Accelerated Testing Background
Accelerated Reliability Testing
Applications and Pitfalls
Reliability is a powerful marketing tool
Today's manufacturers face strong pressure to:
William Q. Meeker
Department of Statistics and
Center for Nondestructive Evaluation
Iowa State University
Ames, IA 50011
I Develop newer, higher technology products in record time.
I Improve productivity, product eld reliability, and overall
quality using new technology.
1999 Quality and Productivity Research Conference
Schenectady, NY
May 20, 1999
Much of the material in this talk has been taken from Meeker and Escobar (1998).
Implies increased need for up-front testing of materials, components and systems.
Accelerated tests provide timely information for product design and development.
Users must be aware of potential pitfalls
1
2
Overview
Dierent kinds of accelerated tests
Example 1|Evaluation of an insulating structure
Example 2|New-technology microelectronic logic device
Accelerated Life Tests versus Accelerated Degradation Tests
Importance of physics of failure and physical/chemical models
(and sensitivity analysis)
Example 3|Microelectronic RF amplier device
Other problems and pitfalls
Links with six-sigma.
Concluding remarks
Types of Accelerated Tests
Assess component or material reliability or durability.
Identify and x potential failure modes at system/subsystem
level (STRIFE TESTS).
Screening (100% or audit) testing of manufactured product
(e.g. ESS and burn-in).
System test to simulate eld-use at accelerated use-rates.
3
Breakdown Times in Minutes of a Mylar-Polyurethane
Insulating Structure (from Kalkanis and Rosso 1989)
Minutes
10
4
10
3
10
2
10
1
10
0
•••
•
•
•
•
••
•
••
•
nor
•
••
•
•
•
•
where
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•
-1
200
= 0 + 1x, and
10
150
Inverse Power Relationship-Lognormal Model
The inverse power relationship-lognormal model is
"
#
Pr[T t; volt] = log(t) ; •
••
•
•
•
•
100
4
250
300
x = log(Voltage Stress).
350 400
assumed to be constant.
kV/mm
5
6
Plot of Inverse Power Relationship-Lognormal Model
Fitted to the Mylar-Polyurethane Data (also Showing
361.4Kv Data Omitted from the ML Estimation)
Lognormal Probability Plot of the Inverse Power
Relationship-Lognormal Model Fitted to the
Mylar-Polyurethane Data
.99
10
5
10
4
.98
10
3
10
2
10
1
10
••
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•
•
.9
•
•••
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•
.8
•
•••
•
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•
Proportion Failing
Minutes
.95
•
••
••
•
90%
•
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•
•
•
•
0
-1
10
50
100
200
50%
10%
.7
.6
.5
.4
.3
.2
.1
.05
.02
219.0
.01
500
10
0
157.1
1
10
122.4
10
50 kV/mm
100.3
2
10
3
10
4
10
5
Minutes
kV/mm
7
8
Analysis of Interval ALT Data for a New-Technology
IC Device
Methods of Acceleration
Three fundamentally dierent methods of accelerating a reliability test:
Increase the use-rate of the product (e.g., test a toaster 400
times/day). Higher use rate reduces test time.
Use elevated temperature or humidity to increase rate of
failure-causing chemical/physical process.
Increase stress (e.g., voltage or pressure) to make degrading
units fail more quickly.
Use a physical/chemical (preferable) or empirical model relating degradation or lifetime at use conditions.
Tests run at 150, 175, 200, 250, and 300C.
Developers interested in estimating activation energy of the
suspected failure mode and the long-life reliability.
Failures had been found only at the two higher temperatures.
After early failures at 250 and 300C, there was some concern
that no failures would be observed at 175C before decision
time.
Thus the 200C test was started later than the others.
10
9
Lognormal New-Technology Integrated Circuit Device
ALT Data
Elevated Temperature Acceleration of
Chemical Reaction Rates
Hours
The Arrhenius model Reaction Rate, R(temp); is
10
7
10
6
10
5
10
4
10
3
10
2
R(temp) = 0 exp
;Ea
kB(temp C + 273:15)
= 0 exp
;E 11605 a
temp K
where temp K = temp C + 273:15 is temperature in degrees
Kelvin and kB = 1=11605 is Boltzmann's constant in units
of electron volts per K. The reaction activation energy, Ea,
and 0 are characteristics of the product or material being
tested.
The reaction rate Acceleration Factor is
x
x
x
100
150
200
250
AF (temp; tempU ; Ea)
x
x
x
300
=
=
350
Degrees C
11
R(temp)
R(temp
U)
exp Ea
11605
tempU K
11605
; temp
K
When temp > tempU , AF (temp; tempU ; Ea) > 1.
12
Arrhenius Plot Showing ALT Data and the
Arrhenius-Lognormal Model ML Estimation Results for
the New-Technology IC Device.
The Arrhenius-Lognormal Regression Model
The Arrhenius-lognormal regression model is
"
#
Pr[T t; temp] = log(t) ; nor
where
Hours
= 0 + 1x;
x = 11605=(temp K) = 11605=(temp C + 273:15)
and 1 = Ea is the activation energy
10
7
10
6
10
5
10
4
10
3
10
2
is constant
x
x
x
100
150
200
x
x
x
250
50%
10%
1%
300
350
Degrees C on Arrhenius scale
13
Lognormal Probability Plot Showing the
Arrhenius-Lognormal Model ML Estimation Results for
the New-Technology IC Device with Given Ea = :8
.95
.95
.9
.9
.8
.8
.7
.7
.6
.5
.4
.3
.6
.5
.4
.3
Proportion Failing
Proportion Failing
Lognormal Probability Plot Showing the
Arrhenius-Lognormal Model ML Estimation Results for
the New-Technology IC Device
14
.2
.1
.05
.2
.1
.05
.02
.02
.01
.005
.01
.005
.002
.002
.0005
.0005
300 Deg C
.0001
10
2
250
200
3
10
175
10
4
150
100
10
5
10
6
300 Deg C
.0001
10
7
10
2
250
200
3
10
175
10
Hours
4
150
100
10
5
10
6
10
7
Hours
15
16
Possible results for a typical temperature-accelerated
failure mode on an IC device
Pitfall 4: Masked Failure Mode
Masked failure modes may be the rst one to show up in the
eld.
Masked failure modes could dominate in the eld.
Hours
Accelerated test may focus on one known failure mode, masking another!
10
6
10
5
10
4
10
3
10
2
10
1
10%
40
60
80
100
120
140
Degrees C
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18
Unmasked Failure Mode with Lower Activation Energy
Hours
Pitfall 5: Faulty Comparison
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6
10
5
10
4
10
3
10%
10
2
Mode 1
It is sometimes claimed that Accelerated Testing is not useful
for predicting reliability, but is useful for comparing alternatives.
Comparisons, however, are subject to some of the same difculties.
Mode 2
Beware of comparing products then the have dierent kinds
of failures.
10%
10
1
40
60
80
100
120
140
Degrees C
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19
Comparison of Two Products II
10
6
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6
10
5
10
5
10
4
10
4
10
3
10
3
10
2
Hours
Hours
Comparison of Two Products I
Vendor 1
Vendor 1
10
10%
2
10%
Vendor 2
10%
Vendor 2
10
1
10
40
60
80
100
120
10%
1
140
40
60
80
Degrees C
100
120
140
Degrees C
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22
Percent Increase in Resistance Over Time
for Carbon-lm Resistors
(Shiomi and Yanagisawa 1979)
Some Practical Suggestions
10.0
173 Degrees C
5.0
Percent Increase
Build on previous experience with similar products and materials.
Use pilot tests
Use results from failure mode analysis.
Seek physical understanding of cause of failure.
Seek physical justication for life/stress relationships.
Limit the amount extrapolation used
Use degradation data, if possible
133 Degrees C
1.0
83 Degrees C
0.5
0
2000
4000
6000
8000
10000
Hours
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24
Advantages of Using Degradation Data
Instead of Time-to-Failure Data
Degradation is natural response for some tests.
Can be more informative than time-to-failure data.
(Reduction to failure-time data loses information)
Useful reliability inferences even with 0 failures.
More justication and credibility for extrapolation.
(Modeling closer to physics-of-failure)
1000
Hours
2000
3000
Percent Increase in Operating Current
for GaAs Lasers Tested at 80C
0
A1
"
k1
-A2
;Ea
kB (temp + 273:15)
#
25
4000
27
Arrhenius Model
Temperature Eect on Chemical Degradation
Percent Increase in Operating Current
and the rate equations for this reaction are
dA1
A2 = k A ; k > 0:
= ;k1A1 and ddt
(2)
1 1
1
dt
Solving these gives
A1(t) = A1(0) exp(;k1t)
A2(t) = A2(0) + A1(0)[1 ; exp(;k1t)]
where A1(0) and A2(0) are initial conditions. The Arrhenius
model describing the eect that temperature has on the rate
of a simple rst-order chemical reaction is
k1 = 0 exp
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Limitations of Degradation Data
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2000
237 Degrees C
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150 Degrees C
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3000
195 Degrees C
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Hours
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Degradation data may be dicult or impossible to obtain
(e.g., destructive measurements).
Obtaining degradation data may have an eect on future
product degradation (e.g., taking apart a motor to measure
wear).
Substantial measurement error can diminish the information
in degradation data.
Analyses more complicated; requires statistical methods not
yet widely available.
(Modern computing capabilities should help here)
Degradation level may not correlate well with failure.
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Device-B Power Drop
Accelerated Degradation Test Results
at 150C, 195C, and 237C
(Use conditions 80C)
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
.99
.98
.9
.95
.8
.7
.6
.5
.4
.3
.2
.1
.05
.02
.01
.005
.001
237 Degrees C
10^1
10^2
195
10^3
10^4
150 Degrees C
Hours
80 Degrees C
10^5
30
Lognormal-Arrhenius Model Fit to the Device-B
Time-to-Failure Data with Degradation Model
Estimates
Power drop in dB
Proportion Failing
15
10
5
0
Strife Test
Degrees C
20
40
x
x
x
x
x
0
x
-20
Most accelerated tests are run under carefully controlled, usually constant, conditions.
Prediction of life in environments (e.g., eects of outside
weathering) is complicated.
For example, manufacturers of paints and coatings still rely
on outdoor testing.
Substituting \average" conditions into simple acceleration
modes can give misleading results in predicted spread and
location.
There is some hope of using kinetics cumulative damage
models to make useful predictions.
60
Pitfall 8: Predictions of Variable Environments
is Complicated
0
50
100
150
Hours
200
31
Eect of Component Drift Over Time
3- process
250
32
Eect of Component Drift Over Time
6- process
LSL ->
<- USL
33
34
Planning Accelerated Tests
Relationship to 6--Type Strategy
Measure critical (failure-related) reliability variables at time
0 and over time.
Analyze causes of failure, sources of variability (identify important ones), and eect of critical reliability variables on
failure.
Improve by using designed experiments, searching for robust
design options, degradation reduction alternatives, strengthening critical components, etc.
Control manufacturing processes to maintain reduced variability.
35
Limit, as much as possible the amount of extrapolation used.
In accelerated life tests (failure time is response) allocate
more test units to low acceleration factor level than high
acceleration factor levels.
Consider including some tests at the use conditions.
Use simulation to investigate properties of alternative ALT
plans.
36
Concluding Remarks
Simulation of a
Proposed Accelerated Life Test Plan
Temp= 78,98,120 n= 155,60,84
centime= 183,183,183 parameters= -16.7330, 0.7265, 0.6000
5
10
4
10
3
10
2
10
1
Days
10
10
Log time quantiles at 50 Degrees C
Average( 0.1 quantile)= 8.014 SD( 0.1 quantile)= 0.4632
Average( 0.5 quantile)= 9.138 SD( 0.5 quantile)= 0.5116
Average(Ea)= 0.7266 SD(Ea)= 0.08594
10%
0
Results based on 500 simulations
Lines shown for 50 simulations
40
60
80
100
120
140
160
Degrees C
Accelerated Testing can be valuable tool when used carefully
There is no magic in Accelerated Testing
Cross-disciplinary teams are needed to deal eectively with
all issues
I Product/reliability/design engineers to identify productuse proles, environmental considerations, potential failure modes or weaknesses that need to be evaluated, etc.
I Experts in materials and the chemistry/physics of failure
to help in the understanding of an suggest/develop appropriate models for acceleration of particular failure modes.
I Statisticians to help with stochastic modeling, plan tests,
t models, and to help quantify uncertainty in results.
Users of Accelerated Testing must beware of pitfalls and land
mines
38
37
References
References
D. Byrne, J. Quinlan, Robust function for attaining high reliability at low cost, 1993 Proceedings Annual Reliability and
Maintainability Symposium, 1993, pp 183-191.
L. W. Condra, Reliability Improvement with Design of Experiments, 1993, New York: Marcel Dekker, Inc.
M. Hamada, Using statistically designed experiments to improve reliability and to achieve robust reliability, IEEE Transactions on Reliability R-44, 1995 June.
M. Hamada, Analysis of experiments for reliability improvement and robust reliability, in Recent Advances in Life-Testing
and Reliability, 1995, N. Balakrishnan, editor, Boca Raton:
CRC Press.
Meeker, W.Q. and Hamada, M. (1995), Statistical Tools
for the Rapid Development & Evaluation of High-Reliability
Products, IEEE Transactions on Reliability R-44, 187-198.
39
Meeker, W.Q. and Escobar, L.A. (1998a), Statistical Methods for Reliability Data. John Wiley and Sons, Inc.
Meeker, W.Q. and Escobar, L.A. (1998b), Pitfalls of Accelerated Testing. , IEEE Transactions on Reliability R-47,
114-118.
W. Nelson, Accelerated Testing: Statistical Models, Test
Plans, and Data Analyses, 1990, New York: John Wiley &
Sons, Inc.
G. Taguchi, System of Experimental Design, 1987; White
Plains, NY: Unipub/Kraus International Publications.
T. S. Tseng, M. Hamada, C. H. Chiao, (1995), Using degradation data from a factorial experiment to improve uorescent lamp reliability, Journal of Quality Technology, 363-369.
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