1. Statistics and Electronic Reliability

4. 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

5. Reliability of Electronic Circuits
Causes of Electronic Systems Failure
Reliability of Electronic Circuits
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 failures
Wearout failures are usually due to intrinsic failures

6. PCB Assembly Failure Mechanisms Stresses & Major Factors
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
Mechanical Shock and Vibration
Mass of Components and Overall Assembly
Height of Component Center of Mass (COG)
Thickness, Rigidity and Support Pts of PCB

7. Printed Circuit Board Assemblies
CTE Mismatches in PCB Assemblies
Si Die CTE = 2.8e-6/C
Gold CTE = 14.2e-6/C 5 – 15 μ in.
NiAu Pad
Thin Epoxy Solder Mask
Nickel CTE = 13.4e-6/C > ~100 μ in.
Copper
FR4 Laminate
CTE = ~20e-6/C
Copper CTE = 16.5e-6/C > ~1.2 mil
SnPb Eutectic Solder Joint CTE = ~25e-6/C

8. PCB Assembly Failure Mechanisms Stresses & Major Factors - continued
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 using Ion Chromatography for high reli assemblies. IPC-6012/15 mandate a total ionic cleanliness of less than 1.56ug/cm2 = 10ug/in2.

9. Ionic Test Methods for PCBs
Resistivity of Solvent Extract (ROSE) Test Method IPC-TM The 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 mg/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 This 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.

10. Specifying 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
Infantile
Period
~ Constant Failure Rate
Minimize or Precipitate using ESS in factory
Warranty Period Using ESS
Warranty Period

11. Basic Statistics and Reliability Statistics2 5 8 10 12 15 18 20 22 25
1.238
1.240
1.242
1.244

12. Std Deviation is a measure of the inherent spread in the data
Basic 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
where X = index notation for each individual.
where n = 7 people i i m = X i S 1 n
where S X = Sum of the individual times
where X and m = Average or Mean
Calculate the mean(average): i
Equation
n = 7 people Mean: X = ( )/7 = minutes s = ( X i - ) 2 S 1 n
where s = s = Standard Deviation
Sum or Variance
Calculate the standard deviation:
Equation
Step Step 2
(Xi - X) (Xi - X)
2-5.7=
6-5.7=
5-5.7 =
2-5.7 = =
8-5.7 =
7-5.7 =
S (Xi - X) =
Step 4 2
Definition:
Range = Max - Min
Median = Middle number when arranged low to high
Mode = Most common number
This Example:
Range = = 8 minutes
Median = 6 minutes
Mode = 2 minutes
53.43
Square each one
Then Add All s = s = 7 - 1
Standard Deviation: s = s
= 2.98 minutes 2
Step 3
Std Deviation is a measure of the inherent spread in the data

13. Bar Chart or Histogram Provides a visual display of data distribution2 5 8 10 12 15 18 20 22 25
1.238
1.240
1.242
1.244
Provides a visual display of data distribution
Shape of Distribution May be Key to Issues
Normal (Bell Shaped)
Uniform (Flat)
Bimodal (Mix of 2 Normal Distributions)
Skewed left or right
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

14. Normal (Gaussian) Distributions

15. Histogram vs Spec Limits
Target
Specification Limit 3s
Histogram vs
Spec Limits
Area under curve
Is probability of
failure 1s
Z is the number of Std Devs between the Mean and the spec limit. The higher the value of Z, the lower the chance of producing a defect 
66807ppm
PPM = Part per Million Defects
Z = 3s
Much Less
Chance of
Failure 1s
3.4ppm*
* Assumes Z is 4.5 long term
Normal Distribution
Z = 6s

16. Area under Distribution Curve Yields Probabilities
34%
34% 2% 2%
14%
14%
-3s
-2s
-1s m
+1s
+2s
+3s
Characterized by Two Parameters
m and s2
Normal Distribution = N( m,s2 )

17. Life Cycle of a Component
Standard Normal Distribution
Apply
Transformation
Standard Normal Distribution
Original Distribution
x-m Z=
Area under Curve =1 s
m-s m m+s X Z
Examples:
Z = is one Standard Deviations above the mean
Z= is 0.5 Standard Deviations below the mean

18. 1 Sided Normal Distribution, Probability TableZ Z
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-001
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-002
e e e e e e e e e e-003
e e e e e e e e e e-003
e e e e e e e e e e-003
e e e e e e e e e e-003
e e e e e e e e e e-003
e e e e e e e e e e-003
e e e e e e e e e e-003
e e e e e e e e e e-003
e e e e e e e e e e-004
e e e e e e e e e e-004
e e e e e e e e e e-004
e e e e e e e e e e-004
e e e e e e e e e e-004
e e e e e e e e e e-004
e e e e e e e e e e-005
e e e e e e e e e e-005
e e e e e e e e e e-005
e e e e e e e e e e-005
e e e e e e e e e e-005
e e e e e e e e e e-006
e e e e e e e e e e-006
e e e e e e e e e e-006
e e e e e e e e e e-006
e e e e e e e e e e-006
e e e e e e e e e e-007
e e e e e e e e e e-007
e e e e e e e e e e-007

19. Normal Distribution (cont.)Z
e e e e e e e e e e-007
e e e e e e e e e e-007
e e e e e e e e e e-008
e e e e e e e e e e-008
e e e e e e e e e e-008
e e e e e e e e e e-008
e e e e e e e e e e-009
e e e e e e e e e e-009
e e e e e e e e e e-009
e e e e e e e e e e-009
e e e e e e e e e e-010
e e e e e e e e e e-010
e e e e e e e e e e-010
e e e e e e e e e e-011
e e e e e e e e e e-011
e e e e e e e e e e-011
e e e e e e e e e e-011
e e e e e e e e e e-012
e e e e e e e e e e-012
e e e e e e e e e e-012
e e e e e e e e e e-013
e e e e e e e e e e-013
e e e e e e e e e e-013
e e e e e e e e e e-014
e e e e e e e e e e-014
e e e e e e e e e e-014
e e e e e e e e e e-015
e e e e e e e e e e-015
e e e e e e e e e e-015
e e e e e e e e e e-016
e e e e e e e e e e-016
e e e e e e e e e e-016
e e e e e e e e e e-017
e e e e e e e e e e-017
e e e e e e e e e e-017
e e e e e e e e e e-018
e e e e e e e e e e-018
e e e e e e e e e e-019
e e e e e e e e e e-019
e e e e e e e e e e-019
e e e e e e e e e e-020
e e e e e e e e e e-020
e e e e e e e e e e-021
e e e e e e e e e e-021
e e e e e e e e e e-021
e e e e e e e e e e-022
e e e e e e e e e e-022
e e e e e e e e e e-023
e e e e e e e e e e-023
e e e e e e e e e e-024
e e e e e e e e e e-024

20. • Examples of Fault/Failure Rates on The Sigma Scale PPM Defects
(with ± 1.5  shift)
1,000,000
Tax Advice
(phone-in)
(140,000 PPM)
100,000
Restaurant Bills
Doctor Prescription Writing
10,000 •
Restaurant Checks
Average
Company
Airline Baggage Handling
1,000
100
AircraftCarrier Landings 10
Best-in-Class 1 2 3 4 5 6 7 Z
Domestic Airline Flight
Fatality Rate
Examples of Fault/Failure Rates on
The Sigma Scale
(0.43 PPM)

21. Short Term Capability Snapshots of the Product
Over time, a “typical” product process may shift or drift by ~ 1.5
. . . also called “short-term capability”
. . . reflects ‘within group’ variation
Shift and Drift
Time 1
Time 2
Time 3
Time 4
Actual Sustained Capability of the Process
. . . also called “long-term capability”
. . . reflects ‘total process’ variation
LSL T
USL
Two Challenges:
Center the Process and Eliminate Variation!

22. Statistics Example: IPC Workmanship Classes: Solder Volume, Shape, Placement Control
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
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
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.
100 %
75 %
50 %
25 %
0 %
100 %
75 %
50 %
25 %
0 %
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
Min PTH Vertical Fill: Class 2 = 75% Class 3 = 100%
Ref: IPC-A-610, IPC-JSTD-001

23. BGA Void Size and Locations, Uniform Void Position Distribution, Varying Diameter
Sampling_Grid
Position
Model
Solder_Joint_Radius
Void_Distance
Void_Radius S
Void_Solder Interface Distance
S = Shell
Potential for Early Life Failure (ELFO) if S < D/10 = (solder_joint_radius)/10
S =Shell = solder_joint_radius – (void_distance + void_radius)

24. CLASS 3 - BEST P(D<10) = 81.11 % CLASS 2 - BETTER
CLASS 1 - GOOD
Solder Joint_Radius: mm
Void_Radius: mm
Void_Area: 36% of Joint Area
Failure criteria: D/10
P(D<10) = %
CLASS 2 - BETTER
Solder Joint_Radius: mm
Void_Radius: mm
Void_Area: 20% of Joint Area
Failure criteria: D/10
P(D<10) = %
CLASS 3 - BEST
Solder Joint_Radius: mm
Void_Radius: mm
Void_Area: 9% of Joint Area
Failure criteria: D/10
P(D<10) = %

25. Class vs Shell Size Relative Probabilities ~ 2x more likely to exceed D/10 threshold with Class 2 vs Class 3
S = Shell
Depth

26. Exponential Distributions
= Reliability
= Time

27. R(t) = e-lt, Note: l is in failures/time, and t is time
Definitions
l General Failure Rate Variable:
Recall the Bathtub Curve- Failure Rate (l) 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-lt, Note: l is in failures/time, and t is time
Note: At T=0, R(0)=1.0 (100%)
l FIT = FITs = Failures per 109 hours
MTBF (years) = 1x109 / (l FIT * 8766 hours /year )
l MTBF = 1/MTBF = 1/Mean time between failure in hours
R(t) = e-lt, Note: lMTBF in hr-1 and t in hr

28. Definitions l 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-lt, Note: l 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-lt, Note: l is in failures/time, and t is time
Note: At T=0, F(0)=0.0 (0%)

29. Weibull 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/ h)b, Note: h is the dimensionless scale parameter (stretches)
b is the shape or slope parameter (exponent)
Note: At T=0, R(0)=1.0 (100%)
Relationship of Weibull parameters to Failure Rate
= (/h)(t/h)-1
R(t) = e-(t/ h)b
F(t) = 1-e-(t/ h)b

30. Typical Reliability Plot using Weibull Dist
= (/h)(t/h)-1
F(t) = 1-e-(t/ h)b
F(t) = (1 – R(t))100%
Time to Failure(s)
At some time, t, 100% of the population will fail

31. Typical Reliability Plot assuming Weibull Dist
= (/h)(t/h)-1
R(t) = e-(t/ h)b
F(t) = 1-e-(t/ h)b
Time to failure plot using Weibull tool
Decreasing
Failure Rates
<1
Increasing
Failure Rates
>1
The Bathtub Curve
Constant
Failure Rates
=1
Exponential Distribution
Failure Rate, 
Weibull slope indicates where the product may be on the bathtub curve.
Early
Life
Wear out
Useful Life
Time

32. Reliability Prediction: Assume Constant Failure Rate b = 1.0
Basic Series Reli Method of an Electronic System:
Component 1 l1
Component 2 l2
Component i li
Component N lN
Each component has an associated reliability l
The System Reli lss is the sum of all the component l
lss = S li
Reli l is expressed in “FITs” failure units
x FIT = x Failures/109 hours
Note: 109 hours = 1 Billion Hours

33. Example: MTBF not so good to use for Reliability Specification
An electronics assembly product has an MTBF of 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-lt
l = 1/MTBF = 1/20000 hr
l = hr-1 (Failure rate)
t = 8766 hours (1 year)

34. Example: MTBF not so good to use for Reliability Specification
An electronics assembly product has an MTBF of hours; constant failure rate
What is the probability that a given unit will work continuously for one year?
Reliability R(t) = e-lt
l = 1/MTBF = 1/20000 hr
l = 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 years
But … 35% of the units would likely fail in the first year of operation.
Remember, after 1 MTBF period R(t) = 1/e =  63.2% of population will fail!

35. Intro to Reliability Evaluation
Basic Series Reli Method of an Electronic System:
Component 1 R1
Component 2 R2
Component i Ri
Component N RN
Each component also has an associated reliability R
The System R is the product of all the component R
R = P Ri
Recall, Reli R is a probability (0 to 1) expressed in percent

36. Reliability R Flowdown Example
Power supply
R = 0.94
Drive System,
needs R= 0.9 at 10 years
Subsystem Level
System Level
Motor
R = 0.97
Part
R=0.9999
Control Card
R = 0.99
R=0.999
Component Level

37. Reliability Requirements Flowdown- Example
Customer’s need: Meet 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

38. More Reason to use R(t) and not MTBF Example
An electronics product team has a goal of warranty cost which requires that a
Minimum reliability after 1 year be 99% or higher, R(1yr) >= Assume Constant
Failure Rates.
What MTBF should the team work towards to meet the goal?
Recall Equations: R = e -lt and MTBF = 1/l
Solve for MTBF: MTBF = 1/ l = 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.

39. 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

40. Environmental Conditions Susceptible Parts and Materials
Common 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
Distortion
Softening, melting, evaporation, sublimation
Metals, plastics materials, thermal fuse
Oxide film formation
High temperature oxidation
Contact material
Broken wire
Thermal diffusion
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
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

41. Intro to Reliability Estimation
Each l may be impacted by other factors or stresses, p:
Some commonly used factors
pT = Temperature Stress Factor
pV = Electrical Stress Factor
pE = Environmental Factor
pQ = Quality Factor
Overall Component l = lB * pT * pV * pE * pQ
Where lB = Base Failure Rate for Component

42. Reliability Prediction Methods/Standards
Bellcore (TR-TSY ):
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

44. Reliability Prediction Methods/Standards
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

45. Reliability Prediction Methods/Standards
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

46. Reliability Prediction
Basic Series Reli Method of an Electronic System:
Component 1 l1
Component 2 l2
Component i li
Component N lN
Above Reliability Prediction Model is flawed because;
Components may not have constant reliability rates l
lss = S li
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

47. 595 Standard Failure Rates in FIT (Data is not accurate in all cases)
Component Type
Method A - l
Method B - l
Method C - l
Method D - l
Method E - l
BJT/FET
5.0
3.8
3.2
7.6
4.0
Switch
44.0
30.0
1.0
20.0
Metal Film Res
0.7
2.5
0.05
0.2
Carbon Res
18.2
2.7
1.1
2.6
Varistor, tc Res
6.0
10.0
Electrolytic Cap
210
22.0
120
16.0
Polyester Cap
8.5
2.0
3.0
0.5
7.0
Tantalum Cap
15.0
8.0
Ceramic Cap
0.25
1.2
Si PN, Shottkey, PIN Diode
2.4
1.6
3.6
Zener Diode
13.6
17.4
18.8
70.0
LED
9.0
280
65.0
BJT Dig IC <100 Gates
138
2.3
6.7
BJT Dig IC < 1000 Gates
150
1.5
MOS Dig IC < 1000 Gates
27.3
301
13.3
MOS Dig IC => 1000 Gates
55.0
550
2.2
31.0
EM Coil Relay
385
302
220
715
SSR, Optocoupler
105
47.0
190
12.0
BJT Linear IC < 1000 Transistors
14.0
27.0
4.3
50.0
MOS Linear IC < 1000 Transistors
19.0
54.0
Transformer < 1VA
33.0
90.0
60.0
Transformer > 1VA

48. 595 Standard Failure Rates in FIT (Data is not accurate in all cases)
Component Type
Method A - l
Method B - l
Method C - l
Method D - l
Method E - l
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
Diode Bridge
4.8
1.6
3.6
2.4
LED Display
19.0
280
165.0
21.0
LCD Display
119.0
215.0
380
1165.0
206.0
BJT Linear IC > 1000 Transistors
217.0
41.3
91.0
MOS Linear IC > 1000 Transistors
29.0
74.0
113.3

49. 595 Standard Stress Factors
Factor Definitions (may not represent standard models)
pT = Temperature Stress Factor = e[Ta/(Tr-Ta)] – 0.4
Where Ta = Actual Max Operating Temp, Tr = Rated Max Op Temp, Tr>Ta
pV = 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
pE = Environmental (Overall) Factor >>>
Indoor Stationary = 1.0
Indoor Mobile = 2.5
Outdoor Stationary = 3.0
Outdoor Mobile = 5.0
Automotive = 7.0
pQ = 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

50. Example: Method A, 0-50C Ambient, Indoor Mobile, Distributor Components
+5VDC
+12VDC
C1 0.1uf 50V
Polyester
C4 0.1uf 50V
Ceramic
+5VDC
LED
Vf=1.5V
R1 2KW 1/4W
Brand A Metal Film
Vin
BPLR
OP AMP
C2 0.1uf 50V
Polyester
5V 1W
Zener
74HCT14
R2 150W 1/4W
Brand B Metal Film
C3 10uf 15V
Electrolytic
-12VDC
Part
Max Tr
Max Vr pT pV pE pQ C1
105C
 50V
 2.082
 0.186
 2.5
 1.25 C2 C3
85C
 15V
 3.773
 0.223 C4
125C
50V 
 1.548
 0.151 R1
120C
20V
 1.643
 0.232 R2
150C 6V
 1.249
 0.549
Zener Diode
100C
N/A
 2.318
1.0
Op Amp
36V
 1.0
74HCT14 7V
 1.649
1.25 
LED  
lFITS
10.29
10.29
552.2
1.46
0.83
1.50
23.18
67.73
217.77
106.16
Fits  Yrs MTBF

51. Stress 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.

52. EXAMPLE: Actual Reli Tool Input List of components, their number,
MTBF Data Input Sheet for e-Reliability.com COST: $500 per report
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 CL Parts Quality: Select Either: Mil-Spec or Commercial/Bellcore   Quantity  Description Bipolar Integrated Circuits    IC / Bipolar, Digital Gates    IC / Bipolar, Digital Gates    IC / Bipolar, Digital Gates    IC / Bipolar, Digital Gates    IC / Bipolar, Digital Gates    IC / Bipolar, Digital Gates    IC / Bipolar, Linear Transistors    IC / Bipolar, Linear Transistors    IC / Bipolar, Linear 301-1K Transistors    IC / Bipolar, Linear K Transistors , etc. 
EXAMPLE: Actual Reli Tool Input
List of components, their number,
Environment conditions, components quality

53. Example Reliability calculation using actual MIL-HDBK-217F
Failure rate of a Metal Oxide Semiconductor (MOS) can be expressed as
Parameters are listed in MIL Data base.
Temperature factor is modeled using Arrhenius type Eqn
595 charts are greatly simplified from actual parts count Reli

54. Example Reliability report
| | | | | 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/ | | | | |
| Bipolar, Digital | B | | | | |
| Gates | | | | | |
| Integrated Circuit/ | Mil-M-38510/ | | | | |
| Bipolar, Linear | B | | | | |
| Transistors | | | | | |
| Diode/ | Mil-S-19500/ | | | | |
| Switching | JAN | | | | |
| Diode/ | Mil-S-19500/ | | | | |
| Voltage Ref./Reg. | JAN | | | | |
| (Avalanche & Zener) | | | | | |
| Transistor/ | Mil-S-19500/ | | | | |
| NPN/PNP | JAN | | | |

55. Reliability Prediction Drawbacks

56. 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.

57. Reliability Growth Methods

58. Reliability Growth Methods: HALT
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
Repeat

59. 2 Types of Acceleration 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

60. Estimation of the test protocol, plan and execution time.
Example 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 fatigue
failure 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 = =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

61. Stress Accelerations. High Temperature. High Voltage. Thermal Cycling
Stress Accelerations * High Temperature * High Voltage * Thermal Cycling * Vibration

62. High Temperature Acceleration Factor
Modified Arrhenius Equation:
Svante August Arrhenius
AT = Acceleration Factor
Ea = Activation Energy Depends on failure modes; incl electromigration, contamination, etc.

63. Examples of Arrhenius Temperature Acceleration

64. Voltage Stress Acceleration Factor
Modified Arrhenius Equation:

65. Thermal Cycle Stress Accelerations
Primarily used to stress CTE mismatch, accumulated fatigue damage failures
Basic Coffin-Manson Equation – Temperature Cycle
SnPb Eutectic Solder Joint Creep Failure Application
Failure Mechanism/Material E
316 Stainless Steel
1.5
4340 Steel
1.8
Solder (97Pb/03Sn) T > 30°C
1.9
Solder (37Pb/63Sn) T < 30°C
1.2
Solder (37Pb/63Sn) T > 30°C
2.7
Solder (37Pb/03Ag & 91Sn/09Zn)
2.4
Aluminum Wire Bond
3.5 Au 4
Al fracture in wire bonds
4.0
PQFP Delamination / Bond Failure
4.2
ASTM 2024 Aluminum Alloy
Copper
5.0
Au Wire Bond Heel Crack
5.1
ASTM 6061 Aluminum Alloy
6.7
Alumina Fracture
5.5
Interlayer Dielectric Cracking
Silicon Fracture
Silicon Fracture (cratering)
7.1
Thin Film Cracking
8.4
AF = (DTs/ DTa)E
Where;
DTs = Stress Test Thermal Excursion Range oK
DTa = 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

66. Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK
Example
SnPb Eutectic Solder Joint Creep Failure Application, Conservative Acceleration
AF = (DTs/ DTa)1.9
Application, 1 Cycle/Day;
Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK
Stress Test Design;
Tmin = -40 oC = 233 oK, Tmax = 125 oC = 398 oK
DTs = 165 oK, DTa = 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 = Application Day Cycles

67. Modified Coffin-Manson Equation – Temp and Temp Gradient
SnPb Solder Joint Creep Failure
AF = (DTs/ DTa)E (Fa/Fs)1/3 e(DTsa/100)
Where;
DTs = Stress Test Thermal Excursion Range oK
DTa = Application Thermal Excursion Range oK
E = Material Dependent Exponent (1.9 – 2.7 SnPb Solders)
Ts(max) = Max Stress Temp oK
Ta(max) = Max Application Temp oK
DTsa = Ts(max) – Ta(max) oK
Fs = Thermal Cycle Frequency of Stress Test
Fa = Thermal Cycle Frequency of Application
AF = Per Cycle Stress Test Acceleration Factor

68. Alternate Form Modified Coffin-Manson Equation (Common)
Norris-Landsberg Equation for Solder Joint Creep Failure
AF = (DTs/ DTa)E (Fa/Fs)1/3 e1414(1/Tamax – 1/Tsmax)
Where;
DTs = Stress Test Thermal Excursion Range oK
DTa = Application Thermal Excursion Range oK
E = Material Dependent Exponent (1.9 – 2.7 SnPb Solders)
Tsmax = Max Stress Temp oK
Tamax = Max Application Temp oK
DTsa = Ts(max) – Ta(max) oK
Fs = Thermal Cycle Frequency of Stress Test
Fa = Thermal Cycle Frequency of Application
AF = Per Cycle Stress Test Acceleration Factor

69. Modified Coffin-Manson Equation
SnPb Solder Joint Creep Failure
Example
Application;
Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK, DTa = 40 oK
Fa = 1 cycle/day
Stress Test Design;
Tmin = -40 oC = 233 oK, Tmax = 125 oC = 398 oK, DTs = 165 oK
Ts(max) = 398 oK, Ta(max) = 323 oK, DTsa = 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
1 Stress Test Day = Fs X AF = Application Cycles
(Taking thermal gradient into account is more conservative)

70. Reliability Growth Methods: HAST
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)
Repeat

71. Reliability Growth Methods: HASS
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
Repeat

72. Reliability Bathtub Curve
LFailures/Time
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

73. Life Stress Models and Qualification
Specify Device Storage/Shipment Profiles:
Specify Device Heavy User Profiles:
Number of Power Cycles
Number of Thermal Cycles and Min-Max Excursion (oC) per cycle
Number, Amplitude (G force) and Direction of Mechanical Shocks
Amplitude (Grms), Duration (Hrs), Freq Range (Hz) and Direction (1, 2 or 3 axis) Mechanical Vibration
Total airflow volume (M3) and particulates (Kg)

74. Appendices

75. More on Component Derating Intentional limiting of usage stress vs rated capability Voltage Power

78. Physics of Failure: Accumulated Fatigue Damage (AFD) is related to the number of stress cycles N, and mechanical stress, S, using Miner’s rule
Exponent B comes from the S-N diagram. It is typically between 2 and 20
Example: Solder Joint
Shear
Force
voids
Effective cross-sectional
Area: D/2
Effective cross-sectional
Area: D F
Applied stress:
Applied stress:
Let  = 10, then
AFD with voids will “age” about
1000x faster than AFD with no voids
Voids in solder joints

79. Physics of failure: Thermal Fatigue Models
Coefficients 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 electronic
failures are mechanical in nature) b
cycles T a N D =
N cycles = number of cycles to failure at reference condition
b = typical value for a given failure mechanism, a = prop constant •
The values of the coefficient b for various failure mechanisms and materials
(derived or taken from empirical data)
Failure Mechanism/Material b
316 Stainless Steel
1.5
4340 Steel
1.8
Solder (97Pb/03Sn) T > 30°C
1.9
Solder (37Pb/63Sn) T < 30°C
1.2
Solder (37Pb/63Sn) T > 30°C
2.7
Solder (37Pb/03Ag & 91Sn/09Zn)
2.4
Aluminum Wire Bond
3.5 Au 4
Al fracture in wire bonds
4.0
PQFP Delamination / Bond Failure
4.2
ASTM 2024 Aluminum Alloy
Copper
5.0
Au Wire Bond Heel Crack
5.1
ASTM 6061 Aluminum Alloy
6.7
Alumina Fracture
5.5
Interlayer Dielectric Cracking
Silicon Fracture
Silicon Fracture (cratering)
7.1
Thin Film Cracking
8.4
General Failure Mechanism b
Ductile Metal Fatigue
1 to 2
Commonly 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.

80. 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
Calculated acceleration factor and MTTF (and normal stress:
AF = Nstress / Nuse = (DT/DT)b = (165/45)2.7 = 33.4
MTTF (use)=MTTF(stress)*AF = 4570*33.4 = hrs = 17.4 yrs b
cycles T a N D =

81. Reliability Distributions are non-Normal, require 2 parameters
beta, b - slope/shape parameter
Intro: Weibull Distribution
F(t) = 1 - e
- ( )
t / h b
ln ln (1 / (1 – F(t))) = b ln(t) – b ln(h)
F(t) = Cumulative fraction of parts that have failed
at time t
Y = b X + a
eta, h – characteristic life or
scale parameter
when t = h
F(t) = 63.2%
Knowing the distribution Function allows to
address the following problem (anticipated future failure):
What is the probability, P , that the failure will occur for the
period 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)]=

82. Physical Significance of Weibull Parameters Cumulative Failure (%)
When Weibull distribution parameters are defined, B10 and MTTF can be computed. 99
MTTF = mean time to failure (non-repairable)
= h G ( 1 + 1/b )
When b = 1.0, MTTF = h
When b = 0.5, MTTF = 2h
Cumulative Failure (%)
F(t)
MTBF = mean time between failure (repairable)
(MTBSC)
Slope = b
= total time on all systems / # of failures 10
When there is no suspension data, MTBF = MTTF 1
B10 10
100
Time to Failure (t)
The slope parameter, Beta (b), indicates failure type
b < 1 rate of failure is decreasing infantile (early) failure
b = 1 rate of failure is constant random failure
b > 1 rate of failure is increasing wear out failure

83. 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 / c 2
In this equation, c2 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%)

84. 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 c2 = 7.78 (at 90% confidence)
Second, determine number of hours = 19 samples * * 500 = 19, 500 hours
So, the answer is:
MTBF = 2 * (total hours) * 10 (acceleration factor) / 7.78 = 50, 128 hours

85. Pass/Fail Test Sample Sizes?
The 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
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.

86. i.e. 63% of units on average will fail for 10 years
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.
System Reliability Target Must be Allocated

87. Commonly Used Methods to Present and Analyze Data

88. Plot or Scatter Plot Used to Illustrate Correlation or Relationships
Linear Correlation of Input to Output
0.2
0.4
0.6
0.8 1
1.2
1.4
0.5
1.5
Input
Output
mArms
Vrms
Used to Illustrate Correlation or Relationships

89. Pareto Chart Used to Illustrate Contributions of Multiple Sources
Root Cause Failures Example
Used to Illustrate Contributions of Multiple Sources
Excellent when data is abundant

90. Illustrates Cause & Effect Relationship
Fishbone Diagram
Ambient Temp
Load Res
Line Voltage
Effect:
Temp
Of Amp
For example
Line Frequency
Volume
Input Amplitude
Illustrates Cause & Effect Relationship

91. Replacement Parts Example
Year to Date Summary
Replacement Parts Example