RELIABILITY ENGINEERING REPORTS AND SERVICES

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RELIABILITY ENGINEERING REPORTSAND SERVICES*INSTANT MTBF REPORTS!*PSI will send you a RELIABILITY PREDICTIONREPORT within minutes to your e-mail address. Click on the "Instant MTBF" button to access input datasheets. Just enter quantities of each part type in your equipment. It's that easy!! Fill in the headerinformation as you want it to appear in the report. More than one assembly? Just repeat the aboveinstructions. Predictions are per MIL-HDBK-217F (N1/2) or Commercial/Bellcore. Your Choice!Probabilistic Software, Inc. (PSI) is a thirty-five year old California corporation specializing in thepreparation of the following reliability engineering reports to meet Commercial, DOD, DOT, DOE, FAA,NASA, FDA, etc. qualification requirements: RELIABILITY PARTS COUNT OR PARTS STRESS PREDICTION (MTBF) MAINTAINABILITY PREDICTION (MTTR) DERATING ELECTRICAL STRESS ANALYSIS FAILURE MODE, EFFECTS AND CRITICALITY ANALYSIS (FMEA / FMECA) SAFETY HAZARD ANALYSIS WORST CASE (PARTS/CIRCUITS) TOLERANCE ANALYSIS THERMAL ANALYSIS FAULT TREE ANALYSIS MECHANICAL RELIABILITY PREDICTION TESTABILITY / BIT ANALYSIS CONFIDENCE LEVEL ANALYSISPSI will perform, document and deliver the above listed reliability analysis reports from your design data ona firm, fixed price basis, in final typed form, suitable for reproduction and submittal to your customer. Allprices include our guarantee of the acceptance and approval of the reports by you and your customer.Click on the "Brochure" button to view PSI Clients, Projects, Capabilities.Click on the "Examples" button to view our typical Mil-Spec engineering data analysis tabulations.Probabilistic Software, Inc. (PSI), PSI Building Suite 101, 4536 Indianola Way, La Canada Flintridge, CA 91011, Telephone: (818) 790-6412 * Facsimile: (818) 790-9743 *e-mail: PSIREL1@aol.com * URL: http://www.e-Reliability.com * Copyright 2002 Probabilistic Software, Inc. All rights reserved.

PERFORMANCE: PAST AND PRESENTThe following is a partial list of Systems/Equipment on which PSI has performed:AH-64 Apache HelicopterPBTS Proton Beam Treatment SystemImproved Thermal Sight System, Light Armored Vehicle (LAV-25)Geostationary Operational Environmental Satellite (GOES) N-QXM-Radio Missile System Prelaunch Safety Data Package (MSPSP)ICO Final Missile System Prelaunch Safety PackageETS-8 Propellant TankEmergency Escape Sequencing System Tester (EESST)ITAS/IBAS/Missile Control Subsystem (MCS) Power Supply Assembly (PSA)IBAS/TAS Periscope Head Subassembly (PHS) Power Supply Assembly (PSA)IBAS/MCS Line Filter (FL1) CCAIBAS/TAS/LTAS Reticle Projector AssemblyWireless Ground Link Quick Access Recorder InterlockC-17A Drogue Parachute Camera Video SystemP2 Fuel Control Isolation ValveDOT Scan Terminal and Communication CradleSpace Based Infra Red System (SBIRS)/Central Theater Processing Program (CTPP)Talon ShieldAutomated Tape Library SystemsAttack and Launch Early Reporting to TheaterStabilized Infrared ScannerPassenger Entertainment SystemHigh Performance Power SupplyASW Digital Computer Unit, MK38/MOD 0IDL System Pod Data Terminal and Peculiar Support Equipment (PSE)Torpedo System, MK49/MOD 1L-1011 (Airbus) Automatic Flight Control SystemNASA/Houston Recorder-Reproducer (Mag Tape)Airborne Warning and Control System (AWACS) Avionics SystemAir Traffic Control SystemDPC Model 4910 Line Printer

ELINT SystemsECM SystemsComputer Card-reader SystemP-3C Aircraft Automatic Flight Control SystemF-16 Aircraft Automatic Flight Control SystemA&C Band JammersMagnetic Tape TransportSingle Pole Double Throw (SP2T) IF Switch With DriverCommunications Recorder Model No. VR2004ASea Sparrow Fire Control SystemSea Wolf Submarine Power SupplyStatic Frequency Changer & Direct Current Output Supply (407L)Low Light Level Television Camera Subsystem/Type 18 PeriscopeAWACS Magnetic Tape TransportAEGIS Shipboard MK84/Mod 1 400 Hz Power Supply SystemUninterruptible Power Supply SystemSEAFIRE ProgramSpace Shuttle Mass Memory SystemGalileo Space Program Tape RecorderInternational Solar Polar Mission Magnetic Tape TransportSpace Telescope Recorder/Reproducer SystemFIDS/BISS, Facility Intrusion Detection System RF Data LinkBoeing Aircraft 767 Auto-Brake/Anti-Skid SystemsTADS, Target Acquisition & Detection System DisplaysSolar Panel Charger & ControlsInfra Red Aiming LightKC-10A Inflight Refueling SystemTornado Aircraft Inflight RefuelingCommercial Aircraft Audio Entertainment System400 Hz Frequency ConvertersStatic Inverter Power SuppliesMagnetic Card Reader, Mark SenseVideo Display MonitorsRF Data Link SystemsTelephone Switching Systems/Message Centers

Filter Connector for Telephone PBX EquipmentHigh Speed Impact Computer PrinterHigh Performance Aircraft Flap ControlsElint SystemsAutomated Information Storage & Retrieval SystemsFloppy Disk DrivesAdvanced RF Receivers, Transmitters, and RepeatersBouy RF Receivers/ASWInstrument Calibration EquipmentsAircraft Windshield Defrosters/DeicersElectro-Mechanical Submarine Decoy SystemsAN/TPX-42A, Air Traffic Control SystemsDish Radar, Pedestal, and Control SystemRadio Management SystemRADOPS RF ScorerNuclear Power Generating Station EquipmentAlphanumeric Graphics PrinterDeep Space Network Software TestingC-17A Aircraft Autobrakes/Antiskid SystemMD-11 Aircraft Autobrakes/Antiskid SystemBoeing 747-400 Aircraft Autobrakes/Antiskid SystemUSN A-12 Aircraft Autobrakes/Antiskid SystemRADARSAT Satellite Digital Tape RecorderCatapult Launched Fuel-Air Explosive Land Mine Countermeasures SystemSpace Station Freedom EVA Portable Contamination DetectorSPOT, ERS-1 & JERS-1 Satellites Digital Tape RecordersSounding Rocket Inertial Navigation System

PERFORMANCE: PAST AND PRESENTThe following is a partial list of customers for which PSI has performed:Advanced Retail Technology, Inc.Aerojet Electro Systems CompanyAeronautical AccessoriesAirborne CCTV, Division of Puritan-Bennett Aero Systems/NellcorAmpex Corporation, Computer Products DivisionAmerican Nucleonics CorporationAnadexAPS SystemsArco Solar Inc., Division of Atlantic Richfield CompanyArral IndustriesAudio-In-MotionAVICOM InternationalAvtel Corporation, Division of Aertronics, Inc.B/E Aerospace, Avionics DivisionBeckman Instruments, Inc.Bell & Howell, Video Division/AVICOMBell & Howell, Instrumentation DivisionBermite, Division of Tasker IndustriesBHK Inc.Boeing Satellite Systems, Inc.Canavco, Inc.Cartwright Engineering IncorporatedChatsworth Data SystemsClary Instruments CompanyConrac Corporation, Systems-West DivisionContinental Telecommunications Corporation, Division ofContinental Telephone CompanyCubic CorporationData Products CorporationDowty Corporation, Resdel Engineering DivisionDRS Sensor Systems

DRS Optronics, Inc.EECO IncorporatedEEMCO Division of Datron Systems, Inc.Electronics Resources, Inc.Electronics Specialty CompanyElectro Optics Systems, Division of Xerox CorporationElgar Corporation, Division of Onan, Inc./McGraw EdisonHoneywell, Inc., Defense & Electronics DivisionHoneywell, Inc., Marine Systems CenterHydro-Aire Division of The Crane CompanyIncosym, Inc., Division of Textron CorporationIndustrial Electronic Engineers, Inc.Infodetics, Inc.International Telephone & Telegraph, Cannon Electric DivisionKinelogic CorporationLear Siegler, Inc., Astronics DivisionLibrascope Division of Singer Aerospace & Marine SystemsLitton Data Systems DivisionLockheed Electronics Company, Division of Lockheed Aircraft CompanyMagnavox Electronics Systems Company, West Coast DivisionMagneTek Defense Systems CorporationMcDonnell Douglas CorporationNaval Ship Missile Systems Engineering, Systems Effectiveness DivisionOcean Technology, Inc.Odetics, Inc., Spaceborne, Kode and Omutec DivisionsOdetics, Inc., Advanced Intelligent Machines DivisionOptivus Technologies, Inc.Perkin-Elmer Corporation, Applied Science DivisionPertec Computer CorporationPressure Systems, inc.Phaostron Instrument and Electronics Company, Division ofSterling Electronics, Inc.Radtec, Inc./Division of Guide Scientific CompanySargent-Fletcher CompanySargent Industries

Science Applications, Inc.Sierracin Corporation/Sylmar DivisionSignal Design, inc.Static Power, Inc., Division of Gates Rubber CompanyTasker Industries/Whittaker CorporationTeledyne Control Electronic Safety ProductsTeledyne ControlTeledyne Electronic TechnologiesTransco Products, Inc.US Naval Metrology Engineering CenterVari-L Company, Inc.Volt TechnicalXerox Electro-Optical System Corporation

EXAMPLES OF RELIABILITY ANALYSIS TABLESTABLE OF CONTENTSSection1.0TitleRELIABILITY PARTS STRESS PREDICTION1.1 Mathematical Modeling1.2 Parts Stress and Failure Rate Data2.0MAINTAINABILITY PREDICTION3.0DERATING ELECTRICAL STRESS ANALYSIS4.0FMECA-MI4.1 Failure Mode and Effects Analysis4.2 Criticality Analysis4.3 Maintainability Information5.0SAFETY HAZARD ANALYSIS6.0WORST CASE (PARTS/CIRCUITS) TOLERANCE ANALYSIS7.0THERMAL ANALYSIS8.0FAULT TREE ANALYSIS9.0MECHANICAL RELIABILITY10.0EXAMPLE FAILURE RATE ANALYSIS FOR POPPET VALVEASSEMBLY11.0TESTABILITY / BIT ANALYSIS12.0CONFIDENCE LEVEL ANALYSISCopyright 2002 by Probabilistic Software, Inc., All Rights Reserved.

Section 1.0RELIABILITY PARTS STRESS PREDICTION

Section 1.1RELIABILITY MATHEMATICAL MODELLINGMIL-STD-785B, Task 201MIL-STD-756B, Task 102Reliability Logic Block DiagramReliability Mission Mathematical Model

BlockAssembly NameSchematic erter A/30684942Inverter B/30684943Splitter/30684945Sam Power SupplyFailureRate, λ-- PPMλA 12.1937λB 6.1375λC 15.2983λD 16.3430λE 4.1355λSPS 54.1080RSPS R A (2 RB RB2 ) (3RC 3RC2 RC3 ) RD RE 6 R A RB RC RD RE 6 R A RB RC2 RD RE 2 R A RB RC3 RD RE 3R A RB2 RC RD RE 3R A RB2 RC2 RD RE R A RB2 RC3 RD RERSPS (t ) 6e λ SPS t 6e ( λ C λ SPS ) t 2e ( 2 λ C λ SPS ) t 3e ( λ B λ SPS ) t 3e ( λ B λ C λ SPS ) t e ( λ B 2 λ C λ SPS ) tMTBFSPS 662 2λ C λ SPSλ C λ SPS RSPS ( t ) dt 331 λ B λ SPSλ B λ C λ SPSλ B 2λ C λ SPS0λ SPS MTBFSPS 27,020 HoursFigure 1, Reliability Logic Block Diagram and Mean Time Between Failure (MTBF)Mathematical Model for Redundancy EquationCopyright 2002 by Probabilistic Software, Inc.

Section 1.2RELIABILITY STRESS AND FAILURE RATE DATAMIL-STD-785B, Task 203MIL-HDBK-217F, Section 5.1MIL-STD-756B, Type III, Method 2005, Task 202System: SAM Power SupplyAssembly: ConverterSchematic No.: 30684941Part Ambient Temperature,Worst Case: 55 Degrees CelsiusEnvironment: Space, Flight (SF)

Section 2.0MAINTAINABILITY PREDICTIONMean Time To Repair (MTTR)MIL-HDBK-472, Procedure IIAMIL-STD-470A, Task 203

Total Failure Rate,./ 106 Hoursλ 11080For normal distribution ofR: nRλ ii 26.4869 MTTR i 1n λ i 1.1080 i 1 23.9051 Minutes 0.3984 HoursForR M ct , M maxctat 95% Confidence Level isM maxct µ 1.645σ 28.3871 Minutes 0.4731 HoursWhere, n2 ()Rµ i σ i 1 1n 0.5 2.3022 Minutesnµ Rii 1n 24.6000 Minutesn Quantity of repairables, 5 LRUsFigure 1, MTTR and Mmaxct Calculation for Normal DistributionCopyright 2002 Probabilistic Software, Inc.

Total Failure Rate,./ 106 Hoursλ 11080For log-normal distribution ofR: n LogRλ ii MTTR Antilog i 1 n Antilog λi i 1 3.5134 1.1080 23.8294 Minutes 0.3972 HoursForR M ct , M maxctat 95% Confidence Level isM maxct Antilog [ µ 1.645σ ] 28.5441 Minutes 0.4757 HoursWhere,2 n(LogM)µ ct i i 1σ n 1 0.5 Log 0.0925 Minutesnµ Log M ct ii 1n Log 3.1993 Minutesn Quantity of repairables, 5 LRUsFigure 2, MTTR and Mmaxct Calculation for Log-Normal DistributionCopyright 2002 Probabilistic Software, Inc.

Section 3.0DERATING ELECTRICAL STRESS ANALYSISMIL-STD-785B, Task 207MIL-STD-975G

Section 4.0FAILURE MODE, EFFECTS AND CRITICALITYANALYSIS - MAINTAINABILITY INFORMATION(FMECA-MI)MIL-STD-785B, Task 204MIL-STD-1629A, Tasks 101, 102 and 103MIL-STD-470A, Task 205

Section 4.1FAILURE MODE AND EFFECTS ANALYSISTask 101 of MIL-STD-1629A

Section 4.2CRITICALITY ANALYSISTask 102 of MIL-STD-1629A

Section 4.3MAINTAINABILITY INFORMATIONTask 103 of MIL-STD-1629A

Section 5.0SAFETY HAZARD ANALYSISMIL-STD-882B, Tasks 203 and 204

Section 6.0WORST CASE ELECTRONIC PARTS/CIRCUITSTOLERANCE ANALYSISMIL-STD-785B, Task 206

WORST CASE CIRCUIT TOLERANCE ANALYSIS SUMMARYSystem: SAM Power SupplyAssembly: ConverterSchematic No.: 30684941Circuit: Voltage DividerPart Ambient Temperature, Worst Case: 55.00 Degrees CelsiusPrepared By: J. SmithVO f ( Ei , R1 , R2 )V0 Ei R2 /( R1 R2 )VO 9.090909 Voltsσ V2O (δVO / δEi ) 2 σ E2i (δVO / δR1 ) 2 σ R21 (δVO / δR2 ) 2 σ R22σ V2O 0.016200 0.00015 0.000157σ V2O 0.0165143σ VO 3 0.016514 0.385522µ 3σ VO 9.090909 Volts 0.385522 Voltsµ 3σ VO 8.705386 Volts to 9.476432 VoltsCopyright 2002 by Probabilistic Software, Inc.

Section 7.0THERMAL ANALYSISMIL-HDBK-251MIL-D-18300MIL-T-23103

Section 8.0FAULT TREE ANALYSISMIL-HKBK-338

Mathematical ModelSince all the events in the fault tree of Figure 1 are independent, the event probabilities are asfollows:P ( C ) P ( D ) P ( E ) [ P ( D ) x P ( E )]P(Top) P( A) x P( B) x P(C )WhereP( A) Probability of Event A, Servo Valve Driver Failure,1 e λ A t , 4.29576 / 1012 .λA Failure rate of Servo Valve Driver, U1, Hybrid Current Driver,0.61368 / 106t P( B) Hours.Risk Exposure Time,0.025 seconds or 7 / 106hours, for all events.Probability of Event B, Shutoff Valve Watchdog Failure,1 e λ B t , 113323./ 1012 .λB Failure rate of Shutoff Valve Watchdog Circuit, U2, ErrasableProgrammable Logic Device (EPLD),t 7 / 106P(C) 0.16189 / 106hours.hours.Probability of Event C, Display Electronics Unit (DEU) fails to display ABSfault status,P( D) P( E ) [ P( D) x P( E )], (1 e λ D t ) (1 e λ E t ) [(1 e λ D t ) x (1 e λ E t )], 2.26646 / 1012 .P ( D) Probability of Event D, ABS Arm Watchdog Failure,1 e λ D t , 113323./ 1012 .

λD Failure rate of the ABS Arm Watchdog Circuit, U3, EPLD,0.16189 / 106t 7 / 106P( E ) hours.hours.Probability of Event E, Servo and Shutoff Valve Monitor Failure,1 e λ E t , 113323./ 1012 .λE Failure rate of the Servo and Shutoff Valve Monitor Circuit, U4, EPLD,0.16189 / 106t 7 / 106hours.hours.Therefore,P(Top) P( A) x P( B) x P(C )./ 1012 ) (2.26646 / 1012 ) (4.29576 / 1012 ) (113323./ 1036 11033317or zero.Copyright 2002 by Probabilistic Software, Inc.

Section 9.0MECHANICAL RELIABILITY(RADC-TR-85-194)October 1985Stress/Strength Interference Method

Section 10.0EXAMPLEFAILURE RATE ANALYSISFORPOPPET VALVE ASSEMBLYCarderock Div, NSWC-92/L01,“Handbook of Reliability Prediction Proceduresfor Mechanical Equipment”, May 1992

Poppet Valve Assemblyλ PO λ PO, BQaQfWhere:λ PO λ PO , B Failure rate of the poppet assembly, failures/million operationsBase failure rate for poppet assembly, failures/million operationsQa Leakage rate, in3/minQf Leakage rate considered to be valve failure, in3/min2 x104 DMS f 3 ( P12 P22 )Qa Va LW ( S S ) 3 / 2Where:Qa DMS f Actual fluid leakage, in3/minMean seat diameter, inMean surface finish of opposing surfaces, minP1 Upstream pressure, lb/in2P2 Downstream pressure, lb/in2

Va Absolute fluid viscosity, lb-min/in2LW Radial seat land width, in.SS Apparent seat stress, lb/in2λ PO λ PO , B CP CQ CF CV CN CS CDT CSW CWWhere:λ PO λ PO , B CP Failure rate of poppet assembly in failures/million operations; 1.26Base failure rate of poppet assembly, 1.40 failures/million operationsMultiplying factor which considers the effect of fluid pressure on the basefailure rate, 1.0CQ Multiplying factor which considers the effect of allowable leakage on thebase failure rate, 1.0CF Multiplying factor which considers the effect of surface finish on the basefailure rate, 1.0CV Multiplying factor which considers the effect of fluid fiscosity/temperature onthe base failure rate, 1.0CN Multiplying factor which considers the effect of contaminants on the base

failure rate, 1.0625CS Multiplying factor which considers the effect of the apparent seat stress onthe base failure rate, 0.621119CDT Multiplying factor which considers the effect of the seat diameter on thebase failure rate, 1.09CSW Multiplying factor which considers the effect of the seat land width on thebase failure rate, 1.001182CW Multiplying factor which considers the effect of flow rate on the base failurerate, 1.25Where: P P2 CP 1 3000 2CQ 0.055 / Q f For leakage (Per GPM R ) 0.03,. ( 79Q f ) For leakage (Per GPM R ) 0.03,CQ 41 V CF O V Where:Vo 2 x 10 8 lb min / in 23 C CN 0 N10 GPM R C10 Where:

GPM R Rated Flow in gallons/min, 5.0C10 Standard System Filter Size 10 micronC0 System Filter Size in microns 5 micronN10 1.7 Particles under 10 microns/Hour/GPMCS 1S R3/ 2 0.621119Where:SR 12πDM LW 0.758DS2PS DS2 12.SS 4 DM LWSS Force on SeatF SSeat Land Area ASLπPS DS2FS 4Stress Ratio SC / S S S R

Therefore, leakage varies with the seat stress as: 1 S 3/ 2Minimum Contact Pressure SC 3PSapproximately three times the fluid pressure.ASL πDM LWWhere:ASL Seat land area, in2LW Land area width, inDM Mean land width diameter, inASTπ ( D s )2 4Where:AST DS Seat Area, in2Diameter of seat exposed to fluid pressure, PS, 0.70 in. DS 0.32CDT 1123. 24.52 LW 72.99 LWfor LW 6CSW 355 85.75 LW F CW 1 L 100 2Where:FL Ratio of actual flow rate to manufacturer's rating

Section 11.0TESTABILITY / BIT ANALYSISMIL-STD-2165

Section 12.0CONFIDENCE LEVEL

Copyright 2002 by Probabilistic Software, Inc.

confidence level analysis PSI will perform, document and deliver the above listed reliability analysis reports from your design data on a firm, fixed price basis, in final typed form, suitable for reproduction and submittal to your customer.

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Keywords: Reliability Block Diagrams (RBD); hierarchical reliability model; reliability curve; reliabil-ity evaluation; software libraries 1. Introduction Reliability is defined as "the ability of a system or component to perform its required functions under stated conditions for a specified period of time" [1]. Reliability is often