When scientifically planned and conducted, Burn-In and Environmental Stress Screening (ESS) provide one of the most effective methods of reliability screening at the component, sub-assembly, assembly, and system levels. Burn-in and ESS have been practiced in industry for many years, yet they are often conducted without scientific understanding, design, planning, quantification, and optimization. Based on his two co-authored books in the subject, the author of this talk presents a high-level introduction to the quantification of reliability-centered Burn-In and ESS.

1. An Introduction to Quantification
of Reliability‐Centered Burn‐In and
of Reliabilit Centered B rn In and
ESS (以可靠性为中心的老炼和环
境应力筛选定量分析简介)
境应力筛选定量分析简介
Feng‐Bin (Frank) Sun(孙凤斌）,
Ph.D.
©2012 ASQ & Presentation Sun
Presented live on May 20th, 2012
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3. An Introduction to Quantification of
Reliability-Centered Burn-In and ESS
(以可靠性为中心的老炼和环境应力筛选定量分析简介)
Feng-Bin (Frank) Sun, Ph.D.
HDD Reliability Engineering
HGST, a Western Digital Company

4. Overview (综述)
 Why Stress Screen?
 Definition of ESS and Burn-in and Their Relationship
 Phenomenological Observations and the Physical Insight of the
Failure Process During Screen
 Flaw-Stimulus Relationships and Typical Stress Screen Types
 Burn-in and ESS Quantification
 Statistical Modeling √
 Physical Modeling
 Optimum Screening Time Determination √
 References
2

5. Why Stress Screen?（为什么要进行应力筛选?）
1. $500 TO $1,500 WORTH OF ELECTRONICS ARE USED IN EACH
VEHICLE BY AUTOMOBILE MANUFACTURERS.
2. ABOUT 60% OF A MILITARY AIRCRAFT'S COST NOW GOES TO ITS
ELECTRONIC SYSTEMS.
3. "NEVER BUY A CAR MADE ON MONDAY OR FRIDAY!!!"
4. OVER HALF THE EFFORT HAS BEEN REPORTEDLY APPLIED TO
REWORK IN THE U.S.
5. CORRECTIONS OF DEFECTS AT THE MANUFACTURER'S FACILITY
IS MORE ECONOMICAL THAN SHIPYARD FAILURE CORRECTIONS
AND SHIPYARD FAILURE CORRECTIONS ARE MORE ECONOMICAL
THAN POST DELIVERY FAILURE CORRECTIONS DURING FIELD
OPERATION.
3

6. Why Stress Screen? (continued) （为什么要进行应
力筛选 - 续）
4

7. Why Stress Screen? (continued) （为什么要进行应
力筛选 - 续）
5

8. What Is ESS? (什么是环境应力筛选?)
 Is a process or series of processes.
 Involves the tailored applications of environmental stimuli
(such as thermal cycling and random vibration, and/or
electrical stresses).
 To electronic and electromechanical items (parts, modules,
units, and systems).
 On an accelerated basis, but within design capability.
 Ideally at the most cost-effective point of assembly.
 To expose, identify and eliminate latent defects.
(such defects can’t be detected by visual inspection, or
electrical testing and would in all likelihood, if undetected,
manifest themselves in the operational or field environment)
6

9. What Is Burn-In? (什么是老练?)
Burn-in is a test performed for the purpose of screening or
eliminating marginal devices, those with inherent defects or
defects resulting from manufacturing aberrations which cause
time and stress dependent failures.
-- MIL-STD-883C
Burn-in can be regarded as a special case of ESS where the
appropriate electrical conditions are combined with the
appropriate thermal conditions to accelerate the aging of a
component or device.
7

10. Phenomenological Observations and the Physical
Insight of the Failure Process during Screen (应力
筛选过程中的现象表征以及失效过程的物理机制洞察)
 Conventional Bathtub Curve Concept
 The “S”-shaped CDF Pattern
 Roller-Coaster Failure Rate Curve
 Stress-Strength Interference and Component
Failure Patterns
8

11. Conventional Bathtub Curve Concept （传统失效
率浴盆曲线概念）
1 Quality failures 2 Stress-related failures
3 Wearout failures
Early-
Failure rate
failure Wearout
period Useful-life period period
1
3
2
0 Cumulative operating time
9

12. The S-Shaped CDF Pattern (“S”形累积分布图特征）
A cdf plot based on the experimental data of CMOS transistors.
10

13. Roller-Coaster Failure Rate Curve (“过山车”形失效
率曲线特征）
Latent defects
removed in checkout
Latent defects removed in
process inspections and tests
Failure rate
Wearout
failures
Roller-Coaster
curve
0 Cumulative operating time
11

14. Stress-Strength Interference and Bathtub Curve
（应力-强度干涉与浴盆曲线的关系）
12

15. Flaw-Stimulus Relationships (缺陷与激发因子的关系）
1. Patent Defect
 flaw which has advanced to the point where an anomaly
actually exists ,or
 out-of-tolerance, or a specification, condition which can be
readily detected by an inspection or a test procedure.
2. Latent Defect
 Irregularity due to manufacturing processes, or
 materials which will advance to a patent defect when
exposed to environmental or other stimuli.
13

16. Flaw-Stimulus Relationships (continued) (缺陷与
激发因子的关系 - 续）
Examples of Patent Defect
1. Parts 2. Interconnections
(1.1) Broken or damaged in (2.1) Incorrect wire termination.
handling. (2.2) Open wire due to handling
(1.2) Wrong part installed. damage.
(1.3) Correct part installed (2.3) Wire shorted to ground due to
incorrectly. misrouting or insulation damage.
(1.4) Failure due to electrical (2.4) Missing wire.
overstress or electrostatic (2.5) Open etch on printed wiring
discharge. board.
(1.5) Missing parts. (2.6) Open plated through-hole.
(2.7) Shorted etch.
(2.8) Solder bridge.
(2.9) Loose wire strand.
14

17. Flaw-Stimulus Relationships (continued) (缺陷与
激发因子的关系 - 续）
Examples of Latent Defect
1. Parts 2. Interconnections
(1.1) Partial damage through (2.1) Cold solder joint.
electrical overstress or (2.2) Inadequate/excessive solder.
electrostatic discharge. (2.3) Broken wire strands.
(1.2) Partial physical damage during (2.4) Insulation damage.
handling.
(2.5) Loose screw termination.
(1.3) Material or process induced
hidden flaws. (2.6) Improper crimp.
(1.4) Damage inflicted during (2.7) Unseated connector contact.
soldering operations (excessive (2.8) Cracked etch.
heat). (2.9) Poor contact termination.
(2.10) Inadequate wire stress relief.
15

18. Flaw-Stimulus Relationships (continued) (缺陷与
激发因子的关系 - 续）
Screening processes for IC failure mechanisms
Screening Failure
Test Mechanism
Substrate Bulk Substrate Bonding Particle External
mounting silicon surface and contamination Seal Package lead Thermal Electrical
defects defects defects wire + extraneous defects defects defects mismatch stability
material
Internal     
visual exam
External   
visual exam
Stabilization    
bake
Thermal      
cycling
Thermal      
shock
Centrifuge    
Shock    
Vibration    
X ray     
Burn-in     
Leakage tests 
16

19. Flaw-Stimulus Relationships (continued) (缺陷与
激发因子的关系 - 续）
* PIND: particle impact noise detector
17

20. Typical Stress Screen Types (典型应力筛选类型)
1. Temperature cycling
2. Random vibration
3. High temperature burn-in
4. Electrical stress
5. Thermal shock
6. Sine-wave vibration, fixed frequency
7. Sine-wave vibration, swept frequency
8. Low temperature
9. Combined environment
18

21. Typical Stress Screen Types (continued)
(典型应力筛选类型 – 续)
An Example of Input Power Spectral Density
An Example of Input Temperature Profile for
for Random Vibration
Temperature Cycling
19

22. Governing Parameters of Stress Profiles (应力筛选
激发谱的关键参数）
1. High Temperature Burn-in
 Temperature Delta
 Duration
2. Temperature Cycling
 Maximum/Minimum Temperature
 Temperature Change Rate
 Dwell Duration
 Number of Cycles
3. Random Vibration
 Grms
 Input Acceleration Profile (Power Spectral Density)
 Duration
 Axes of Vibration
20

23. ESS/Burn-In Quantification Classification （老炼
及环境应力筛选定量分析分类）
1. Statistical Modeling: Mathematical Description of Failure
Time Behavior
2. Physical Modeling: Life-stress Relationship
3. Optimum Screening Time Determination under a Given Stress
Profile:
• Cost Criteria: Cost/Profit
• Reliability Criteria: Failure Rate/Mean Life/Mission Reliability
• Screening Efficiency Criteria: Efficiency/Residue/Power/Strength
4. Optimum Screening Profile (Parameter) Determination:
• Screening Strength
• Life-Stress Relation (Accelerated Stress Testing)
21

24. Mathematical Description Of The Failure
Process During Screen (应力筛选过程的数学描述)
1. Mixed Weibull Life Distribution √
2. Two-Parameter Bathtub Model
3. Three-Parameter Bathtub Model
4. Five-Parameter Bathtub Model
5. Six-Parameter Bathtub Model
22

25. Model Selection and Parameter Estimation (模型
选择以及参数估计)
 Model Selection:
(1) Bimodal Mixed Weibull Life Distribution
– with physical meaning and commercial software available for
parameter estimation
(2) Two-Parameter Bathtub Model
– simple and easy to estimate parameters
 Parameter Estimation:
(1) Analytical Method: MLE
– mathematically complicated, but more efficient & accurate
23

26. Mixed Life Distribution – General (混合寿命分布 –
通用模型)
R1, 2,...,n (T )  p1 R1 (T )  p2 R2 (T )  p3 R3 (T )  ...  pn Rn (T )
f1, 2,...,n (T )  p1 f1 (T )  p2 f 2 (T )  p3 f 3 (T )  ...  pn f n (T )
p1 f1 (T )  p2 f 2 (T )  p3 f 3 (T )  ...  pn f n (T )
1, 2,...,n (T ) 
p1 R1 (T )  p2 R2 (T )  p3 R3 (T )  ...  pn Rn (T )
where n = total number of subpopulations; fi(T), Ri(T), and λi(T) are
failure probability density function, reliability function, and failure
rate function of ith subpopulation at age T; pi = proportion of ith
subpopulation, and n
 pi  1
i 1
24

27. Mixed Life Distribution – Bimodal Weibull (混合
寿命分布 – 双态威布尔模型)
1 2
 T  1   T  2 

  
 
  

R1, 2 (T )  p1 e  1 
 p2 e  2 
1 2
 1 1  T  1   2 1  T  2 
1  T   1  
  
 2  T   2  
  

f1, 2 (T )  p1 
   e  1 
 p2 
   e  2 
1  1   2  2


1 2
 1 1  T  1   2 1  T  2 
1  T   1  
  
 2  T   2  
  

p1 
   e  1 
 p2 
   e  2 
1  1   2  

1, 2 (T )  1
2
2
 T  1   T  2 

  
 
  

p1 e  1 
 p2 e  2 
where i, βi, i are Weibull location, shape, and scale parameters of
ith subpopulation; pi = proportion of ith subpopulation, and
p1  p2  1
25

28. Two-Parameter Bathtub Curve Model (两参数浴盆
曲线模型)
    1 T /  
 (T )     T e , T  0,   0,   0
 
    1 T /   1 e T /  
f (T )     T e e
 
1 e T /  
R(T )  e
26

29. Maximum Likelihood Estimation (MLE) Method
For Mixed Weibull Distribution (混合威布尔寿命分布
的极大似然估计)
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Probability - Weibull
99.000 Probability-W eibull
90.000 D ata 1
W eibull-Mixed
MLE RRM K-M FM
F= 74/ S= 40
50.000 Probability Line
p=23%
U n r e lia b ilit y , F ( t )
10.000
5.000
1.000
0.500
Results Summary
Distribution: Weibull-Mixed
Analysis: MLE
0.100 CB Method: FM
0.050
Ranking: K-M
Beta 1.497589756 2.244569659
Eta 7656.365785 519.3829595
0.010 Portion 0.7699722126 0.2300277874
0.005
LK Value -703.6170419
Fail Susp 74 40
0.001
1.000 10.000 100.000 1000.000 10000.000
Time, (t)
                                                                               
27

30. Optimum Screen Time Determination Based On
Bimodal Mixed Exponential Life Distribution (基
于双态混合指数寿命分布的最佳筛选时间确定)
1. Bimodal Mixed Exponential Life Distribution – A
Special Case of Bimodal Mixed Weibull
2. An Ever Decreasing Failure Rate Function
3. Screen Duration for a Post-Screen Mission Reliability
4. Screen Duration for a Post-Screen Mean Residual Life
5. Screen Duration for a Post-Screen Failure Rate Function
6. Screen Duration for a Screen Power Function
7. The Number and Cost of Failures During Screen
28

31. Bimodal Mixed Exponential Life Distribution --
A Life Distribution With Ever Decreasing Failure Rate
(双态混合指数寿命分布 – 一个失效率永远递减的特殊寿命分布)
 Reliability Function:
 t  t
R(t) =p e b  pg e g
b
 Probability Density Function (pdf):
 t  t
f(t) =p  e b  pg g e g
b b
 Failure Rate Function:
λg t  (λ b  λ g ) t
f(t) pb λ be  λ b t  p g λ ge p b (λ b  λ g )e
λ(t)   λb t λg t
 λg   (λ b  λ g ) t
R(t) pbe  pge p g  pbe
 (t )
where pb>pg, pb+pg  1 and Failure Rate Is Always Decreasing!!! t
0
 Initial Failure Rate: λ(0) = pb λb + pg λg
 Limiting Final Failure Rate: λ() = λg
29

32. Failure Rate Function of Mixed Exponential Life
Distribution -- An Ever Decreasing Function (混合指数
寿命分布失效率函数– 一个永远递减的函数)
Failure Rate Function of Mixed Exponential Life Distribution
(Lambda_b=5E-3 fr/hr; p_b=10%; Lambda_g=1E-6 fr/hr; p_g=90%)
5.E-04
Failure Rate, fr/hr
4.E-04
3.E-04
2.E-04
1.E-04
0.E+00
0 500 1,000 1,500 2,000
Operating Time, hr
30

33. Optimum Screen Duration For A Specified Post-
Screen Mission Reliability Goal (满足指定的筛选后
工作可靠度目标的最佳筛选时间)
 
  t 

 p R (t)  e
 b 

   b G
 
    
1
T* =
 
Loge   
b  





  t




b g   g
 
pg 
e
  R (t) 
 G 

  

where
RG(t) = specified post-burn-in reliability goal for a
mission time of t.
Constraints:  t  t  t
(p e b  p e g ) < R (t) < e g
b g G
31

34. Optimum Screen Duration For A Specified Post-
Screen Mission Reliability Goal – An Example
(满足指定的筛选后工作可靠度目标的最佳筛选时间 - 举例)
Screen Time Versus Post-screen Mission Reliability
(Lambda_b=5E-3 fr/hr; p_b=10%; Lambda_g=1E-6 fr/hr; p_g=90%; t=1000 hr)
700
600
Screen Time, Hours
500
400
300
200
100
0
0.8900 0.9100 0.9300 0.9500 0.9700 0.9900
Desired Post-screen Mission Reliability Goal
32

35. Optimum Screen Duration For A Specified Post-
Screen Mean Residual Life Goal (满足指定的筛选
后剩余寿命目标的最佳筛选时间)
  1 
 p  MRL  
 1    b G
λb  
TS  
*
Log e   
 λb  λg    1 
 
 pg 
  λg
 MRLG  

  
where
MRLG = specified post-screen mean residual life goal.

 p pg 

Constraints:  b +  < MRL < 1

  g 

G g
 b 
33

36. Optimum Screen Duration For A Specified Post-
Screen Mean Residual Life Goal -- An Example
(满足指定的筛选后剩余寿命目标的最佳筛选时间 – 举例)
Screen Time Versus MRL
(Lambda_b=5E-3 fr/hr; p_b=10%; Lambda_g=1E-6 fr/hr; p_g=90%)
600
Screen Time, Hours
500
400
300
200
100
0
900,000 950,000 1,000,000
Desired MRL Goal, hr
34

37. Optimum Screen Duration For A Specified Post-
Screen Failure Rate Goal (满足指定的筛选后失效率目
标的最佳筛选时间)
 1   p b λ b - λ G ( t ) 
*
 Log e  t
TS
 λb  λg 
  
 pg λ G (t )  λ g 
  
where
G (t) = specified post-screen failure rate goal at
the end of t-hr mission.
 
Constraints: 



 p g   - g 

 
 
 b
g <  (t) <  -


 

G b
 -   - g  t
  
   
 b 

 pg + p e 

 b 
35

38. Optimum Screen Duration For A Specified Post-
Screen Failure Rate Goal -- An Example (满足指定
的筛选后失效率目标的最佳筛选时间 – 举例)
Screen Time Versus Post-screen Failure Rate
(Lambda_b=5E-3 fr/hr; p_b=10%;Lambda_g=1E-6 fr/hr; p_g=90%; t=100 hr)
(Lambda_b=5E-3 fr/hr; p_b=10%; Lambda_g=1E-6 fr/hr; p_b=90%; t=100 hr)
700
600
Screen Time, Hours
500
400
300
200
100
0
1.00E-05 6.00E-05 1.10E-04 1.60E-04 2.10E-04 2.60E-04 3.10E-04
Desired Post-screen Failure Rate Goal
36

39. Optimum Screen Duration for a Desired Screen
Power Goal (满足指定的筛选功效强度目标的最佳筛选时
间)
Actual failure rate reduction due to screen
Screen Power 
Maximum potential failure rate reduction due to screen
1 Log 1

 PS 

*
Ts  
G 
e p (1 PS )

D 
g


 G 
where
PSG = the screen power goal,
D = λb - λg
Constraints: 0 < PSG < 1
37

40. Optimum Screen Duration for a Desired Screen
Power Goal – An Example (满足指定的筛选功效强度
目标的最佳筛选时间 – 举例)
Screen Power Screen Time, hr
0% 0.00
5% 10.36 Screen Time Versus Screen Power
10% 21.27 (Lambda_b=5E-3 fr/hr; p_b=1%;Lambda_g=1E-7 fr/hr; p_b=99%)
(Lambda_b=5E-3 fr/hr; p_b=10%; Lambda_g=1E-6 fr/hr; p_g=90%)
15% 32.81
600.00
20% 45.03
Screen Time, Hours
25% 58.04
500.00
30% 71.94
35% 86.86
400.00
40% 102.97
45% 120.48
300.00
50% 139.64
55% 160.81 200.00
60% 184.47
65% 211.28 100.00
70% 242.21
75% 278.77 0.00
80% 323.50
0% 10% 20% 30% 40% 50% 60% 70% 80% 90%
85% 381.14
90% 462.34 Screen Power
95% 601.07
38

41. The Number and Cost of Failures During Screen
(筛选过程中的失效次数和费用模型)
1  A Ts
H(Ts )  h Ts  (h  h )(1  e )
f A i f
C(Ts )  H(Ts ) C
f
where
A  p  g + pg 
b b
h  pg  g + p 
i b b
 
b g
h 
f A
C  average cost of a single failure.
f
39

42. Optimum Screen Time for the Minimum Cost (使
总费用最小的的最佳筛选时间)
C (TS )  N [C0  C STS  C fS H S (TS )  C fW HW (TW | TS )]
Where
TS = screen time,
TW = warranty time,
N = total # of units to be screened,
C0 = fixed cost of screen for each unit,
CS = screen cost per hour per unit,
CfS = cost of replacing a failed unit during screen,
CfW = cost of replacing a failed in the field during warranty,
HS(TS) = expected number of renewals of a unit during screen,
HW(TW|TS) = expected number of renewals of a screened unit during
warranty.
40

43. References (参考文献)
 D. Kececioglu and F. Sun, Environmental Stress Screening (ESS) - Its
Quantification, Optimization, and Management, 544 pp., 1st Printing by Prentice
Hall, June 1995, 2nd Printing by DEStech Inc., 2003.
 D. Kececioglu and F. Sun, Burn-in Testing - Its Quantification and Optimization,
704 pp., 1st Printing by Prentice Hall, May 1997, 2nd Printing by DEStech, 2003.
 W. Kuo, W. Chien, T. Kim, Reliability, Yield, and Stress Burn-In: A Unified
Approach for Microelectronics Systems Manufacturing and Software Development ,
Springer; 1st edition January 31, 1998.
 F. Jensen and N. E. Peterson, Burn-in, John Wiley & Sons, Inc., 167 pp., 1982.
 D. Kececioglu and F. Sun, "Mixed-Weibull Parameter Estimation for Burn-in Data
Using the Bayesian Approach," Microelectronics and Reliability, Vol. 34, No. 10,
pp. 1657-1679, 1994.
 F. Sun and D. Kececioglu, "Determine the Optimum Burn-in Time for the Maximum
MRL Directly from the TTT Plot," Proceedings of 5th International Conference of
the Decision Sciences Institute, Athens, Greece, July 4-7, 1999.
 F. Sun and D. Kececioglu, "A Physical Approach for the Determination of the
Optimum Random-Vibration Screening Duration,” Proceedings of 1996 Annual
Reliability and Maintainability Symposium, Las Vegas, NV, pp. 177-184, January
22-25, 1996. 41

44. My Contact Information
(联络方式)
Feng-Bin (Frank) Sun, Ph.D.
Email: franksun9999@gmail.com
Thanks for Your Time!
42