318-595 Statistics & Reliability Statistics and Electronic Reliability

318-595 Statistics & Reliability

Statistics and Electronic Reliability




Printed Circuit Board Assemblies

Review of Printed Circuit Board Technology– 3 Basic Types of PCB-Component Assembly Technology

• Thru Hole (TH) using prepackaged devices• Surface Mount (SMT) using prepackaged devices• Micro-electronic using bare die and prepackaged devices

– 3 Basic Types of PCB Substrates (fabs)• Rigid copper-epoxy laminate PCB (single, dual up to ~40 layers)• Alumina, Alum Nitride or other ceramic materials (up to ~20 layers)• Flexible Substrate (Polyimide-Copper, up to 8 layers)

– Surface Metalization Finishes• HASL – Hot Air Solder Leveling (Eutectic SnPb Surfaces, lowest cost)• ENIG – Electroless Ni – Immersion Au (flatter for wirebonding, BGA, ACF)• IAg – Immersion Silver (co-deposited with organics to reduce reactivity, replacement for

ENIG)• Electroplated Finishes – NiAu over Cu, not always possible depending on circuit


Causes of Electronic Systems Failure• Failures can generally be divided between intrinsic or extrinsic failures

•Intrinsic failures- Inherent in the component technology• Electromigration (semiconductors, substrates)

• Contact wear (relays, connectors, etc)• Contamination effects- e.g. channeling, corrosion, leakage

• CTE mismatch and other Interconnection joint fatigue

•Extrinsic failures- External stress to the components• ESD or Electrostatic discharge energy

• Electrical overstress (over voltage, overload, overheat)• Shock (Sudden Mechanical Impact)

• Vibration (Periodic Mechanical G force)• Humidity or condensable water

• Package Mishandling, Bending, Shear, Tensile

Many “random” and infantile failures of components are due to extrinsic failuresWearout failures are usually due to intrinsic failures

Reliability of Electronic Circuits

318-595 Statistics & Reliability PCB Assembly Failure Mechanisms

Stresses & Major FactorsI. Thermal Excursion and Cycling

• Coef of Thermal Expansion (CTE) mismatches

• Package and Substrate Dimensions (Larger is worse)

• # of Interconnects on Package (More failure opportunities)

• Solder joint geometry including cracks, voids and skew

II. Mechanical Shock and Vibration

• Mass of Components and Overall Assembly

• Height of Component Center of Mass (COG)

• Thickness, Rigidity and Support Pts of PCB

• Solder joint geometry including cracks, voids and skew


Printed Circuit Board Assemblies

CTE Mismatches in PCB Assemblies

FR4 LaminateCTE = ~20e-6/C

Thin Epoxy Solder MaskNiAu Pad

Copper

Gold CTE = 14.2e-6/C

5 – 15 μ in.

Nickel CTE = 13.4e-6/C

> ~100 μ in.

Copper CTE = 16.5e-6/C

> ~1.2 mil

Si Die CTE = 2.8e-6/C

SnPb Eutectic Solder Joint CTE = ~25e-6/C

318-595 Statistics & Reliability PCB Assembly Failure Mechanisms

Stresses & Major Factors - continued

III. Electrochemical

• Usage environment incl ambient temp & humidity

• Usage environment incl corrosive materials, salts, etc

• Maximum electrical field (induced by spacing, voltage on PCB)

• Ionic Cleanliness of PCB over/under solder mask and other coatings

• Cations: Including Lithium, Sodium, Ammonium, Potassium, Magnesium and Calcium. Many companies limit each individual cation contribution to be less than 0.2ug/cm2 and the combined total of all cations to be less than 0.50ug/cm2.

• Anions: Most Destructive Includes Fluoride, Chloride, Nitride, Bromide, Sulfate, and Phosphates. Many companies limit each individual anion contribution to be less than 0.1ug/cm2 and the combined total of all anions to be less than 0.25ug/cm2.

• Weak Organic Acids: May include Acetate, Formate, Succinate, Glutamate, Malate, Methane Sulfonate (MSA), Phthalate, Phosphate, Citrate and Adipic Acids. Many companies limit the combined total of all weak organic acids to be less than or equal to ~0.75ug/cm2

• Ion cleanliness is tested per IPC TM-650 2.3.28 using Ion Chromatography for high reli assemblies. IPC-6012/15 mandate a total ionic cleanliness of less than 1.56ug/cm2 = 10ug/in2.


Ionic Test Methods for PCBs

Resistivity of Solvent Extract (ROSE) Test Method IPC-TM-650 2.3.25The ROSE test method is used as a process control tool (rinse) to detect the presence of bulk ionics. The IPC upper limit is set at 10.0 g/in2 .(1.56ug/cm2) This test method provides no evidence of a correlation value with modified ROSE testing or ion chromatography. This test is performed using an ionograph or similar style ionics testing unit that detects total ionic contamination, but does not identify specific ions present. Non destructive test.

Modified Resistivity of Solvent Extract (Modified ROSE)The modified ROSE test method involves a thermal extraction. The PCB is exposed in a solvent solution at a predetermined temperature for a specified time period. This process draws the ions present on the PCB into the solvent solution. The solution is tested using an ionograph-style test unit. The results are reported as bulk ions present on the PCB per square inch, similar to the standard ROSE method above. Can be destructive.

Ion Chromatography IPC-TM-650 2.3.28This test method involves a thermal extraction similar to the modified ROSE test. After thermal extraction, the solution is tested using various standards in an ion chromatographic test unit. The results indicate the individual ionic species present and the level of each ion species per unit area. This test is an excellent way to pinpoint likely process steps which are leaving residual contaminants that can lead to early reliability failures. Destructive test.

318-595 Statistics & ReliabilitySpecifying Warranty: Must Understand Reliability of Product (1, 5 yrs, etc)

• Life of Product should be less than wear out failure mode period

• Bathtub Reli Curve: (Failure Rate vs Time) Area under curve = total failures

Minimize or Precipitate using ESS in factory

~ Constant Failure Rate

Warranty Period Using ESS

Warranty Period

Infantile

Period


Basic Statistics and Reliability Statistics

0

2

5

8

10

12

15

18

20

22

25

1.238 1.240 1.242 1.244

318-595 Statistics & ReliabilityBasic Statistics ReviewBasic Statistics Review

Example: The following data represents the amount of time it takes 7 people to do a 355 exam problem.

X = 2, 6, 5, 2 ,10, 8, 7 in min.n = 7

i where X = index notation for each individual.where n = 7 people

i

Calculate the mean(average): m= X =X i

i = 1

n

n

where X = Sum of the individual times

where X and m = Average or Meani

n = 7 people Mean: X = (2+6+5+2+10+8+7)/7 = 5.7 minutes

Calculate the standard deviation: =s=( Xi - X )

2i = 1

n

n - 1

where = s = Standard DeviationSum or Variance

Step 1 Step 2 (Xi - X) (Xi - X) 2-5.7= -3.7 13.696-5.7= .3 .095-5.7 = -.7 .492-5.7 = -3.7 13.6910-5.7 = 4.3 18.498-5.7 = 2.3 5.297-5.7 = 1.3 1.69 (Xi - X) = 53.43

2

2

= s =7 - 1

53.43

= 2.98 minutes= s

Definition:Range = Max - Min Median = Middle number when arranged low to highMode = Most common number

This Example: Range = 10 - 2 = 8 minutesMedian = 6 minutesMode = 2 minutes

Equation

Equation

Standard Deviation:

Square each one

Then Add All

Step 4

Step 3

Std Deviation is a measure of the inherent spread in the data


Bar Chart or Histogram

Provides a visual display of data distributionProvides a visual display of data distribution

Shape of Distribution May be Key to IssuesShape of Distribution May be Key to Issues

1. Normal (Bell Shaped)2. Uniform (Flat)3. Bimodal (Mix of 2 Normal Distributions)4. Skewed left or right5. Total number of bins is flexible but usually no more than 10

By using an infinite number of bins, resultant curve is a distribution

Use T-Test to Compare Means, F-Test to Compare Variances

0

2

5

8

10

12

15

18

20

22

25

1.238 1.240 1.242 1.244


• Normal (Gaussian) Distributions


Histogram vs Histogram vs Spec Limits Spec Limits

11

Specification LimitSpecification Limit

Area under curve Is probability of

failure

Z = 3

TargetTarget

Much Less Chance of

Failure11

Z = 6

Z is the number of Std Z is the number of Std Devs between the Mean Devs between the Mean and the spec limit. The and the spec limit. The higher the value of Z, higher the value of Z,

the lower the chance of the lower the chance of producing a defectproducing a defect

Z is the number of Std Z is the number of Std Devs between the Mean Devs between the Mean and the spec limit. The and the spec limit. The higher the value of Z, higher the value of Z,

the lower the chance of the lower the chance of producing a defectproducing a defect

66807ppmPPM = Part per Million Defects

3.4ppm** Assumes Z is 4.5 long term

33

Normal Normal DistributionDistribution

Normal Normal DistributionDistribution


Area under Distribution Curve Yields Probabilities

34% 34%

14% 14%2% 2%

and 2

Characterized by Two Parameters

Normal Distribution = N( )

318-595 Statistics & ReliabilityLife Cycle of a Component

Standard Normal Distribution

Original Distribution

Apply

TransformationStandard Normal

Distributionx-Z=

-1 0 1 Z

Z = +1.0 is one Standard Deviations above the mean

Z= -0.5 is 0.5 Standard Deviations below the mean

Area under Curve =1

Examples:

X

318-595 Statistics & Reliability1 Sided Normal Distribution, Probability Table

ZZ 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.00 5.00e-001 4.96e-001 4.92e-001 4.88e-001 4.84e-001 4.80e-001 4.76e-001 4.72e-001 4.68e-001 4.64e-0010.10 4.60e-001 4.56e-001 4.52e-001 4.48e-001 4.44e-001 4.40e-001 4.36e-001 4.33e-001 4.29e-001 4.25e-0010.20 4.21e-001 4.17e-001 4.13e-001 4.09e-001 4.05e-001 4.01e-001 3.97e-001 3.94e-001 3.90e-001 3.86e-0010.30 3.82e-001 3.78e-001 3.74e-001 3.71e-001 3.67e-001 3.63e-001 3.59e-001 3.56e-001 3.52e-001 3.48e-0010.40 3.45e-001 3.41e-001 3.37e-001 3.34e-001 3.30e-001 3.26e-001 3.23e-001 3.19e-001 3.16e-001 3.12e-0010.50 3.09e-001 3.05e-001 3.02e-001 2.98e-001 2.95e-001 2.91e-001 2.88e-001 2.84e-001 2.81e-001 2.78e-0010.60 2.74e-001 2.71e-001 2.68e-001 2.64e-001 2.61e-001 2.58e-001 2.55e-001 2.51e-001 2.48e-001 2.45e-0010.70 2.42e-001 2.39e-001 2.36e-001 2.33e-001 2.30e-001 2.27e-001 2.24e-001 2.21e-001 2.18e-001 2.15e-0010.80 2.12e-001 2.09e-001 2.06e-001 2.03e-001 2.00e-001 1.98e-001 1.95e-001 1.92e-001 1.89e-001 1.87e-0010.90 1.84e-001 1.81e-001 1.79e-001 1.76e-001 1.74e-001 1.71e-001 1.69e-001 1.66e-001 1.64e-001 1.61e-001





318-595 Statistics & ReliabilityNormal Distribution (cont.)

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09






10.00 7.62e-024 6.89e-024 6.23e-024 5.63e-024 5.08e-024 4.59e-024 4.15e-024 3.75e-024 3.39e-024 3.06e-024


3 4 5 6 7

1,000,000

100,000

10,000

1,000

100

10

1

2

Examples of Fault/Failure Rates onThe Sigma Scale

PPM Defects

•

Restaurant Bills

Doctor Prescription Writing

Restaurant Checks

Airline Baggage Handling

Domestic Airline Flight

(0.43 PPM)

Fatality Rate

Tax Advice (phone-in)

(140,000 PPM)

(with ± 1.5 shift)

Best-in-ClassBest-in-Class

Average Company

Average Company

Z

AircraftCarrier Landings


Shift and DriftShift and Drift

Over time, a “typical” product process may shift or drift by ~ 1.5

LSL USLT

Time 1

Time 2

Time 3

Time 4

Short Term Capability Snapshots of the Product

Actual Sustained Capability of the Process

. . . also called “short-term capability”

. . . reflects ‘within group’ variation

. . . also called “long-term capability”

. . . reflects ‘total process’ variation

Two Challenges: Two Challenges:

Center the Process and Eliminate Variation!Center the Process and Eliminate Variation!

318-595 Statistics & ReliabilityStatistics Example: IPC Workmanship Classes: Solder Volume, Shape, Placement Control

3. High Reliability Electronic Products: Includes the equipment for commercial and military products where continued performance or performance on demand is critical. Equipment downtime cannot be tolerated, and functionality is required for such applications as life support or missile systems. Printed board assemblies in this class are suitable for applications where high levels of assurance are required and service is essential.

• Requirement for Aero-Space, Certain Military, Certain Medical

4. Dedicated Service Electronic Products: Includes communications equipment, sophisticated business machines, instruments and military equipment where high performance and extended life is required, and for which uninterrupted service is desired but is not critical. Typically the end-use environment would NOT cause failures.

• Requirement for High Eng Telecom, COTS Military, Medical

5. General Electronic Products: Includes consumer products, some computer and peripherals, as well as general military hardware suitable for applications where cosmetic imperfections are not important and the major requirement is function of the completed printed board assembly.

IPC-7095 BGA Std

Class 1 Class 2 Class 3

Max Void Size 60% Dia

36% Area

45% Dia

20.3% Area

30% Dia

9% Area

Max Void Size at Interfaces

50% Dia

25% Area

35% Dia

12.3% Area

20% Dia

4% Area

100 %

75 %

50 %

25 %

0 %

100 %

75 %

50 %

25 %

0 %

Min PTH Vertical Fill: Class 2 = 75% Class 3 = 100%

Ref: IPC-A-610, IPC-JSTD-001


Solder_Joint_Radius

Void_Distance

Void_Radius

Void_Solder Interface Distance

Sampling_Grid

PositionModel

Potential for Early Life Failure (ELFO) if S < D/10 = (solder_joint_radius)/10

S =Shell = solder_joint_radius – (void_distance + void_radius)

BGA Void Size and Locations, Uniform Void Position Distribution, Varying Diameter

S

S = Shell


CLASS 3 - BESTSolder Joint_Radius: 0.225 mmVoid_Radius: 0.0675 mmVoid_Area: 9% of Joint AreaFailure criteria: D/10

CLASS 2 - BETTERSolder Joint_Radius: 0.225 mmVoid_Radius: 0.1013 mmVoid_Area: 20% of Joint AreaFailure criteria: D/10

P(D<10) = 81.11 %

P(D<10) = 52.21 %

P(D<10) = 27.00 %

CLASS 1 - GOODSolder Joint_Radius: 0.225 mmVoid_Radius: 0.135 mmVoid_Area: 36% of Joint AreaFailure criteria: D/10

318-595 Statistics & ReliabilityClass vs Shell Size Relative Probabilities

~ 2x more likely to exceed D/10 threshold with Class 2 vs Class 3

S = Shell

Depth


• Exponential Distributions

= Reliability

= Time

318-595 Statistics & ReliabilityDefinitions

General Failure Rate Variable:

Recall the Bathtub Curve- Failure Rate () vs. Time behavior

For CONSTANT FAILURE RATES – Exponential Distribution Applies and R(t) = (Reliability at Time t) = Probability that a system will not fail for a time period “t,” assuming constant failure rate;

R(t) = e-t, Note: is in failures/time, and t is time

Note: At T=0, R(0)=1.0 (100%)

FIT = FITs = Failures per 109 hours

MTBF (years) = 1x109 / ( FIT * 8766 hours /year )

MTBF = 1/MTBF = 1/Mean time between failure in hours

R(t) = e-t, Note: MTBF in hr-1 and t in hr

318-595 Statistics & ReliabilityDefinitions

General Failure Rate Variable:

For CONSTANT FAILURE RATES – Exponential Distribution Applies and R(t) = (Reliability at Time t) = Probability that a system will not fail for a time period “t,” assuming constant failure rate;

R(t) = e-t, Note: is in failures/time, and t is time

Note: At T=0, R(0)=1.0 (100%)

F(t) = (UnReliability at Time t or Failures at Time t) = Fraction of population that has failed at Time t, probability that a given system will fail for a time period “t,” assuming constant failure rate;

F(t) = 1-e-t, Note: is in failures/time, and t is time

Note: At T=0, F(0)=0.0 (0%)

318-595 Statistics & ReliabilityWeibull or 2 Parameter Distributions

For VARYING FAILURE RATES – Weibull Distribution Applies and R(t) = (Reliability at Time t) = Probability that a system will not fail for a time period “t,”;

R(t) = e-t/ ), Note: is the dimensionless scale parameter (stretches)

is the shape or slope parameter (exponent)

Note: At T=0, R(0)=1.0 (100%)

Relationship of Weibull parameters to Failure Rate

= (/)(t/)-1

R(t) = e-t/ )

F(t) = 1-e-t/ )

318-595 Statistics & ReliabilityTypical Reliability Plot using Weibull Dist

= (/)(t/)-1

F(t) = 1-e-t/ )

1.00

5.00

10.00

50.00

90.00

99.00

1.00 100000.0010.00 100.00 1000.00 10000.00

Generated by: ReliaSoft's Weibull++ 5.0 - www.Weibull.com - 888-886-0410

Probability Plot

Time, (t)

Unr

elia

bilit

y, F

(t)

1:31:22 PM2/22/00GE AppliancesDouglas C. Kemp

WeibullSupplier 1

P=2, A=RRX-S F=10 | S=0

Supplier 2

P=2, A=RRX-S F=10 | S=0CB/FM: 90.00%2 Sided-BC-Type 2

Time to Failure(s)

F(t) = (1 – R(t))100%

At some time, t, 100% of the population will fail

318-595 Statistics & ReliabilityTypical Reliability Plot assuming Weibull Dist

= (/)(t/)-1

R(t) = e-t/ )

F(t) = 1-e-t/ )

1.00

5.00

10.00

50.00

90.00

99.00

1.00 100000.0010.00 100.00 1000.00 10000.00

Generated by: ReliaSoft's Weibull++ 5.0 - www.Weibull.com - 888-886-0410

Probability Plot

Time, (t)

Unr

elia

bilit

y, F

(t)

1:31:22 PM2/22/00GE AppliancesDouglas C. Kemp

WeibullSupplier 1

P=2, A=RRX-S F=10 | S=0

Supplier 2

P=2, A=RRX-S F=10 | S=0CB/FM: 90.00%2 Sided-BC-Type 2

Time to failure plot using Weibull tool

Fai

lure

Rat

e,

Constant Failure Rates

=1Exponential Distribution

Time

The Bathtub Curve

Useful LifeEarlyLife Wear out

DecreasingFailure Rates

<1

IncreasingFailure Rates

>1

Weibull slope indicates where the product may be on the bathtub curve.

318-595 Statistics & ReliabilityReliability Prediction: Assume Constant Failure Rate

= 1.0

• Basic Series Reli Method of an Electronic System:

Component 1

1

• Each component has an associated reliability • The System Reli ss is the sum of all the component

ss = i

• Reli is expressed in “FITs” failure units

x FIT = x Failures/109 hoursNote: 109 hours = 1 Billion Hours

Component 2

2

Component i

i

Component N

N


Example: MTBF not so good to use for Reliability Specification

• An electronics assembly product has an MTBF of 20000 hours; constant failure rate

• What is the probability that a given unit will work continuously for one year?

• For this problem, we have the following facts;

• Reliability R(t) = e-t

• = 1/MTBF = 1/20000 hr• = 0.00005 hr-1 (Failure rate)

• t = 8766 hours (1 year)


Example: MTBF not so good to use for Reliability Specification

• An electronics assembly product has an MTBF of 20000 hours; constant failure rate

• What is the probability that a given unit will work continuously for one year?

• Reliability R(t) = e-t

• = 1/MTBF = 1/20000 hr• = 0.00005 hr-1 (Failure rate)

• t = 8766 hours (1 year)

• R(1yr) =e-(8766/20,000) = 0.65 = 65% F(1yr) = 35% of population has failed !

In other words, the Mean Time Between failures is 20,000 hours or about 2.3 yearsBut … 35% of the units would likely fail in the first year of operation.

Remember, after 1 MTBF period R(t) = 1/e = 0.368 63.2% of population will fail!


Intro to Reliability Evaluation


Component 1

R1

• Each component also has an associated reliability R• The System R is the product of all the component R

R = Ri

• Recall, Reli R is a probability (0 to 1) expressed in percent

Component 2

R2

Component i

Ri

Component N

RN


Reliability R Flowdown Example

Power supplyR = 0.94

Drive System,needs R= 0.9 at

10 years

Subsystem Level

System Level

MotorR = 0.97

PartR=0.9999

Control CardR = 0.99

PartR=0.9999

PartR=0.9999

PartR=0.999

PartR=0.9999

PartR=0.9999

PartR=0.999

Component Level


• Customer’s need: Meet R=90%@ 10 years

• Partition requirements to subsystems

– Based on engineering analysis, experience, vendor data, parts count, etc.

• Allocation:

Rsystem = Rpower * Rcontroller * Rmotor

Rsystem = 0.94 * 0.99 * 0.97 = 0.90

Each of the 3 subsystems should in turn be allocated to components

Reliability Requirements Flowdown- Example


More Reason to use R(t) and not MTBF Example

• An electronics product team has a goal of warranty cost which requires that aMinimum reliability after 1 year be 99% or higher, R(1yr) >= 0.99. Assume Constant Failure Rates.

• What MTBF should the team work towards to meet the goal?

Recall Equations: R = e -t and MTBF = 1/

Solve for MTBF: MTBF = 1/ = 1/ {(-1/t) * ln R }, R = 0.99, t = 8766 hrs

MTBF >= 872,000 hours (99.5 yrs) !

What is your product warranty cost goal expressed as an R(t)?:

Answer: What is the scrap or repair cost of a given % of failures during the warranty period? Need to know, annual production, and an assumed R(t). Good products have less than 1% annualized warranty cost as a percentage of the total contribution margin for that product.


Some Typical Stresses

• Environmental: Temp, Humid, Pressure, Wind, Sun, Rain

• Mechanical: Shock, Vibration, Rotation, Abrasion

• Electrical: Power Cycle, Voltage Tolerance, Load, Noise

• ElectroMagnetic: ESD, E-Field, B-Field, Power Loss

• Radiation: Xray (non-ionizing), Gamma Ray (ionizing)

• Biological: Mold, Algae, Bacteria, Dust

• Chemical: Alchohol, Ph, TSP, Ionic

318-595 Statistics & ReliabilityCommon Circuit Bd Temperature-Induced Failures

Failure Category Failure Mode Root Cause Environmental Conditions

Susceptible Parts and Materials

High temperature degradation

Strength/insulation degradation

degradation Temperature + Time

Plastic materials, resins

Heat disintegration Chemical change Temperature Plastic materials, resins

Distortion Softening, melting, evaporation, sublimation

Temperature Metals, plastics materials, thermal fuse

Oxide film formation High temperature oxidation

Temperature + Time

Contact material

Broken wire Thermal diffusion Temperature + Time

Metal plating involving different metals, and contact areas

Creep Fatigue, damage Metal/Plastic under mechanical stress

Temperature + Stress + Time

Springs, structural parts

Migration Disconnection, broken wire

Electro-migration Temperature + Current

W, Cu, Al (especially Al wiring on IC)

Low temperature brittleness

Damage Chemical property of metal

Low temperature Body-centered cubic crystalline (Cu, Mo, W), closed-packed cubic crystalline (Zn, Ti, Mg) & alloys

Flux loose Noise, imperfect contact

Flux steam adheres to cold metal surface

Low temperature Parts attached to printed board (e.g. switches, connectors)

Thermal Cycling Change in conductor resistance

PCB through holes degradation; solder cracking

Thermal cycling Printed circuit board w/ solder


Intro to Reliability Estimation

• Each may be impacted by other factors or stresses, :• Some commonly used factors

T = Temperature Stress Factor V = Electrical Stress Factor E = Environmental Factor Q = Quality Factor

• Overall Component = B * T * V * E * Q

Where B = Base Failure Rate for Component


Reliability Prediction Methods/Standards

• Bellcore (TR-TSY-000332): – Developed by Bell Communications Research for general use in electronics

industry although geared to telecom.– Highest Stress Factor is Electrical Stress – Data based upon field results, lab testing, analysis, device mfg data and US

Military Std 217– Stress Factors include environment, quality, electrical, thermal

• US Military Handbook 217F:– Developed by the US Department of Defense as well as other agencies for

use by electronic manufacturers supplying to the military– Describes both a “parts count” method as well as a “parts stress” method– Data is based upon lab testing including highly accelerated life testing

(HALT) or highly accelerated stress testing (HAST) – Stress factors include environment and quality




• HRD4 (Hdbk of Reliability Data for Comp, Issue 4): – Developed by the British Telecom Materials and Components Center for

use by designers and manufacturers of telecom equipment– Stress factors include thermal as well as environment, quality with quality

being dominant– Standard describes generic failure rates based upon a 60% confidence

interval around data collected via telecom equipment field performance in the UK

• CNET:– Developed by the French National Center of Telecommunications– Similar to HRD4, stress factors include thermal as well as environment

and dominant quality – Data is based upon field experience of French commercial and military

telecom equipment



• Siemens AG (SN29500): – Developed by Siemens for internal uniform reliability predictions

– Stress factors include thermal and electrical however thermal dominates

– Standard describes failures rates based upon applications data, lab testing as well as US Mil Std 217

– Components are classified into technology groups each with tuned reliability model


Reliability Prediction


Component 1

1

• Above Reliability Prediction Model is flawed because;• Components may not have constant reliability rates

ss = i

• Component applications, stresses, etc may not be well matched by the method used to model reliability

• Not all component failures may lead to a system failure• Example: A bypass capacitor fails as an open circuit

Component 2

2

Component i

i

Component N

N

318-595 Statistics & Reliability595 Standard Failure Rates in FIT (Data is not accurate in all cases)

Component Type Method A - Method B - Method C - Method D - Method E -

BJT/FET 5.0 3.8 3.2 7.6 4.0

Switch 5.0 44.0 30.0 1.0 20.0

Metal Film Res 0.7 2.5 0.05 0.05 0.2

Carbon Res 18.2 2.7 1.0 1.1 2.6

Varistor, tc Res 6.0 1.0 10.0 1.0 10.0

Electrolytic Cap 210 22.0 120 16.0 120

Polyester Cap 8.5 2.0 3.0 0.5 7.0

Tantalum Cap 15.0 7.0 8.0 4.0 10.0

Ceramic Cap 2.0 1.0 0.5 0.25 1.2

Si PN, Shottkey, PIN Diode 2.4 1.6 3.6 1.6 2.4

Zener Diode 3.2 13.6 17.4 18.8 70.0

LED 9.0 15.0 280 65.0 1.0

BJT Dig IC <100 Gates 20.0 138 2.3 1.0 6.7

BJT Dig IC < 1000 Gates 30.0 150 4.0 1.5 10.0

MOS Dig IC < 1000 Gates 27.3 301 9.0 1.0 13.3

MOS Dig IC => 1000 Gates 55.0 550 16.0 2.2 31.0

EM Coil Relay 385 302 220 715 44.0

SSR, Optocoupler 120 105 47.0 190 12.0

BJT Linear IC < 1000 Transistors 14.0 27.0 4.3 1.0 50.0

MOS Linear IC < 1000 Transistors 19.0 54.0 9.0 1.0 13.3

Transformer < 1VA 33.0 90.0 70.0 60.0 50.0

Transformer > 1VA 3.0 9.0 7.0 6.0 5.0

318-595 Statistics & Reliability595 Standard Failure Rates in FIT (Data is not accurate in all cases)

Component Type Method A - Method B - Method C - Method D - Method E -

Plastic Shell Connector, Plug, Jack 100.0 55.0 150.0 120.0 105.0

Metal Shell Connector, Plug, Jack 33.0 18.0 57.0 40.0 35.0

Pb, NCd, Li, Lio, NmH Battery 7.0 1.0 50.0 8.0 22.0

Quartz Crystal Thru Hole 115.0 113.8 113.2 117.6 114.0

Quartz Crystal SMT 15.0 34.0 30.0 51.0 20.0

Quartz Oscillator Module CMOS 10.0 12.5 10.5 20.0 15.0

Diode Bridge 4.8 1.6 3.6 1.6 2.4

LED Display 19.0 115.0 280 165.0 21.0

LCD Display 119.0 215.0 380 1165.0 206.0

BJT Linear IC > 1000 Transistors 114.0 217.0 41.3 91.0 150.0

MOS Linear IC > 1000 Transistors 29.0 74.0 19.0 21.0 113.3

318-595 Statistics & Reliability595 Standard Stress Factors

• Factor Definitions (may not represent standard models)

T = Temperature Stress Factor = e[Ta/(Tr-Ta)] – 0.4 Where Ta = Actual Max Operating Temp, Tr = Rated Max Op Temp, Tr>Ta

V = Cap/Res/Transistor Electrical Stress Factor = e[(Va)/Vr-Va]-2.0

Where Va = Actual Max Operating Voltage, Vr = Abs Max Rated Voltage, Vr>Va

E = Environmental (Overall) Factor >>> Indoor Stationary = 1.0 Indoor Mobile = 2.5 Outdoor Stationary = 3.0 Outdoor Mobile = 5.0 Automotive = 7.0

Q = Quality Factor (Parts and Assembly) Mil Spec/Range Parts = 0.75 100 Hr Powered Burn In = 0.75 Commercial Parts Mfg Direct = 1.0 Commerical Parts Distributor = 1.25 Hand Assembly Part = 3.0


C3 10uf 15VElectrolytic

C4 0.1uf 50VCeramic

C2 0.1uf 50VPolyester

C1 0.1uf 50VPolyester

74HCT145V 1W Zener

R1 2K 1/4WBrand A Metal Film

R2 150 1/4WBrand B Metal Film

BPLROP AMP

+12VDC

-12VDC

Vin

+5VDC

LEDVf=1.5V

+5VDC

Example: Method A, 0-50C Ambient, Indoor Mobile, Distributor Components

Part Max Tr Max Vr T V E Q

C1 105C 50V 2.082 0.186 2.5 1.25

C2 105C 50V 2.082 0.186 2.5 1.25

C3 85C 15V 3.773 0.223 2.5 1.25

C4 125C 50V 1.548 0.151 2.5 1.25

R1 120C 20V 1.643 0.232 2.5 1.25

R2 150C 6V 1.249 0.549 2.5 1.25

Zener Diode 100C N/A 2.318 1.0 2.5 1.25

Op Amp 125C 36V 1.548 1.0 2.5 1.25

74HCT14 125C 7V 1.548 1.649 2.5 1.25

LED 85C N/A 3.773 1.0 2.5 1.25

FITS

10.29

10.29

552.2

106.16

1.50

23.18

1.46

0.83

991.37 Fits 115.1 Yrs MTBF

217.77

67.73

318-595 Statistics & ReliabilityStress Factors Drive Simple:

595 Standard Deratings

• Resistors, Potentiometers <= 50% maximum power

• Caps/Res <= 60% maximum working voltage

• Transistors <= 50% maximum working voltage

• Note: Most discrete devices as well as linear IC’s have parameters which will vary with temperature which is expressed as Tc (temp coefficient). Typically a delta or percent of change per deg C from ambient.


System / Equipment Name: Assembly Name: Quantity of this assembly: Parts List Number: Environment: Select One Of : GB, GF, GM, NS, NU, AIC, AIF, AUC, AUF, ARW, SF, MF, ML, or CLParts Quality: Select Either: Mil-Spec or Commercial/Bellcore Quantity Description---------- Bipolar Integrated Circuits IC / Bipolar, Digital 1-100 Gates IC / Bipolar, Digital 101-1000 Gates IC / Bipolar, Digital 1001-3000 Gates IC / Bipolar, Digital 3001-10000 Gates IC / Bipolar, Digital 10001-30000 Gates IC / Bipolar, Digital 30001-60000 Gates IC / Bipolar, Linear 1-100 Transistors IC / Bipolar, Linear 101-300 Transistors IC / Bipolar, Linear 301-1K Transistors IC / Bipolar, Linear 1001-10K Transistors, etc.

EXAMPLE: Actual Reli Tool InputList of components, their number,Environment conditions, components quality

MTBF Data Input Sheet for e-Reliability.com COST: $500 per report


Example Reliability calculation using actual MIL-HDBK-217F

Failure rate of a Metal Oxide Semiconductor (MOS) can be expressed as

hoursLQECTCp60failures/1 )21(

Parameters are listed in MIL Data base.Temperature factor is modeled using Arrhenius type Eqn

base. data MILin listed is Ea componentsmany For

eV. 0.35Ea MOSFor energy. activation theis Ea where

)]/1/1(5617.8/exp[1.0

workingTaccelTeEaT

595 charts are greatly simplified from actual parts count Reli


---------------------------------------------------------------------------------------| | | | | Failure Rate in || | | | | Parts Per Million Hours || Description/ | Specification/ | Quantity | Quality |-------------------------|| Generic Part Type | Quality Level | | Factor | | || | | | (Pi Q) | Generic | Total || | | | | | ||=====================|================|==========|=========|============|============|| Integrated Circuit/ | Mil-M-38510/ | 16 | 1.00 | 0.07500 | 1.20000 || Bipolar, Digital | B | | | | || 30001-60000 Gates | | | | | || | | | | | || Integrated Circuit/ | Mil-M-38510/ | 8 | 1.00 | 0.01700 | 0.13600 || Bipolar, Linear | B | | | | || 101-300 Transistors | | | | | || | | | | | || Diode/ | Mil-S-19500/ | 2 | 2.40 | 0.00047 | 0.00226 || Switching | JAN | | | | || | | | | | || | | | | | || Diode/ | Mil-S-19500/ | 4 | 2.40 | 0.00160 | 0.01536 || Voltage Ref./Reg. | JAN | | | | || (Avalanche & Zener) | | | | | || | | | | | || Transistor/ | Mil-S-19500/ | 4 | 2.40 | 0.00007 | 0.00067 || NPN/PNP | JAN | | | |

Example Reliability report


Reliability Prediction Drawbacks


Parts Count Method Reliability Prediction Drawbacks

• Prediction Methods not always effective in representing future reality of a product. Tend to be pessimistic, however they are generally inaccurate.

• Best utilized for design comparison and order of magnitude reliability prediction (must use same methods for comparisons)

• Single Stress Factors must be employed to represent a composite average or worst case of the population. Difficult to predict average stress levels, peak stress levels

• Methods give an overall average failure rate, one dimensional • Time to failure distributions (Weibull) are two dimensional describing

infantile failures as well as end of life failures• Reli growth using actual stress testing is a much more effective process

(however also more expensive approach)• MIL-STD-217F Notice 2 was the last revision of this long used standard (Jan

1995), No further releases planned.


Reliability Growth Methods


HALT Strategy: Highly Accelerated Life Testing

• One or more stresses used at accelerated amplitudes from what the product would see during application

• Stress level is gradually increased until failure is detected

• Failure is then autopsied to fundamental root cause

• Corrective/Preventive action taken to remove chance of recurring failure

• Test is then restarted

• Must be prepared to destroy prototypes, spend money

• Failure must be detectable, identifiable

Reliability Growth Methods: HALT

Rep

eat


Time Compression or Time Acceleration

Basic usage cycle is reduced by eliminating idle time and or off time.

Example: Opening and Closing a car door 10,000 times in 1 day. ~10 year:1day Acceleration

Stress Acceleration or Amplitude Acceleration

Amplitude of Stress is increased above normal usage cycle levels

Example: Thermal cycling a circuit board from –40 to 125C knowing the board will see a maximum ambient range of only 10 to 35C in its application. ~163cyles:1cycle Acceleration

2 Types of Acceleration

318-595 Statistics & ReliabilityExample of Time Accelerated Life Test (595 Team Project):

“Rotating Bicycle Apparatus Project”

Potential reliability stress is the periodic g-load (start-stop cycles). This causes fatiguefailure mode (cracks in ceramic material, creep of plastics, adhesives, solder electrical contacts failure).

Estimation of the test protocol, plan and execution time.The start-stop requirements for cycle: •10 s to accelerate from 0 to 5 rev/sec max rotational speed (60 mph)•5 s to decelerate from 5 rev/sec to 0.•35 starts-stops cycles per day•One cycle time (from start to stop) is going to be: T = 10+5+5=20s, where 5 s is added as a lag time to accommodate the transition from stopping back to starting

Assuming the throughput 35 start-stops/day for 365 days/year the total number of rotation cycles for 1 year is 35*365=12775 cycles /year (=12775 start-stops).Assuming 20% overhead the total number of cycles is going to be 1.2*12775=15330 cycles/year.Test time worth of 1 year of the number of cycles is going to be 15330*20/(3600*24)=3.5 days

life time, years

test time, days

1 3.53 10.55 17.5

10 35


Stress Accelerations

* High Temperature

* High Voltage

* Thermal Cycling

* Vibration


High Temperature Acceleration Factor

Svante August Arrhenius

Modified Arrhenius Equation:

AT = Acceleration Factor

Ea = Activation Energy Depends on failure modes; incl electromigration, contamination, etc.


Examples of Arrhenius Temperature Acceleration

0

1

2

3

4

5

6

7

20 40 60 80

Temp (deg C)

Rela

tive f

ailu

re r

ate Ceramic Caps

Resistors- Film

Bipolar transistors

Bipolar IC

RAM, CMOS


Voltage Stress Acceleration Factor

Modified Arrhenius Equation:


AF = (Ts/ Ta)E

Where;

Ts = Stress Test Thermal Excursion Range oK

Ta = Application Thermal Excursion Range oK

E = Material Dependent Exponent

E = 1.9 – 2.7 for 63/37 SnPb Eutectic Solders

AF = Per Cycle Stress Test Acceleration Factor

Basic Coffin-Manson Equation – Temperature CycleSnPb Eutectic Solder Joint Creep Failure Application

Thermal Cycle Stress AccelerationsPrimarily used to stress CTE mismatch, accumulated fatigue damage failures

Failure Mechanism/Material E316 Stainless Steel 1.54340 Steel 1.8Solder (97Pb/03Sn) T > 30°C 1.9Solder (37Pb/63Sn) T < 30°C 1.2Solder (37Pb/63Sn) T > 30°C 2.7Solder (37Pb/03Ag & 91Sn/09Zn) 2.4Aluminum Wire Bond 3.5Au4Al fracture in wire bonds 4.0PQFP Delamination / Bond Failure 4.2ASTM 2024 Aluminum Alloy 4.2Copper 5.0Au Wire Bond Heel Crack 5.1ASTM 6061 Aluminum Alloy 6.7Alumina Fracture 5.5Interlayer Dielectric Cracking 4.8-6.2Silicon Fracture 5.5Silicon Fracture (cratering) 7.1Thin Film Cracking 8.4


AF = (Ts/ Ta)1.9

Application, 1 Cycle/Day;

Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK

ExampleSnPb Eutectic Solder Joint Creep Failure Application, Conservative Acceleration

Stress Test Design;

Tmin = -40 oC = 233 oK, Tmax = 125 oC = 398 oK

Ts = 165 oK, Ta = 40 oK

AF = (165/ 40)1.9 = 14.8

1 Stress Cycle = 14.8 Applications Cycles

If 1 Stress Cycle takes ~60 minutes (average chamber ramp rate)

1 Stress Cycle Day = 24 x 14.8 = 355.2 Application Day Cycles


AF = (Ts/ Ta)E (Fa/Fs)

1/3 e(Tsa/100)

Where;



E = Material Dependent Exponent (1.9 – 2.7 SnPb Solders)

Ts(max) = Max Stress Temp oK

Ta(max) = Max Application Temp oK

Tsa = Ts(max) – Ta(max) oK

Fs = Thermal Cycle Frequency of Stress Test

Fa = Thermal Cycle Frequency of Application


Modified Coffin-Manson Equation – Temp and Temp GradientSnPb Solder Joint Creep Failure


AF = (Ts/ Ta)E (Fa/Fs)

1/3 e1414(1/Tamax – 1/Tsmax)

Where;



E = Material Dependent Exponent (1.9 – 2.7 SnPb Solders)

Tsmax = Max Stress Temp oK

Tamax = Max Application Temp oK

Tsa = Ts(max) – Ta(max) oK

Fs = Thermal Cycle Frequency of Stress Test

Fa = Thermal Cycle Frequency of Application


Alternate Form Modified Coffin-Manson Equation (Common)Norris-Landsberg Equation for Solder Joint Creep Failure


Example

Application;

Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK, Ta = 40 oK

Fa = 1 cycle/day

Stress Test Design;

Tmin = -40 oC = 233 oK, Tmax = 125 oC = 398 oK, Ts = 165 oK

Ts(max) = 398 oK, Ta(max) = 323 oK, Tsa = 75 oK

Fs = 1 cycle/hr = 24 cycle/day

AF = (165/40)1.9 (1/24)1/3 e(75/100) = 10.8

1 Stress Test Cycle = 10.8 Application Cycles

Modified Coffin-Manson EquationSnPb Solder Joint Creep Failure

1 Stress Test Day = Fs X AF = 259.2 Application Cycles

(Taking thermal gradient into account is more conservative)


HAST Strategy: Highly Accelerated Stress Testing

• One or more stresses used at accelerated amplitudes from what the product would see during application

• Stress level is constant, time to failure is primary measurement

• Failure may also be autopsied to fundamental root cause

• Corrective/Preventive action NOT necessarily taken

• Test is then restarted using higher or lower stress amplitude to get additional data points

• Used to find empirical relationship between stress level and time to failure (life)

Reliability Growth Methods: HAST

Rep

eat


HASS Strategy: Highly Accelerated Stress Screening

• Used in production to accelerate infantile failures and keep them from shipping to customers

• Must have HAST data to understand how much life is expended with stress screen

• One or more stresses used at slightly accelerated amplitudes from what the product would see during application

• Common application is powered burn-in time during which electronics are powered and thermal cycled. (Example MIL-STD-883) Assemblies tested during or after burn-in for failure inducements

Reliability Growth Methods: HASS

Rep

eat


Reliability Bathtub Curve

Fai

lure

s/T

ime

Time

infant mortality constant failure rate wearout

• Infant mortality- often due to manufacturing defects ….. Can be screened out

• In electronics systems, prediction models assume constant failure rates (Bellcore model, MIL-HDBK-217F, others)

• Understanding wearout requires knowledge of the particular device failure physics - Semiconductor devices should not show wearout except at long times - Discrete devices which wearout: Relays, EL caps, fans, connectors, solder

318-595 Statistics & ReliabilityLife Stress Models and Qualification

• Specify Device Storage/Shipment Profiles:

• Specify Device Heavy User Profiles:1. Number of Power Cycles

2. Number of Thermal Cycles and Min-Max Excursion (oC) per cycle

3. Number, Amplitude (G force) and Direction of Mechanical Shocks

4. Amplitude (Grms), Duration (Hrs), Freq Range (Hz) and Direction (1, 2 or 3 axis) Mechanical Vibration

5. Total airflow volume (M3) and particulates (Kg)


Appendices


More on Component DeratingIntentional limiting of usage stress vs rated capability

VoltagePower



318-595 Statistics & ReliabilityPhysics of Failure: Accumulated Fatigue Damage (AFD) is related to the number of stress cycles N, and mechanical stress, S, using Miner’s rule

SNAFD *Exponent B comes from the S-N diagram. It is typically between 2 and 20

Example: Solder JointShear Force

FApplied stress:

D

FS

Effective cross-sectional Area: D

Let = 10, then10* voids)( SNnoAFD

voids Effective cross-sectionalArea: D/2

Applied stress: SD

FS *2

*2

voids)(*102410**1024 noAFDSNAFD

AFD with voids will “age” about1000x faster than AFD with no voids

Voids in solder joints


Physics of failure: Thermal Fatigue ModelsCoefficients for Coffin - Manson Mechanical Fatigue Model

• The Coffin-Manson model is most often used to model mechanical failures caused by thermal cycling in mechanical parts or electronics. (Most electronicfailures are mechanical in nature)

• The values of the coefficient b for various failure mechanisms and materials(derived or taken from empirical data)

bcycles T

aN

N cycles = number of cycles to failure at reference condition

b = typical value for a given failure mechanism, a = prop constant

Failure Mechanism/Material b316 Stainless Steel 1.54340 Steel 1.8Solder (97Pb/03Sn) T > 30°C 1.9Solder (37Pb/63Sn) T < 30°C 1.2Solder (37Pb/63Sn) T > 30°C 2.7Solder (37Pb/03Ag & 91Sn/09Zn) 2.4Aluminum Wire Bond 3.5Au4Al fracture in wire bonds 4.0PQFP Delamination / Bond Failure 4.2ASTM 2024 Aluminum Alloy 4.2Copper 5.0Au Wire Bond Heel Crack 5.1ASTM 6061 Aluminum Alloy 6.7Alumina Fracture 5.5Interlayer Dielectric Cracking 4.8-6.2Silicon Fracture 5.5Silicon Fracture (cratering) 7.1Thin Film Cracking 8.4

General Failure Mechanism bDuctile Metal Fatigue 1 to 2Commonly Used IC Metal Alloys and Intermetallics

3 to 5

Brittle Fracture 6 to 8

Reference: “EIA Engineering Bulletin: Acceleration Factors”, SSB

-

1.003, Electronics

Industries Alliance, Government Electronics and Information

Technology Association Engineering Department, 1999.


Calculated acceleration factor and MTTF (and B10) @ normal stress:

AF = Nstress / Nuse = (b(165/45)2.7 = 33.4

MTTF (use)=MTTF(stress)*AF = 4570*33.4 = 152638hrs = 17.4 yrs

yrsAFuseB 9.612/1105.0*3.15*4768/1105.0**)10(

Normal operating conditions cycling 15C to 60C (T=45C)

Plan for N Stress (Accelerated) cycles –40 to 125 C (T=165C)

Find Mean life at stress level MTTF=4570 hrs=0.5 yrs

bcycles T

aN


Intro: Weibull Distribution

F(t) = Cumulative fraction of parts that have failedat time t

F(t) = 1 - e- ( )t /

ln ln (1 / (1 – F(t))) = ln(t) – ln()

Y = X + a

beta, - slope/shape parameter

eta, – characteristic life or scale parameter

when t = F(t) = 63.2%

Reliability Distributions are non-Normal, require 2 parameters

Knowing the distribution Function allows toaddress the following problem (anticipated future failure):

What is the probability, P , that the failure will occur for theperiod of time T if it did not occur yet for the period of time t ? (T>t)

P={F(T)-F(t)}/[1-F(t)]= ]})()[(exp{1

tT

318-595 Statistics & ReliabilityPhysical Significance of Weibull Parameters

99

10

Cu

mu

lati

ve F

ailu

re (

%)

F(t

)

Time to Failure (t)1 10 100

Slope =

B10

When Weibull distribution parameters are defined, B10 and MTTF can be computed.

The slope parameter, Beta (), indicates failure type

< 1 rate of failure is decreasing infantile (early) failure = 1 rate of failure is constant random failure> 1 rate of failure is increasing wear out failure

MTTF = mean time to failure (non-repairable)

MTBF = mean time between failure (repairable)(MTBSC)

= ( 1 + 1/ )

When = 1.0, MTTF = When = 0.5, MTTF = 2

When there is no suspension data, MTBF = MTTF

= total time on all systems / # of failures


Estimating Reliability from Test Data

• In testing electronics assemblies or parts, there are frequently few (or no) failures

• How do you estimate the reliability in this case?

• Use the chi-squared distribution and the following equation:

MTBF = 2 * Number of hours on test * Acceleration factor / 2

In this equation, 2 is a function of two variables

n, the degrees of freedom, defined as n= 2 * number of failures + 2

and F, the confidence level of the results (e.g. 90%, 95%, 99%)


Example

The following test was conducted:

• A new design was qualified by testing 20 boards for 1000 hours

• The test was conducted at elevated temperatures, where the test would accelerate

failures by 10X the usage rate

• One board failed at 500 hours, the other 19 passed for the full 1000 hours

What is the MTBF of the board design at 90% confidence?

Solution:

• First, determine n = 2 * number of failure + 2 = 4; so 2 = 7.78 (at 90% confidence)

• Second, determine number of hours = 19 samples * 1000 + 1 * 500 = 19, 500 hours

• So, the answer is:

MTBF = 2 * 19500 (total hours) * 10 (acceleration factor) / 7.78 = 50, 128 hours

318-595 Statistics & ReliabilityThe calculations are based on the Binomial Distribution and the following formula:

Confidence Level CL =

where:

n = sample size

p = proportion defective

r = number defective

= probability of k or fewer failures occurring in a test of n units

Pass/Fail Test Sample Sizes?

Example:

Suppose that 3 failed parts have been observed in the test equivalent to 1 year life, what minimum sample size is needed to be 95% confident that the product is no more than 10% defective?

Inputs in the formula are:

p =0.1(10%), r = 3, CL = 0.95(95%), P(r<k) = 0.05 and calculate n.

The minimum sample size will be 76.

Reliability test should start using just a few parts in order to get preliminary number of failed parts. Using this data a required sample size can then be estimated.


Number of subsystems: 3Equal Allocation

SystemB(10), years

SystemMTTF, years

SubsystemMTTF years

1 9.5 28.55 47.5 142.4

10 94.9 284.7

System Reliability Target Must be Allocated

MTTF~=10 years (B10=1 year) results in failure rate 1-F=1-exp(-1/10*10)=0.63, i.e. 63% of units on average will fail for 10 years

MTTF= 47.5 years (B10=5 years) results in failure rate 1-F=1-exp(-1/47.5*10)=0.19,i.e. 19% of units on average will fail for 10 years.


• Commonly Used Methods to Present and Analyze Data


Plot or Scatter Plot

Used to Illustrate Correlation or RelationshipsUsed to Illustrate Correlation or Relationships

Linear Correlation of Input to Output

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5

Input

Ou

tpu

t mArms

Vrms


Failure Root Causes

0

10

20

30

40

50

60

70

Dehumidif ier Pow er Supply No Defect Found Workmanship Other

Root Cause

#

OW

IW

Used to Illustrate Contributions of Multiple Sources

Excellent when data is abundant

Used to Illustrate Contributions of Multiple Sources

Excellent when data is abundant

Pareto ChartRoot Cause Failures Example


Fishbone Diagram

Effect:TempOf AmpFor example

Load ResLoad Res Line VoltageLine Voltage

VolumeVolumeLine FrequencyLine Frequency Input AmplitudeInput Amplitude

Ambient TempAmbient Temp

Illustrates Cause & Effect Relationship


Warranty Replacements

0

5

10

15

20

25

30

35

40

J F M A M J J A S O N D

Tota

l Uni

ts

0%

5%

10%

15%

20%

25%

30%

35%

40%

> W

arra

nty

Rate

Units

Rate

Year to Date SummaryReplacement Parts Example

Documents

318-595 Statistics & Reliability Statistics and Electronic Reliability