1. Std Deviation is a measure of how spreadout the data is
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 how spreadout the data is

2. 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

3. Histogram Specification
Target
Specification Limit
Histogram Specification
Some
Chance of
Failure 1s 
3s = z
The higher the number (Z) in front of the sigma symbol the lower the chance of producing a defect
66807ppm
Much Less
Chance of
Failure 1s
3.4ppm
6s = z

4. Sigma vs Specification
Target
Specification Limit
Sigma vs Specification
Some
Chance of
Failure 1s 
3s = z
The higher the number (Z) in front of the sigma symbol the lower the chance of producing a defect
66807ppm
Much Less
Chance of
Failure 1s
3.4ppm
6s = z

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

6. MANUFACTURABILITY ASPECT
Critical Measurement in Production:
The desired state
reality.... Unless you designed for it
L'HISTORIQUE NOUS A MONTRE DE NOMBREUX DECALAGES ENTRE LA PREVISIOBN ET LA REALITE
L'UTILSATION DE LA STATISTIQUE 5SOIT SUR DES DONNEES HISTORIQUE ou PAR ANALOGIES PERMET UNE MEILLEURE PREVISIBILITE PAR UNE DEMARCHE ET UN VOCABULAIRE COMMUN ENGINEERING-MANUFACTURING

7. Over time, a “typical” process will shift and drift by ~ 1.5
Inherent Capability of the Process
Over time, a “typical” process will shift and drift by ~ 1.5
. . . also called “short-term capability”
. . . reflects ‘within group’ variation
Shift and Drift
Time 1
Time 2
Time 3
Time 4
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!

8. Other Methods to Present/Analyze Data

9. 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

10. 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

11. 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

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

13. Intro to Reliability Evaluation
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

14. Note: lMTBF in hr-1 and t in hr
Definitions
l FIT = Failures per 109 hours
l MTBF = 1/MTBF = 1/Mean time between failure in hours
MTBF (years) = 1x109 / (l FIT * 8766 hours /year )
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: lMTBF in hr-1 and t in hr
Bathtub curve- typical reliability vs. time behavior

15. Example
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%
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.

16. 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) >= 0.99
What MTBF should the team work towards to meet the goal?
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) !

17. 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

18. Intro to Reliability Evaluation
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

19. 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 217E:
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

20. 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

21. 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

22. 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

23. 595 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
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
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
15.0
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
Plastic Shell Connector, Plug, Jack
100.0
150.0
120.0
105.0
Metal Shell Connector, Plug, Jack
18.0
57.0
40.0
35.0
Pb, NCd, Li, Lio, NmH Battery
8.0

24. 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 = 1.5
Outdoor Stationary = 2.0
Outdoor Mobile = 2.5
Automotive = 3.0
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

25. 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.

26. 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

27. 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

28. 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 | | | |

29. Reliability Prediction Drawbacks
Prediction Methods not always effective in representing future reality of a product. Tend to be pessimistic
Best utilized for design comparison, only if the same method is used
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

30. 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
Failure must be detectable, identifiable

31. Estimation of the test protocol, plan and execution time.
Example of Accelerated Life Test (595 Team Project): “Rotating Bicycle Apparatus”
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:
12 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

32. 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)

33. 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

34. 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

35. 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 factors
Wearout failures are usually due to intrinsic failures

36. 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 6 and 25
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

37. 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.

38. 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 = Nuse / Nstress = (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 =

39. Appendices

40. 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)]=

41. 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

42. 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%)

43. 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

44. 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.

45. 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