-conditioned compaflments

Hot day ambient temperatures CC) for equipment in ram air-cooled companments Cold day ambient temperatures ~C) for equipment in ram air-cooled companmenls

Temperature ~C) for Class I and Clasi II equipment in air-conditioned companment$ Jet aircrafi random vi brationte$l.

Tabulation of temperature values

5ummary0f lemperaturevalues Tabulat# on of vi bratl on levels

Summary of vibration le.els Composite test pro file ttmehne Temperature ievel tabulal,on hotday(example)

Temperature summary - hot day (example) Temperature level tabulation - cold day (example) Temperature summary. co!d day(e~ample) Vlbralion level tabulatmn (example)

Vibralion level summary (example) Temperature rale of change (example).

Composite :est prof,le timeliew (example) Random viblation tesl for V/5TOL aircratl.

Enwronmenlal profnle sequence Stores host a,rcraft m,ssion utilization rate% for environmental testing Random wbration, g,-, (OVL). level adjustment factors for the max!mum predicted environment (95th percentile with SO percent confidence based on one-side tolerance limit)

Mel hod of calculati ng the acceleration power spenral den!ity spectrum to produce ~+ equaltOauni~-g,m,(OvL)

Preliminary operational design requirements (expected life0f5years) Lifecycle environments Assumed typical attack mimion profiles A method for Calculal, ng test profile times for a specific number of test cycles Attack aircrafl captive-carriage mission profile data (example)

Page

Vlll

FIGuRE

3s

41!

s?

Te$t Plan ”Xlli-D Test Plan XIV-D Test Plan XV-D Test Plan XVI-D Test Plan XV1l-D

Test Plan XIX-D ‘lest Plan XX-D

Tes\Plan XXI-D Test Plan XVllI-D Bounda~line cri!eriun for rejet~ -accept decision .

All Equipment lestplan derived from Tesl Plan I-D All Equipment teslplan derived from Test Plan II-D AIIEquipment leslplan dertved frOm Tes:Plan 111.D

All Equipment lest plan derived from Test Plan IV. D All Equipment leslplan derived from Test Plan V-D All Equipment te>lplan deri.ed from Test Plan W-D All Equipmenl!est planderived frOm Tes3Plan Vii-D All Equipment testplan der, vedf<om Tesl Plan Vlll-D Time truncauon( lypelcen%or, ng) Combnned envlronmenta( lest profkle for fixed.ground equipment

Combined env, ronmenlal Ie$t prof,le for mobile ground equipment

Naval Wrfa<e Crak, mtssion enwronmenlal profde $or externally mounled equipmenl(cold cycle).

Naval surface craft, mwion enwronmental profile for externally mounted equipment (hot cycle) Naval surface CfafI, M#SiOrT efWi10nr_IW71a1 profile for imernally mounted equ!pmenl (cold cycle) Naval surface crab, miwon env, ronmenl~l profile for i nterna!ly mounted equipment (hot cycle) Naval surface Craft, miss, on enwronmental profile for internally mounted temperature controlled

Naval surface craft, m,s%ion environmental profile for internally mounted temperature comrolled

Surface craft and submarine vibration spectrum Submarine pro file Combined environmental test profile, for marine craft equipment

General mission profile and characteristic for six aircraft types and twelve m,wons

General mismon profile and characteristic! for six a!rcrafl typei and Iwelve mt$~!ons

Genera! miwon prof,le and characteristics for four aircraft types and seven m,s%ions

General mts%ion profole and characteristics for an attach aircraft ona high.low.low-h,ghmtsslon

Page

22a

236/237

26s x

Page

I

FIGURE

-te

M

,Q

10s

General mission profile and characteristics for a fighter air~rafl cm an intercept mission

General mission profile and characteri$ticf fOr a ,econna; y=r,:e ~~cr=f~ ofi a hiqh+upemonic mis5i0n

Mis$ion profile for temperature rate of cha~e calculaliOn Dynamic ~rewre (q) as function of Mach number and altitude Ra”dOm vibration tesl envelope. for jet aircrafi

Environmental profile (example)

Missionpi6f;:=f?~~~cPJe)

Teap:Ofite(=amPle!

Attack aircrafl test priflte ( 10w-lOw-lOw)

Attack a,rcra~tesl prOfile (clOse$up~n) Attack aircrah test prOfile (hi9h-10w”hlgh)

;+.h!gh.high) Attack aircraft test pro~tle (h.=.

~t:ack ~,rc:ep. !eg p,ofile (h, gh-low40w. hi9h)

Af!ack atrcrafl iestorOfile(ferry) :

ASW al,craft teSI profile (contact investigation - h19h) ASW ~,rcrah IeSI profile (contacl investigation intermediate).

Asw a,rcrahlesl prOfile(mln?lafi@ *YVV ~ircrap, ;eil ~:cf{!e (h:gh.high. high!.

ASW Z,r<ratl tesl profile (search and attack).

ASW aircrah te$l Profile (surface ‘Surveillance) ASW alrCtaf LteSt PrOflle(ferry).

EcM alrcra~t e~tpfOfiie( penefrat;or~

ECM alrcraf~ ~e~,Pr~!;l@ @tJnd-Of~ EC~wl~ir::af~~e$~pfQf!lP(f@rr~)

Flghler aircrafi test PrOfile (high-hi9h-high).

F,ghter aircraft lest pro flh?(escoti).

flghler air<ratlte$t profile (a, r deiense and capiive ti~gfi,i).

FighWr afircrati 1e51PrOiiie @;er~eWL).

;ighter aircrak :EW wfile (high-[ ow-low”high) F,ghler aircrafi tes~ PrOfile (Iow-lOw-lOw) Fighter aircfati test prOfile (10w.10w-hi9h)

Fighler a,~crah te$t PrOfile (cl~e $“pWn) Fighter airc,af! te$t proiiie (ferry).

. ..,.-.fila /high-l@w-high!Reco””aistii,ce aircratt W%. p.- ..-.

Reconnaissance air~rafi test prOfile [lOw-10w’h’gh) Reconnaissance aircrafi test PrOfile (low-lOw-lOw) :

Reconnaissance airc~afi test prOfile (high-$ uper$On’cJ ‘ Reconnaissance aircrah tes1 PrOiiie (hi9h.QJb@ic;

ReC0nna15SanCe aircrafi tes: FJr6fi:~ ffe:w) Ta”ke, ai,craft Iest profile (high-low.high refuel).

Tanker a,rcraft {low-low-low refuel).

Tanke, aircrafl le$lprofile (%trikerefuel)

COmpOsilelesl prOfi@(example) Compos,lelesl pro file(example)

Type A VfiTOL airborne early warnln9 miS~lOn PrOfile

27’3 2s0

2&4 ~g~

I xi

FIGuRE

I

I I 22

12s

I 132

Type A VSTOL anti-wbmarine warfare mis~ion profile Type A VfSTOL contact investigation mi$!ion profile

Type A VtSTOL marine a$$ault mission profile .

Type A VE.TOL wrface attack mission profile Type A V/STOL tanker mission profile Type AV/5TOLveflica! onboard delivew rnis;on profile Type B V/STOL combat air patrol mision profile Type B V/5TOL deck launched intercept mi$sion profile Type B VfiTOL subsonic nmface NHVeillance mission profiles

Type A V/STOL airborne early warning environmental pro file, Type A VfSTOL anti-submarine warfare environmental pro files .,, . .. ~

Type A V/5TOL contact investigation environmental pr0ftle5, Type AV/STOL marine as$ault environmental prOfile Type AVISTOL surface altackenvirOnmenta fprOfile.

Type AVISTOL tanker environmental profile

Type A VISTOL venical onboard delivery environmental profiles.

Type BV/5TOL combalair paNolenvironment profile Type B VISTOL deck lwnched mtercepl environmental profiles, . .

Type B V/STOL sub$onic surface surveillance environmental profiles. . , .

Turbopropeller vibration test spectra for equipment mounted within lhefuselage (example)

Thermal pro file forturbopropeller aircvafl Typical mission test cycle pro ffile

Combined environmental test profile for rolarywing aircrah .

Combined mission profile for rotary wing aircrak (hot andcold dayoperation) . .

Typical reliability captive flight test sequence (onecycle)

Typical reliability free flight test sequence (onecycle)

Random vibration maximum predicted ~nvi,o”ment for combined air-launched weapons and as!embled externalslores .

Random vibration maximum predicted environment for air-to-surf ace(AGM) air-l aunched weapons

Random vibration maximum predicled environment for alr-to.ai r{ AAM)air-l aLInched weapons

Assembled external $tures and a,r.launched weapons -vi bra[ional reiponte accelerate on PSD versus frequency speclra

Page

;~j xii cONTENTS (Continued)

Page

I

FIGuRE

14s

1b?

Equipment installed in amembled ●xternal stores and air-launched weapons - vibrational refponae acceleration noversus frquencyspectra Induced buffet maneuver random vibration response spectrum Low- low free-flight mimion profile (example) Environmental engineering program Khemalic Logistics functional schematic diagram European scenario assumed maintenance

$chedule and po$$ible operational utilization rate for environmental analfie} (example)

Target movement timeline for ●nvironmental design criteria (European scenario) - large quantities (example)

Estimated percentage of time distribution for lranspoflalion, holdldelay, and handling, for nominal .probable factory-to-theater movement beeline Assumed typical attack aircrafi operating envelope

[standard day) showing the a~$umed high. medium.low mlmonprofile

Assumed typical attack aircrafi operating ●nvelope

(standard day) showing the assumed h,gh.low-h,gh mis~ion profile

Vibrauon faclor (g,”, (OVL))~ flight missiofl profile high-medium-low use with FIGu RE5 130 and 143 except(”), verw$minimum g,~, (OVL)~(elample) Vibration factor (g, ~$ (OVL))~ fhght mission profile high-low-high use with FIGURES 130 and 144 except (“), versus MiniI’IWm (g,,m (OVL))? (example) Store free. fitght vibration facwr

(g,~, (OVL))2 flight mis~iOn PrOflle IOW-IOW USe with FIGURES 131 thru 134 and TABLE 4B(example)

Unit-grm, (OVL)-acceleration P5D verws frequency spectra . .

Vibration profile$ for rail transportation Rail transpofiationtest profile Program listing for FORTMN program Program listing for FORTWN program xiiifiiv

MIL-HDE!K-781

1. SCOPE

1.1 -. Thi$ handbook provides test methods, test plans, and test enwronmenlal pro f,les which can be used ,n reliabtltty Iest, ng dur#ng the development, qualification. and producuon of systems and equipment

1,2 Acml,cabilitf Th,s handbook ●xplaim techniques for use in reliability test% performed during Ihe imegraled lest programs $pecil,ed in MI L-STO-785. Procedures. plans, and environments which can be used m Reliability DevelopmentiGrowth Tests (RD/GT), Reliability Qualification Tesls (RC)T), and Pfoduclion Reliability Acceptance Tests (PRAT) arediscus$ed. In addition, Environmental Stress Screening (ESSI methods are provided.

1.2,1 APII Iicatmn of handbook. Data provided inthk handbook can ba u$ed $eIeclively on reliability te$t program~ and can be \pecifted m Depanmem o! Defense contracted prctcutements, reques!s for propo~al$. statement$ of work. and Government in-houw development wh,ch reqwre reliability testing

1.2.2 Tailorinq. The data provided herein can be selected for use on tailored reliability test programs as reQu# red by govern, ng regulauons and as appropriate 10 the particular system or equtpmenl, tintended aPPl, Cation, Pr09ram lYPe, magnitude, and funding,

1.3 Method of refeten<e When referencing the lest methods, test plans. and environmental lest conditions of thts hand booh, the handbook and the fpecific paragraph number(s) are 10 be rated

1.4 Equ, preen\ ca!eqornes The methods in this handbook are apPhcable 10 SIXbroad calegones of equipment, dlst, ngufshee accord, ng to each equipment’s field $arvice applicatmn:

Calegory 1

Category 2

Category 3

Category 4.

Calegory 5

Calegory 6.

F,,ed.grcwnd equipmenl

Mobile ground equipmem A Wheeled vehicle B Tracked .eh, cle C. Sheller con f,gurat, on D. Manpack

Shipboard equipmenl A. Naval surface craft B Naval submarine C Mar!ne crafi D Underwater vefwcle

Eqwpment for jet aircrati A. Ft,ed-wing B vertical and Shorl Takeoff and Landing (v/5TOL)

Turboprop aircrah and helicopter ●quipment A Twboprop E Hel Kop:er

Ml$sile$ and assembled external $mres A A,r.launched miwles B Assembled elternal stores C. Ground.launched mmiles

2. REFEflENCF D():LJMENTS

2 I ~v.e~!a!nen! documen!>

2..1.”! Soecbfocat,on%, standard~, and handbooks Unless olherw!se SPeclf, ed. the followong spe,.iff cation%, standard%, and handbooks of the Issue hsled In the Department of Defense Indes of Specifocatlom and Standards (DODISS) and ,1s supplements specif, ed m the solicllatmn form a par! of Ih, $ documer,t to the exk’ol specifted herein.

SPECIFIuTIONS

MILITARY

MIL. E-5400

MIL-E-605!

MIL-P-9024

STANDARDS

MILITARY

MIL.STD-167-1

MIL-STD-21O

MIL.STO-280

MIL.STD-461

MILSTD.648

MIL.STD.721

MII .s1 0-781

~,, L.5TD.785

MIL.STD-81O

MIL-STD.1385

MI L-STD.2164

MIL.STD-45662

HANDBOOKS

MILITARY

MI L-HDBK.189

MI L. HDBK-237

MIL.HDBK.2S3

Electronic Equjpmenl, Aero$pace, General Specifocauon For Electromagnetic Compatibilny Requirement For Systems Packaging. Materials Handling And Trampoflab!lity, SyJtem And Syslem Segmenw General Specification For

Mechanical Vibrations of Shipboard Equipment (Type I - Environmental hnd Type II. Internally Exctledl Cl,maltc Extremes For M,lllary Equbpment De flnil,om Of Item Levels, Item E,changeabilily. Model%. And Related Terms Electromagnetic Em, won 4nd 5u5ceplab,l, ty 17equlrements For The Control Of Electrc.magnel, c Interference Des, gnCr, te, +a For Speclall?ed Sh#pping Contaoner% De{, n,t, omUf Etlect, ven,:$%le(, tl\ For Rel, ab,llly. Matntatnab,l, ty, Human Faclors, And Safety Reltab,l!ty Te$l, ng For Eny, neermg Development. CJual, focal, on, And Producuon Rel(ab,l,iy Program For 5y!1em\ And Equipment Development Ana Producuon Environmemal Teit Melhnd% And Engineering Gwdeline$ Preclus, on Of Ordnance Hazard% lnElectromagnetlc F#elds, Gener~’ Requirements For Enwronmental Stress Screening Process For Electronic Equipment Cal#bra!ton System Requtremenl>

Reltab,lnly Growlh Managemenl Eleclromagnet,c Compatib,llty Management Gutde For platforms, Systems And Equipment Gwoanre For The Des,gn And Tesl Of Sy$tem* Protected Against The Effecl\ Of Electtomagnet,c Energy

I .

2.1.2 Other Governme~t documents The following other Government documents form a part of Ih,i handbook m the ealent spec, f#ed here, n

PuBLICATIONS

NAVAL AIR SYSTEMS COMMAND (NAVAIR)

AR70.38 Reiearch. Development, lest And Evaluation Of Material Far E.lreme Chmatic Conditions

AD.lll S Electromagnetic Compatibility Design Guide For Avionic$ And Related Ground SuppcIrt

(Copies of specifications. standard$. handbooks, and publications required by contractors in connection with specific procurement functions should be obtained from the procuring activity or a! directed by the contracting of ficer.)

I

I 3

3 UFFINITION\

3 \ ~ Term> used herein arein accordance with l&wdef, nitlons in MI L.5TD.2Lf0, MI L. STD.721, iv:,, ,. TO.785. MI L-STD-81O. and MI L-HDSK-189, w,lh the Pxcept, on andadd, uon of Ihetermsspecafoed O.

~ I ! through3 1,9.

3.1. \ Contractor. Contraaor includes Governmental or ,ndustnal acthwl,es developing or producang {nliitary sys!ems and equipment.

3.1.2 Corrective n,aintenance (reoair]. The acciom performed, as a result o{ failure. to reslore an ,Iem to a specified cendiuon

3.1.3 Decision r,$k$ Deci!ion ri$ks shall be as fpecified in 3.1.3.1 through 3.1.3.3.

3.1.3.1 Consumer’s risk @. Consumer”% risk (&) i$ the probability of accepting equipment which he! a true n!ean-lime.&lween-fa,lure (MTBF) equal 10 the lower te$I MT8F (01 ), The p,obab(l,ty of accepting equipment which ha~ a lrue MTBF less than the lower ?%1 h4TklF (o, ) will be Ie!$ than @)

3.1.3.2 Producer”$rtsk (~ Producer’s risk (CY) IS the probabllltyof refecungequipment which ha> a true MTBF equal to the upper lest MTBF (8D ) The probability of rejecl, ng eqtopmenl wh, ch has a lrue MTSF greater than the upper test MT8F (L90 ) w,II be less than (a)

3.1.3,3 C%<riminaiion ratm (d!. The dmcrimmation ral,o (d) usone of the standard lest plan parameters; it osthe ratio of the upper tesl MTBF (80) 10 Ihe Iowertesl MTBF fe, ): lhat is, d . C?UI0..

3.1.4 _ Failure iypesand clas$ii!ca(ion$ arespec, iled In MIL.5TD.721, wtththe ezcepl)onoi multiple, paltern, and chargeable fa,lureswhnchare $per,l, ed ,$. : ~ 4 1 through 3 1.43

3.1.4.1 Multiple failure% Mull,ple fa,lu!es are !he wmultaneous occurrence of IWO or more independent fatlures When two or more faded parts ale found durtng lrouble$hoollflg and Iaolure$ csnn6:

be \hown 10 be dependefll. mul!lple fa!lures are prmumed to have occurred, 3 ~.d.2 Pattern fa,lures The occurrence of IWO or more Ia,lure%of the%ame pan #n ,dent, cal o.

equ$valenl applucatoons when Ihe fa,lures are cau%ed by the same bawc failure mechanwm ano the teIlu#es occur M a rale wh,ch n tnconsislenl wnh the pan”% predlcled fa!lure ra!e

3 1 4.3 Chargeable failure Arelevanl, Independent failure of equ,pment under test and any Cfependent failure$cau%ed lhereby wh, chareclasmi, eo a%one ia,lure and used todelermine contractual compfaance with acceptance and reject, on criteria

3 1.5 Independent! chargeable fa,lure caleaorte$ Fa,luresdef, ned, n 3.1 5.1 lhrough 3 1 55 are categorized as independent chargeable Ia$lures

3 1.S 1 Eauipment des,qn fa,lure Any Ia,lure wh,ch can be traced dmectly 10 the des$gn of the equspmenl; that ,s. the des#gn of the equtpment caused lhe part tn questoon to degrade or fall. rewlttcg tn anequ, pmenl failure

3.1.5.2 Eau,pmenl manufaclunno failure A failure wh,ch i$caused by poor workmanship or finadequ ale ma”ufactur,”g process conl, ol d“r, ng equipment construction. Iestlng, Or ,epalr Prl Or 10 Ihe slar! of testing: for example, the failure of an ai$embly d“e to cold solder jmnls

3.1.5.3 PandeS!Qn fa,lure The fajlureof pans wh!ch can be traced d,reclly loonadequatedes,gn

3.1.54 pan Manufaclurtna failure Parl fa,lureswh+<h are the rewllof poor workmanship or inadequate manufacturing process control dur, ng par{ assembly, tinad equate nnspecl, on, or Improper te51tng

3 1 55 So flwa~e erro, fa,lure k fa, ture caused by an error inlhe computer pro$~am a%so<$ated wtn the hardware

3 1 6 Meawrwol rel+abil, tt Reliability measurement shall be as speofhed !n 3 16.1 through 3 1.69

3 1.6.1 Demonstrated f4TBF interval (8 d I Demon$tralid MTBF irnerval (@d ] is the probable range of true MTBF under lest cond,l, ens; that I%,an interval e518mate of MTBF al a stated conlldence level

3. 1.6.2 Observed MTff F (j). Observed MTBF [j) is equal to the total operating time of the equipmem divided by the number of relevant failures.

3.1.6.3 Lower test MTE~ (c?L). .Lower tesl MTBF W! ) it that value which ii unacceptable. The $tandard test plans will reject. with high probability, ●quipment with a true MTBF lhat approached (f?, ) d~,r,.i..ti..ra~3.1.6.4 Upper test MTBF f ). Upper test MTBF (L70) is an acceptable value of MTBF ●qual to the t!me$ the lower te$t MTBF (& ). The !tandard test plans WIII accept, witn high probability, equipment with a true MTBF that approached (@.), This value (00) shall be realistically alla, nable, based on experience and ,nformali on.

3.1.6.5 Predicled MTBF (6’Q). Pred!ded MTBF (OP ) i$ that value of MTBF determined by reliability pred, cuon method%. tit asa {unctmn of the equtpmetm design and the uce environment. (&P) should be equal 10 or greater than (8U ) in value. to ensure with high probability, that the ●quipment will be accepted during the reloabollly qual, f,cation lest.

31.6.6 Ob$er.ed cumulali.e failure rate (P(t)l. The observed cumulative failure rate (P(t)) at time (t) I%equal to the number of relevant system Iailurei N(t) accumulated by (t), divided by (I).

3.1 6.7 Intensitv function (P(t)) The intensity function (P(t)) i$ the change per unot lime of the expected value of N(t), the number of system failure$ muluplled by time (t). This is writlen as:

P(i) = dE(N(t))/d!

where E ,epre%ent% the expected value

3. 1.6.B hmtamaneous MT8~ function (M(t)). The instantaneous MTBF function at (t) is equal to the reciprocal of the failure rate {unclmn.

3 1.6.9 Ob$er.ed reltabil,tv (R(t)) A point eslimale 0( reliability equal to the probabfl, [y of survival for a $pecif, ed operaling !tme. (1). g,ven that the equipment was OpwaliOnal at the beginmng of the per80d

31.7 Mission orof,le A genenc definition is specified on MIL-STD.72 I Thi$ ampliflcal,on of that de ftnitqon appltes 10 rel,abilily test programs. A thorough description of all of the major planned events and cond, t,c.ns associated with one spec,fbc miwon. A mission profile is one ~gment of a Ii{e-cycle prof#le (for example. a mil$ile caplive. carry phase or a miisile free-f ligh: pha$e). The profile depicti the Ilme \pan of the event, the expected enwmnmental Cond, tmns, energized and nonenergized periods, and so fonh.

3.1 B Life-cvcle orofile A thorough time-life description of the events and conditions a5socoaled with an item of equipment from the lime of f,nal factory acceptance unlil its ultimate dispositmn (for example, facxo,y.to.target sequence) Each significam life-cycle event. such as tran$pofiation. dormant storage, te%l and checkout. standby and ,eady modes, operational deployment. and mission profiles, #saddressed.

includbng alternate po$!, bil, ues The profile depicts the time span of each event. the environmental conditions, and lhe operating modes

3 1 9 Procur#nq acl,. (ty As used on Ih, s handbook, procuring ac[tvily refers to a Government agency or toa prime contractor on tran%acuomwtth itswppl, en

4 RELIABILITY TEST METHOOSANDTEST PLAN5

4.1 -. Section 4 provides information and gwdance tor Y?lecIing the Iesl melhods and Ies..

plans required 10 implemeni the left program~ specif}ed in MIL.STD-7E1

4.1.1 ~. Section 4 provides test method% and test plans which can be used when performing the reliability test programs $pecified tn Task\ 200.300, and 400 of MI L-STD.7E1. Methods are provided for e.aluatincl data Drocfuced durina RDIGT and ESSDroaram$. lest Dlans are Drovided for MTBF assurance and fixed-d ur;!ion aid sequential re;iabili!y demons~ral;on and awe;srnent le~ts and all-equipment reliability iestk Thaw test plain can ba selected for u$e in ROT and PWT.

4.1.2 Agolications matrix, The interrelation$hip~ between the test methods and test plans described herein and the tasks $pacified in MIL-STD-7BI are provided in TABLE 1.

4.1.3 Test methods Methods for evaluating reliability growth during RD/GT and for evaluating ESS programs are provided in4.1.3.l and 4.1.3.2.

4.1.3.1 Growlh monitor!na method Two growth momloring (data evaluation) methods are described: the Duane Method and the Army Material Systemf Analysis Agency (AMSMJ Method The Duane Method is a graphical and nonstatistical technique which can be used 10 graphically plot changes in reliability. The AMSAA Melhod is based on Ihe a}wmphcm that the time> between successive failures ca” be modeled as the intensity funct, on of a nonimmogeneow Poisson process. Th!$ ,mensity f“ncuon is expre;%ed a$ a Mult!ple of the cumula18ve Ie$t tame raised 10 wme power. The Ouane and AMSm methods are described in MIL-HDBK.1B9

4.1.32 ESS evaluation methods Two ESSevaluat#on melhods are described which prowde a meam to determine when the ESS procetiure should be terminated One of the methods provides a techn,que for calculating a required ESS time Interval (which must be $au$f,ed 10 $IOP screening) prior to the slarf of Ihe

ESS The second method make% use of arbitrary Inmes based on hmlor,cal data.

4. 1.4 Test plarm MTBF ajwrance Iesl$ and the f,.andard test plan, provide a wide selection of Ieits suitable for tailoring IO conform 10 the requirements of any rel#abillty program

4. 1.4,1 MTBF aswrzmce lesl$ The MTBF asswance Iesll we a failure-free interval concept 10 ver, ff

MTBF. Thetestsprowde ades!reo ajwrance Ihal a mln!mum specifoed MTBF level i$achleved inadditnon to providang assurance thal early defect failures have been eliminated This test can be used on production equipments which have prewoudy pa%sed qualnflcatton tewng The MTBF assurance :e>t provides the producef with a high probability of wccess.

4.1.4.2 Stzmdmd test olans The standard lesl plans conta, n slalist!cal criteria for deIerm8nung C0mp18a~Ce w,th spectif,ed rehabillty requtremenl$ and are based on the assumption that the underlying distribution of tnme+belween-fail ures ISexponential The exponential assumption impltes a constant fa)lure rate; therefore, thew test plans cannot be used for the purpose of el)minat$ng design defects or infant mortality failures The standard tell plans are as categorized In a through d:

a. Probability Ratio Sequential Test plans (PRST) (Test Plain I-O through VI-D)

b. Shon-run h!gh.r!sk PRST plans (Test Plans VII-O and VIII-D)

c. Ftxed-duratmn lest plans (Test Plain IX-O through XVII-D and XIX-O through XXI. D)

d. Ail-equipment reliab!hcy te$l plan (Test Plan XVIII-O)

These statistical test plans are to be used to determine contractual compliance with pre-e$tabl!shed accep!.

reject criteraa and should not be used m project equ$pme”t MTa F

4.2 lest method and tesI elan selectnon factor% The rnOSI important factors to be c.anmdetee when selecl, ng an approprna!e lest plan or method are prowded tin 42.1 through 422 S

I 4.2 1 Tesl method and te%! elan selection Thelejl rnethod%and te%: plans to be uwd in RD:GT, RQ7, PRA?, and ESSshall be selected from lrw malerml prowded m a Ih,ough f The test melhom or lest plans

$hould be specified fin the contracl and Ihe equlpmenl specification and described. an delatl, ,n the reliability test plan document.

a. The rel!abil!ty grotih monitoring method should be selected under condtuom where parameters of the ume-to-failure d,stributmn are ●xpected 10 be changing with t#me.

b. The ESSmethods are 10 ba wed to eliminate ●arly defecu (infant morcalily). The Standard Environmental Streis Screen i$ a form of ESSused when ic muff be verifkd that equipn%en!, which has passed previous reliability testing, has not been degraded by the production process

c. The MTBf as$urance I-I can be used to provide assurance that a minimum specifwd MTBF has been achieved and that early defect failure$ have been ●laminated.

d. A flaed-duration lest plan must ba aelecced when it i$ necc.fmry to obtain an estimate of the true MTBF demonstrated by the lest, as well a%an accept-reject decision, or when total test lime must be known in advance.

e. A sequential lest plan maybe aelectad when it is desired toaccepl or reject predetermined MTBF values (eO. @!) with predetermined risks of error (ca~). and when uncertainty in total test ome is relatively unimportant. Tht$ lest will fave test lime, as compared 10 fJxed-du ration le$t plan$ having iimilar risks and doscr, m,naticm ratio%, when the true MTBF is much greater than (@O) O, much less Ihe” (81]

f. The all.eqwpment test plan maybe selected when all units of the production run must undergo a reliability lot acceptance test.

These Stau$tical lest plans are 10 be used to determine conlracluat compliance with pre. e$labtished accept-reject criteria and \hould not be used toproject equipment MTBF.

4.2.2 Tesl me:hod and te$l plan paramelerwlecoon. Themoslimponant pa~ametersmbe considered when select, ng test methods and test plain are discussed in 4.2.2.1 through 4.22.5

4.22 1 Ectu,oment performance. The parameter! to be measured during reliability le%:i and the applicable acceptance I!mtl% should be delermmed by the performance requirements of the equipment destgn control specif,cat,on ana should be included in the test procedures.

A.2 2.2 Equipment auamity lhe number of equipmenl 10 be \ested, not necessarily $,mullaneousby, shall be aelerm$ned as described herein or as specified in the carnracl.

a Sample s,ze [reliab,l,ty growth andqualificat,on). The$ample vzerequired for the growlh and qua! tf,cat,on pha!e lest plain should be as spec!f,ed on the contractor as agreed to by Ihe conwactor and the procur, ng acu., ty

b. Sample $ize (production reliability acceptance). Unles$ olherw45e specif,ed by the procuring acttwty, the mmimum o{ samples ta be tested per [ott% three p,eces al eqwpmenl. The recommendeci Jample s;ze #s10 pewent of the equipment per 101. up 10a maximum of 20pieces of eqwpment per lot

c. All-equipment praductian reliability acceptance test. Under this Iesl plan. all producuon equopment is subjecled to the rel!abtlity acceptance le5t. All-equipment acceptance Iesung (100 percent sample) should only be specif ted under exceptional circumstances. as determined by the requ, remenls af ~fety or mosston success d Sample $ize (ESS) Unless otherwise $pecif,ed by the procuring aCli.itY. ielected development equipment and all equ,pment in production Iats should be wb]ected to ESS In h!gh volume production runs, the sample sflze from each lot shauld be selected by the procuring activity. In,taal 101$ should be 5creened al lhe 100 percent level. Sample size on later lot> may be reduced by the procurtng acttw:y baaed on the screening results.

e $ampiesize (opltonal nonstatistical te$l). The sample stze far1h#5 Iesl isal! equlpmenl tin a lal whase ver,l, ed reliabil,ly charac(er!$ticj may be degraded by m.inufaclur, ng and qu.31f1ydefeC!>

1’””

MII.-HDBK-781

4215 1*.1 du,.+t, o,> Ttw test duratton for ftDIGTshou10 bespec, f,ed ,n advance, by Ihc.

bovemmer. t, 10 the request for proposal. contfacl, and spec, ftcah on, Dur, ng the test program, add, (,ona!

test time may Ix> specif ted ,f needed lo achieve reliabi~!ty goal% ESS lime i$avar, able, wfmchdepencf son 1o,, size, fa,lure d,,.lrf bution 01 the early faiiures, types ofenvi tonmental >Iressappl, ed, and stress levels Some maximum allo.v.lb[e lest tlme$hcwld he wed for test plann, ng For%equenlial lest plans, lest cfwat, or, should be plafi.wd on the baits of maxtmum allowable lest lame (truncation), rather than the expecteo dectision poii~l, (o avoid the probability of ~~nplanned tesl cost and schedule overruns. Testing should continue imt; i (he total UI18t hours together with the total COunt of relevam equipment failures permit either am accepl or rejeci decision in accordance with the specified test plan. However. for the all.

equipment reliability test. testing should contanue until a reject decision is made or all contractually required equipment has been tested. Equipment ON time (that i% equipment Operating time) should be used to determine ten duration and compliance with accept-reject criteria. Testing should be monitored so that the times of fai!ule may be recorded accurately. The monitoring instrumentation and techniques and the method ofesbnating fiA7BF should be included in the proposed reliability test procedures. Each equipmenl should operate al least one. hali the average operating lime of all ●quipmem on test. The duration of fixed-time tests should be speci {tied in the request for proposal, contract. and equipment specification. Thus test duration should be the max, mum allowed by the schedule and l,scal constraints of the program.

4.2.24 Deciwon ris}, > Theconsurner’snsh (fS) i$ the probabiltly lhatequtpmentwilh MTBF equa! :0 the lower test MTBF WIII be accepted by the test plan. The producer’s risk(a) 15the probability Ihat equipments with MTBF equal to the upper test MTBF will be rejected by the test plan. In general. the use of low deckion ri~ks will resull In longer test I,me However. low dec, s,on nsk$ prowde protection aga, nit the rejecu. a” O( satisfactory equipment or acceptance of unsatisfactory equ, pmenl For each of the truncated sequential plain (PRST), the ezact nskswe, e calculated. ShifKsi” the accep[. reject I,nesa”d truncation po, ms were made to bring the True ,isks closer 10 the dewgnated risk~ and 10 make the two risks more nearly equal Ioreach plan Thedecis, on nsksof the all-equipment rellab,litytest vary w,lh the lolal teslt!meancf have !AtIle ~ig,),ft<ance .?! ,><cason forchoos!ng thss plan

4? > 5 >,%t,#,o,ondt,o,~.tilau di I The d,scr, m,nation ralio (d) M the rallo 01 the upper Iesl MTBF ( 80) to tile lower test MTBF (6’:) and Isa measure of the power of the te%llo reacha decision qu, cklyand, together w,th the dec, saon risks, define a sequential tesis accept-reject crtiteria In general, the hsgher the d,scriminat, on ralto (d), the shoner the lest The dtscrim, nalion rauo (d) (and corresponding lesl p!an) m~sl hc chosen carefully 10 pre.enl the resulung (@O)from becoming unalminable due to de$ign I,tn,lat,on$

.I 7 Rel, abilitv DevelopmenUGrov.nh Evaluation Methods

a. The Duane Mel hod was originally developed by J. T. Duane ($ee Reference 1). Thns method make> use of a graphical and non%tat,$t,cal technique wh!ch provides a p,clorial presentation of the changes occurring In the measu reti rel!ab, hty parameter. Numerical estimales of the reliability parameler also can be obtained.

b The AMSAA Melhod for evaluating reliability growth presented here#n was developed by AMSAA. Th, i method t> d,scussed ,n some deta!l in MIL-HDBK-189. Additional ,nformattcm is prowded !n Reference 2, The AMSAA model was selected for inclusion In thi$ handbook becauw it is an analyucal modei which permits confidence interval est, males to be computed from the test data fof current and future values of reliability (MTBF) or failure raie (k), In addition, the model can be applied to wther conwmmus (ume) or discrete (rounds. roiled reliab,lnly systems. single or multiple systems, and testf which are time or failure truncated

4.3.1 The Duane Method. The Duane Method is a graphical technique which is useful in the analysts of reliability growlh data. The :echn,que is quick, simple. and easy to understand The Duane plot or graph can dep!ct facts that may be h!dden by a purely $lalmt!cal analysis For example, a goodness. of. flt Ies! may calf for rejecting the AIVISAA mocJe!, but VVIII “c,t ,“d!cate pombfe reasons for che ,eject’on A plot of the same data may find, cate some reason for the problem, Howevev. (he rel, abil,ly parameter> cannot be estimaled by the Duane Method aswell a$ they can by a $talIshcal model and, of course, no ,r.ter. ai esl, mates can recomputed lnadd#l, on, the Duane plot uses a%traight line which is ftltedby eyetothedala points. Thegraphtcal andstat, st, calmethods should beviewed ascomplemenlary techniques

43 1.1 ~ The%ymbols used, nlheequat, On$oflhe Duane Melhod are:

C(t) = expected number oflailures in(l) un,t$ofdevelOpment lesl,ng dtivided by(t) f(i) = eapected numhcof failures in(t) units ofdeveJopmenl te$1ing m = dOpe Oflhe Duane plOt

* = reciprocal of theordinate of the Duane plolat(t) = 1 e(() = current MTBF r(t) = current failure rate

~ = a.erage failure rateofgrouped datainintemal(i)

4.3 1.2 Construct, onofa Duane olot The Duane plotcan ticon$trucled asspecifted inathroughg:

a. The Duane model can reexpressed in the form:

c(l)= Al-”’ where:

c,,) . y

Since (F(I)) 15Ihe expected number of failures experienced by the sy5tem during (t) units of development Ie\ling, it can be e$timated by (N(t)), the observed number of failures during (1) units. Therefore, Iv(()/( . .\ I - “ usthe observed relationship. Thrs may be expressed as a linear relationship. suitable for plotting, by taking Iogar!Ihms ln(h’(f)lfl = (n(k)– m In(l)

However. since il is easier m wsualize growth a%an upward doping line. a more commonly used reta:lonship is:

ln(Uh’(0) = m 1.[!1 - In (A )

b. As the Iest#ng progresses. record is kept of (1), Ihe total units of operation accumulated among all the systems Thus, !f three systems have been tested for 100 hours each, t = 300 Record alio IS kept of (N(l)), the cumulative number of failure! experienced during the (t) units of OPeralion.

c. Al selected .alue% of (1), the quantily (UN(1)) is computed.

d. .Uvng full-log graph paper, the value$ of (t) and (UN(1)) are plotted on the ab$o$$a and ordlnale, respectively e If Ihe plolted po!nts form a rea$onably$tra, ghl I,ne. II can be concluded Ihal lhe Duane mode! ,$ & reamnable me!hod for tiescrtb, ng the growth pattern observed f After f,tt, nga $ua, ghl Ilne through these po, nls, (), ) may be esltmaled bylhe reC@ro;al of the orddnate al(t)= 1 The paramele, (m) maybe estimated by Ihearnlhmel!c slope of Ihel, ne Each successive point contains all the in fcwna toon contained in earlier points. Therefore. the most recent po,nts should be given heavie$t weight in plol. ung the lane.

9. An e$timate may be made of the current value% oi MTBF (f?(u) and the iatlure rate (r(t)), by means of the relationships:

G(i) - im/(i - m)k and

Any ●xtrapolations beyond the test period are Sen$itive to the a5SumPU0n of using the Guane mOdCl, and me-a ..,* ~swi.mmal S55U%P4WOU.8,-. ..,= ~,q, . .. . . . . . I. o rem.t.. . . . ..-1. .I. -.+ 4... . . . . . h-., .h - .,.-,.,” ++ ,. ~ =.’- r-mctant i“ the ●!?s~,i.ng pened, The

●nalfiis of data from several identical $ystemi being tefted simultaneously may be complicated by (he fact that d-ign modifications may not be introduced on all $fitem~ simultaneously. This will result in a mixture of configuration ages wtiIcn wiii make data anaifiis more aifficuii

4,3.1.3 Ezamole. As an ●xample, three systems were teswd simultaneously until a Iolal of

1000 hours of operation was accumulated among the Ihree $y$tem$. As failure! occurred, appropriate design modifications were introduced on all three symems. The cumulative number of failures encomfered afler selected peraods of testing and the Corresponding vaiues of iu”Nii)) are given beiow:

N(I) UN(1)

(hundred~of hours) —.

1.00 3 0.333

2.00 6 0.333

5.00 !3 03135

8.00 18 0.444

10.00 22 0.454

The MaIue$ of (1) and (1/N(tjj a,e ihowm piotle.j in iiGURE 1. The points form a reasonably straighi i!fle, suggesting thal the Duane model ISappropriate for describing Ihe glOWth pattern observed. A straight l#ne is then f!!!ed ~.hrough th?s? poinw

The ord$nate at (t) = 1 1s0.31. Therefore. ).= 1/0.31 = 3.22 Thear#thmetic slopem = 15 milltmelers(mml divided by 95 mm = 0.1SS. This may ai$o be determined by:

fn(o .445) - ;fi:o.3; o) _ 0,,57 m.

in[l Gj – in(l) –

The MTBF curretwly achieved a! 1000 hours may be esiimated as:

, 0 +0.::?

e(!~o~) . = 0.52 SSAu.ndmdhoum = 52.813 hOUI%

(1 - 0.157)(3.22) and ihe current failure rate may be estimated as:

r(li2@2j = (; - 0.;57 )(3.22) iO+.:$~ = i .8% fuiiutea per hundred hotirs

= 9.0; S9 {iiilures Fr hour

MIL-HDBK-7B1

The MTBF expected al 2000 hours maybe esumated as:

*O +0 1s7 e[2000) = = 0.5696 Aundrcd hours - 58.96 houm

(1 -0. IS7K3.22)

This ●$timate assumes that the Duane model i$ valid for the growth pattern being ●xperienced and that the program effon is so remain constant.

4.3.1.4 Problem$ of olottina aviraae failure rate. One disadvantage of plots, such as the Duane plot which us- cumulative measures, is the fact that the most recent data tends to get buried when it is combined with all the previous data. Pkotting the averaga f?ilure rate of selected intervalf eliminates this problem. The lack of cumulative smoothing. however, does make the atierage failure-rate plot much more sensitive to sampling variation. The average failure-rate (AJ over anytime inlemal i$ the number Of faifufe$ in that interval (n) divided by the total operating time in the interval (TJ.

The choice of interval$ i! arbitrary, bul they should be small ●nough to reflect trends, yet large ●nough to afford some $moothing. The average failure rate is plotted as a horizontal line for the appropriate interval.

The test results used in the previous example are grouped into intervals and the average failure rate i!

computed for each imerval, that is:

Interval m i f!s!m Number of failure% & \FaiIwes/hour~

0-100 3 100 0.0300 100-200 3 100 0,0300

200-500 7 300 0.0233

500-800 s 300 0.0167

80& 1000 4 2’30 0.0200

A.erage failure rate over each interval is shown in FIGuRE 1; however. FIGuRE 2 provides a clearer picture of the trend.

4.3.2 The AM5~ Method. A wmmary of the variable$ used in the AMSAA model is given m

TABLE 2.

4.3.2.1 Determination of trend from test data. Prior to the use of the AMSAA method, any significant trend ,n the test rewltl must be identified. Multiple sywem! should be analyzed on a cumulative test duration ba~i! (time, mile$, and so forth) by combining the failure data on the multiple systems. as if Ihey were a Jingle $ystem, and then analymng the data as a single sywem. (f the period of observation ends with a failure. use Ihe test statistic (/4 generated by equation 1 in TABLE 3. If the failure data is time-truncated, use lhe test statistic (P) generated by ●quation 2 in TABLE 3. At the 10 Percent (lw~~ided) significance Ievel. g = 1.U5; therefore, if:

a. p S - t.645: Significant reliability g,owth is indicated at the 10 percem $ignif, cance Ie.e[ and the AMSAA model can be used for estimaung parameters of interest b p= + 1.645: Slgnif!canl relia~,l!ty decay t> indicated at the 10…