Accelerated tests are conducted at various stages of the product life cycle. When accelerated life tests yield few or no failures at low stress levels, it is difficult or impossible to estimate reliability at the design stress level. In such situations, accelerated degradation tests may be used. This presentation introduces accelerated degradation test methods, degradation models, estimation of model parameters, relationships between degradation and reliability, and estimation of reliability at the design stress level. Several practical examples are presented.

1. Reliability Estimation from
Accelerated Degradation Testing
基于加速退化试验的可靠性估
计
Guangbin Yang (杨广斌), Ph.D.
©2011 ASQ & Presentation Yang
Presented live on Jan 08th, 2011
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3. Reliability Estimation from
Accelerated Degradation Testing
基于加速退化试验的可靠性估计
Guangbin Yang (杨广斌), Ph.D.
Ford Motor Company, Dearborn, Michigan, U.S.A.
Email: gbyang@ieee.org

4. Overview
 ALT (Accelerated Life Test) and ADT
(Accelerated Degradation Test)
 Reliability Estimation from Pseudo-Lifetimes
 ADT with Destructive Inspections
 Takeaways
2

5. ALT Purpose and Test Method
 The primary purpose of ALT is to estimate the
reliability of a product at the design condition in a
shorter time.
 To do an ALT, a number of units are sampled and
divided into two or more groups. Each group is
tested at a different accelerating condition.
 The test at an accelerating condition continues
until all units fail, or until a pre-specified time or
number of failures is reached.
3

6. ALT Data Analysis
 The life data of all groups are combined to
estimate the reliability at the design condition
through an acceleration relationship.
acceleration
S relationship
S2      
S1      
S0
0 t
4

7. Why ADT?
 The time allowed for testing is continuously
reduced, and thus the test at low stress levels
often yields few or no failures. This is especially
the case when we test high-reliability products.
 With few or no failures, it is difficult or
impossible to analyze the life data and make
meaningful inferences about product reliability.
 In these situations, we should consider ADT.
5

8. What Products Are Suitable for ADT?
 Soft failure: failure is defined by a performance
characteristic degrading to an unacceptable level.
 Degradation is irreversible; that is, the
performance characteristics monotonically
increase or decrease with time.
 For convenience of data analysis, a product should
have a critical performance characteristic, which
describes the dominant degradation process and is
closely related to reliability. Such a characteristic
is fairly obvious to identify for many products.
6

9. ADT Method
 ADT are similar to ALT. During ADT, however,
measurements of the critical performance
characteristic are taken at various time intervals.
 Most ADT apply constant stress.
 Other types of stress (e.g., step stress) may be
used, but are not common in practice because of
complexity in data analysis and stress application.
7

10. Methods for Degradation Data Analysis
 Degradation data obtained at higher stress levels
are used to estimate the reliability at the design
level.
 The estimation requires a degradation model that
relates performance characteristic to aging time
and stress level.
 The primary methods for reliability estimation
include
 Pseudo-lifetime analysis.
 Random-process method.
 Random-effect method.
8

11. Advantages of ADT
 An ADT allows reliability to be estimated even
before a test unit fails. Thus an ADT greatly
reduces the test time and cost.
 An ADT often yields more accurate estimates
than those from life data analysis, especially when
a test is highly censored.
9

12. Disadvantages of ADT
 Reliability estimation from degradation data often
requires intensive computations.
 An ADT requires frequent measurement of
performance characteristics during testing. This
increases workload if it cannot be done
automatically.
10

13. Reliability Estimation from
Pseudo Lifetimes
伪寿命及可靠性估计
11

14. Pseudo Life
 A pseudo life is not an observation.
 A pseudo life is obtained by extrapolating a
degradation path.
y
G
0 t0 t1 t2 tn t
12

15. Estimation of Life Distributions
y
S2 S1
G
0 t21 t23 t11 t13 t
13

16. Reliability Estimation from Pseudo
Lifetimes at the Design Stress Level
 The methods for ALT life data analysis apply to
pseudo lifetimes.
 The analysis can be done using commercial
software. acceleration
S relationship
S2      
S1      
S0
0 t
14

17. Application Example: Electrical Connector
 Problem statement
 Electrical connectors fail often due to excessive stress
relaxation.
 Stress relaxation can be measured by the ratio s / s0
(%), where s0 is the initial stress and s is the stress
loss.
 For an electrical connector, failure is defined by the
stress relaxation exceeding 30%.
 Estimate its failure probability at the design life of 15
years and the operating temperature of 40C.
15

18. Application Example: Electrical Connector
 Test method
 A sample of 18 units was randomly selected from a
production lot and equally divided into three groups.
Each group had 6 units.
 The test temperatures were 65, 85 and 100C.
 The censoring times were 2848 hours at 65C, 1842
hours at 85C, and 1238 hours at 100C.
16

19. Application Example: Electrical Connector
 Stress relaxation data
30
s
100C
s0 25
20 85C
65C
15
10
5
0
0 500 1000 1500 2000 2500 3000
t (hr)
17

20. Application Example: Electrical Connector
 Degradation model
s B  Ea 
 At exp  
s0  kT 
where Ea is the activation energy, k is the
Boltzmann’s constant, A and B are unknowns.
Here A usually varies from unit to unit, and B is a
fixed effect parameter.
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21. Application Example: Electrical Connector
 Linearized degradation model
At a given temperature, the degradation model
can be written as
ln( s s0 )  1   2 ln(t ),
where 1  ln( A)  Ea / kT , and  2  B.
19

22. Application Example: Electrical Connector
 The linearized degradation model is fitted to each
of the 18 degradation paths. 1 and 2 are
estimated for each unit using the least squares
method.
 The pseudo lifetime of each test unit is calculated
from
ˆ
 ln( 30)  1 
tˆ  exp  .
 ˆ2 
20

23. Application Example: Electrical Connector
 The lifetimes at the three temperatures are
lognormal.
 The shape parameter is reasonably constant.
21

24. Application Example: Electrical Connector
 Acceleration relationship
From the degradation model, we can assume the
acceleration relationship as
   0  1 / T ,
where  is the lognormal scale parameter, T is the
absolute temperature, 0 and 1 are unknown
parameters.
22

25. Application Example: Electrical Connector
 Estimation of acceleration model parameters
Using Minitab (or other software), we obtain the
ML estimates:
ˆ0  14.56,  1  8373.35,   0.347.
ˆ ˆ
23

26. Application Example: Electrical Connector
 Failure Probability at the Use Temperature
The estimate of the scale parameter at 40C is
  14.56  8373.35 / 313.15  12.179.
ˆ
Then the failure probability at 15 years (131,400
hours) is
 ln(131,400)  12.179 
F (131,400)      0.129.
 0.347 
24

27. ADT with Destructive Inspections
破坏性加速退化试验
25

28. Destructive Inspections
 For some products, inspection to measure
performance characteristics must damage the
function of the test units.
 Example 1: A solder joint must be sheared or pull off to
get its strength.
 Example 2: An insulator must be broken down to
measure its dielectric strength.
 After destructive inspection, units cannot restart
with the same function as before the inspection,
and are removed from testing.
26

29. Destructive Inspections
 A unit is inspected once and generates only one
measurement.
 The performance characteristics usually are
monotonically decreasing strengths.
 The degradation analysis methods described
earlier are not applicable. Instead, the random-
process method can be used.
27

30. Test Method, Degradation Data, and
Analysis
y
S0

 
  
  

 
 
  S1
 

 
 

G   
  S2

t0 t
28

31. Application Example: Copper Wire Bond
 Problem statement
 To reduce cost, it was planned to replace gold wire
with copper wire to provide an electrical
interconnection for a new semiconductor device.
 The shear strength of wire bonds is the critical
characteristic. If it is less than 15 grams force, a bond is
said to have failed.
 We wanted to estimate the reliability of the wire bonds
after the use of 8500 cycles at a temperature profile of
–25C to 75C.
29

32. Application Example: Copper Wire Bonds
 Test plan
Sample High T Low T
Group Inspection Cycles
Size (C) (C)
A 100 125 –55 50, 100, 300, 600, 900
B 100 110 –45 100, 300, 600, 900, 1200
C 100 95 –35 300, 600, 900, 1200, 1500
30

33. 
Shear Strength (gf)
15
0
20
40
60
80
100
A50
A100
A300
A600
Shear strength data
A900
B100
B300
B600
B900
B1200
C300
C600
C900
C1200
C1500
Application Example: Copper Wire Bonds
31

34. Application Example: Copper Wire Bonds
 Lognormal fits to the strength data of group A
99
A50
95 A100
A300
90 A600
A900
80
70
60
Percent
50
40
30
20
10
5
1
5 10 20 40 60 80 120
Shear Strength
32

35. Application Example: Copper Wire Bonds
 Lognormal fits to the strength data of group B
99
B100
95 B300
B600
90 B900
B1200
80
70
60
Percent
50
40
30
20
10
5
1
10 20 40 60 80 100 120
Shear Strength
33

36. Application Example: Copper Wire Bonds
 Lognormal fits to the strength data of group C
99
C300
95 C600
C900
90 C1200
C1500
80
70
60
Percent
50
40
30
20
10
5
1
10 20 40 60 80 100 120
Shear Strength
34

37. Application Example: Copper Wire Bonds
 Plots of estimates of µy vs. log inspection cycles
for all groups
4.5
y
ˆ
4
3.5
3
Group A
2.5 Group B
Group C
2
3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
ln(t)
35

38. Application Example: Copper Wire Bonds
 Degradation model
 The effect of thermal cycling is often described by the
Coffin-Manson relationship. From the previous plots,
we have
 y  1   2 ln(t )   3 ln( T ),
where T is the temperature range.
 Multiple linear regression analysis suggests this model
is reasonable.
36

39. Application Example: Copper Wire Bonds
 Estimation of model parameters
Consider the degradation model as a two-variable
acceleration relationship, where t is also treated as
a stress. Using Minitab, we obtain
1  28.1165,  2  0.6445,  3  4.1416,  y  0.2205.
ˆ ˆ ˆ ˆ
37

40. Application Example: Copper Wire Bonds
 Reliability at the use temperature profile
 The estimate of y after 8500 cycles at the use
condition (T = 100C) is
 y  3.212
ˆ
 The reliability at 8500 cycles is
 ln(G )   y 
ˆ  ln(15)  3.2124 
R(8500 )  Pr( y  G )  1      1     0.9889

 y
ˆ 
  0.2205 
38

41. Takeaways
 ADT is more efficient than ALT, and should be
used whenever possible.
 Pseudo-lifetime method applies to nondestructive
inspections.
 Random-process method can be used for both
destructive and nondestructive inspections.
39