Paper given at RAMS 2013 on a case study for Accelerated Testing for devices expected to withstand a two year storage period. Two accelerated life tests (ALT’s) explored two failure mechanisms of concern for a product expected to experience a 2-year storage period. Each ALT focused on a specific failure mechanism and required different applied stress. Making periodic measurements permitted the experiments to illustrate the stability of the performance of the units over the aging process. The life data analysis for each set of data also permitted the calculation of the expected reliability performance of the population after two years of storage.

1. Accelerated Testing for 2-year Storage
Fred Schenkelberg, Ops A La Carte, LLC
Key Words: accelerated testing, storage, failure mechanisms, test design
SUMMARY & CONCLUSIONS of the failure mechanism we expect increasing the temperature
will increase the rate of chemical degradation of the joint.
Two accelerated life tests (ALT’s) explored two failure
When the joint fails the functional based tests of the entire
mechanisms of concern for a product expected to experience a
assembly permit detection of the failure. The testing includes
2-year storage period. Each ALT focused on a specific failure
current draw, flow rate, and use simulation. It is unclear which
mechanism and required different applied stress.
will provide the best response related to the joint failure and
Making periodic measurements permitted the experiments
post testing failure analysis will need to confirm the failure is
to illustrate the stability of the performance of the units over
due to joint failure.
the aging process. The life data analysis for each set of data
We do not have a reasonable estimate for the reaction’s
also permitted the calculation of the expected reliability
activation energy and we will have to determine that value as
performance of the population after two years of storage.
part of the experiment. Therefore, the test approach will
1 INTRODUCTION include three stress levels in order to determine if there exists
a relationship between temperature stress and time to joint
A small mechanical medical device must function after up
failure. Since the use test is destructive (i.e. the unit is a one-
to a 2-year storage period. Like many accelerated life testing
time use device) we need sufficient samples to make the
plans, this plan must consider the expected failure mechanisms
periodic measurements. The acceleration factor for planning is
and available models.
based on a few assumptions and the actual acceleration factor
The previous product testing and experience narrow the
comes from the test results. For brevity we will focus on
expected failure mechanisms to either mechanical fatigue due
current draw only.
to Coefficient of Thermal Expansion (CTE) mismatches or
Given the testing is on complete units, the stress will also
oxidation of a critical joint within the product. Therefore, the
accelerate any other failure mechanism accelerated through
team created two ALT’s, one for thermal cycling, and one for
thermal cycling. All failures will receive a complete and
thermal exposure. The thermal cycling experienced during
thorough failure analysis to verify root cause.
storage is a the diurnal change in ambient temperature. The
oxidation of the joint adhesive does not have an adequate 1.3 Delivery plate cracking
acceleration model for use in this case; therefore the testing
The early prototypes have micro cracks within the
has to estimate the activation energy and fitting.
delivery plate. There is some evidence through environmental
This paper is a case study of the test design and test
testing that the structure propagates the crack during thermal
results. The paper discusses the use of engineering judgment
cycling. The storage conditions will experience diurnal
and appropriate statistical analysis to estimate the suitability of
temperature change as expected in a sheltered, inhabitable
the design to withstand at least two years of storage.
enclosure. It is not expected to always have environmental
1.1 Failure Mechanisms and Test Approach controls to mitigate the outdoor daily temperature swings.
In addition to the current draw and other functional
Previous work within the design team identified two
testing, it is possible to visually detect the plate cracking.
failure mechanisms of primary concern for the storage period
Excessive cracking does lead to failure and is detectable with
of the product: epoxy joint failure and delivery plate cracking.
a change in the current draw.
Both failure mechanisms led to product failure during use.
The ALT approach is to accelerate the expected daily
Other failure mechanisms are expected to occur at a lower rate
temperature change within a chamber at a faster rate than once
or probability. Past experience does not provide any basis for
per day, and slow enough to achieve the entire range of
lifetime estimates for these two failure mechanisms.
motion caused by the coefficient of thermal expansion effects.
Therefore, the team decided to conduct two ALT’s to estimate
One test cycle equals one day of storage. The acceleration
the storage life related to these specific failure mechanisms.
factor depends only how fast the test cycling occurs.
1.2 Epoxy joint failure
2 ENVIRONMENT
Based on experimentation and vendor information, a
The expected storage environment is indoor sheltered
primary means for the epoxy to fail over time is when poorly
conditions that may or may not have temperature control. In
cured or bonded material oxidizes. Given the chemical nature

2. some situations the storage temperatures may match the 3.1 Sample size life demonstration
outdoor ambient temperatures. The unit’s storage is expected
The basic test is a pass/fail (unit performance within
to be in populated areas of the world.
specifications) after a simulated 2 years of storage under
Rather than use rated limits or absolute maximum storage
cyclic stress. Equation 1 is based on the binomial distribution
temperature expectations which would only apply to a very
and assuming no failures permits the determination of the
few situations and units, we will use the 90th percentile values
sample size for a given confidence and reliability. [2]
for daily average temperature and daily average temperature
range. The National Climatic Data Center [1] has available (1)
worldwide weather station daily data readings.
where C is the type I statistical confidence 0.95,
The weather data is from 20 randomly selected weather
and, R is the reliability, 0.95.
stations with data from July 1st, 2005 to July 1st, 2010 from the
worldwide list of stations within the database. The resulting The calculation results in 58.4 which is rounded up to 59
162,000 lines of daily data readings include minimum, samples that must pass functional tests within specifications
maximum, and average temperatures. after experiencing two years of simulated cyclic stress. Using
60 samples for the test gives the test a small additional margin.
2.1 Thermal cycling conditions
3.2 Sample size stability
Calculating the difference between daily minimum and
maximum temperatures provides the daily temperature range. For the second objective of stability, we are using an
Then using the Excel percentile function to determine the 90 th additional 60 samples with ten being destructively tested at 3,
percentile temperature range to be 19°C. The average 6, 9, 12, 18, and 24 months of simulated storage. The time
temperature range is 10.9°C with a standard deviation of periods and sample sizes are per internal organization
5.8°C for the dataset. guidelines for testing stability. The intent is to evaluate the
The 90th percentile maximum temperature is 31°C and the readings at each time point and test that the slope of a fitted
th
10 percentile minimum temperature is 19.4°C. The test line to the data is not different from zero meaning it is stable.
temperature range is anchored at the maximum value and the
4 THERMAL CYCLING ALT RESULTS
chamber should operate from 31°C to 12°C
Due to thermal cycling stress representing a 2-year
2.2 Thermal exposure conditions
storage period, with 95% confidence, there is a 1.7% chance
The dataset suggests the daily 90th percentile maximum of current draw being above 68mA. Or stated another way,
temperature is 31°C. The maximum temperature is generally there is a 95% confidence of at least 98.3% reliability over a
only obtained for an hour or so per day. The temperature 2-year storage period. The units appear to be stable over the
effect on the epoxy is temperature dependent and the time at entire two-year period.
temperature is important also. Assuming an accumulated The current draw limit is 68mA during functional testing
damage model for the effects of temperature and the expected of the unit. In this paper we are not discussing the other testing
daily temperature changes, we decided to use the daily parameters used to fully evaluate the units.
average temperature rather than the maximum values. The post testing determined all units operated within
The 90th percentile daily average temperature is 24.4°C. specifications. The visual inspection of the units found only
For the expected thermal exposure we rounded this value to modest increases in crack length. The thermal cycling
25°C. The test temperature will be higher than these values to expected during storage appears to have a minor effect of
accelerate the testing. 25°C is the expected environmental product performance.
temperature we will use for the life prediction based on the
4.1 Hypothesis
test results.
We expect a drift up in current draw corresponding to the
3 THERMAL CYCLING ALT PLAN
amount of thermal cycling experienced.
The test plan has two objectives: first to demonstrate at Considering the readings are destructive each unit was
least 95% reliability with 95% confidence; and, to demonstrate measured once. Samples were drawn at random from the
stability over the two-year period. Given an unknown chamber for readings for each scheduled test point.
relationship between the temperature range and crack growth,
4.2 Analysis for stability
we decided to not increase the thermal range to achieve
additional acceleration. One test cycle equals one day in real The analysis uses test points (TP1, TP2, etc.) and hours of
time. Through experimentation we found the units come to testing interchangeablyusing the following conversion, 96
thermal equilibrium in less than 5 minutes. Therefore for hours of testing equals one month of storage time. One test
testing we set the dwell time at both extremes to 5 minutes cycle took approximate 3.2 hours due to increasing the dwell
once the chamber temperature is within 2°C of the set point. time to 30 minutes and the slow ramp rates actually achieved.
The available chamber has a ramp rate of about 3°C per The longer than planned dwell time was to insure complete
minute which will avoid thermal shock damage. thermal saturation of the units.

3. The first step is to view the data. Figure 1 provides a box include the 95% confidence bound error bars about the means.
plot view of the data over the six test points. The vertical axis If one is able to pass a horizontal line through all the error
is current (mA) and has an upper specification of 68mA. The bars, it is likely that all the TPs are reading from the same
highest value of any unit is 59.5mA within the TP4 samples. population, meaning there is no change over time due to
thermal cycling.
Next plot with linear regression fit of the measurements at
Current Draw, TP1,2,3,4,5,6 each test point. Using hours rather than TP number for the plot
to provide a continuous variable for the axis and regression,
60
see Figure 3. Test points correspond to hours and days roughly
as follows: TP1 at 288, TP2 at 551, TP3 at 837, TP4 at 1103,
TP5 at 1672, and TP6 at 2192 (all in hours).
55
50
Current Draw over 2 years thermal cycling
Current Draw (mA)
60
45
55
40
50
Current Draw (mA)
35
45
30
1 2 3 4 5 6 40
Test Points
Figure 1 Box plot of current draw results
35
30
TP Means with 95% Confidence Level error bars
500 1000 1500 2000
Hours
55
Figure 3Linear regression fit of current draw
The coefficients of the fitted line are in Table 1.
Estimate Std. t Pr(>|t|)
Current Draw (mA)
50
Error value
Intercept 48.8 1.7 28.7 <2e-16 Significant
Slope -0.0006 0.001 -0.46 0.647 Not
Significant
45
Table1Linear regression coefficients
The slope is not different than zero and therefore the units
exhibit stability over the duration of the storage period
n=10 n=10 n=10 n=10 n=10 n=15
simulation. A check of the regression residuals (plots not
TP1 TP2 TP3 TP4 TP5 TP6
shown) did not reveal any anomalies or concerns.
Test Points
4.3 Analysis for reliability
Figure 2Test point means and confidence
Fitting the data using a generalized log-linear – Weibull
Given the relative small sample size of TP1 through TP5 model with ALTA Pro software, the software uses the
there is insufficient evidence to conclude the spread (variance) likelihood function in equation 2.[3]
is different or related to time. (2)
Another way to view the data (Figure 2) is by plotting the where, t is time, directly related to number of test cycles
mean of the current draw readings within each test point and 0 and 1 are fitted parameters, where exp( 0) is the y-

4. intercept and 1 is the relationship between thermal cycles 5 THERMAL EXPOSURE ALT PLAN
and current draw.
The failure mechanism of concern related to the epoxy
Each set of data from each test point are fit to a
joint is chemical breakdown of the epoxy over time. It may be
Weibull distribution, where = 0 + 1t, and beta is the
related to a poorly formed or cured joint, yet is not
common beta value to for all test points.
immediately obvious. Prior testing has found that temperature
Using ALT Pro to perform the maximum likelihood
does seem to accelerate the failure mechanism which has been
estimator fit on the data points results shown in Table 2.
confirmed by the adhesive vendor.
Note this is a fit of the expected performance not a failure
Without a reasonable estimate of the activation energy we
distribution.
decided to run an ALT that would provide an estimate of the
activation energy. Three stresses and measuring time to failure
Lower Estimated Upper
information may provide a means to relate stress to time to
bound bound
failure.
Beta, 7.0 8.2 9.6
As with the thermal cycling, there are multiple function
Alpha(0), 0 3.88 3.94 3.99 tests that may indicate product failure. For the purpose of this
Alpha(1), 1 -4.4E-05 -6E-06 3.2E-05 paper we are only considering the current draw test. The full
set of testing is destructive to the unit.
Table2GLL-Weibull fitted parameters
5.1 Thermal Aging ALT Plan
The exp( 0) is approximately 54mA which is very near
Select 200 units at random from latest 3 builds and verify
the grand average of the data. The 1 is the slope of the
the units meet all ‘ready to ship’ requirements. Units are not in
fitted line, and is not different than zero or slope is about
protective boxes, wraps or enclosures.
zero. This indicates, as the fitted line in figure 3, there is no
Set the thermal chambers to temperature set points of
change over the storage time due to thermal cycling stress.
45°C, 52.5°C and 60°C. Place 114, 57, and 29 randomly
The GLL-Weibull model permits one to plot (figure 6)
selected units in the 40°C, 50°C, and 60°C chambers,
and calculate the reliability values for the 2-year storage
respectively. Table 3 shows the days and number to measure
period based on all the available test data.
schedule.
60°C Chamber 52.5°C 45°C Chamber
Chamber
Test Number Day Number Day Number Day
Point
Initial 29 0 57 0 114 0
1 9 2 13 4 27 8
2 3 3 10 6 20 12
3 4 6 10 12 20 24
4 4 9 10 18 20 36
5 9 10 14 20 27 40
Table3Thermal aging sample and time of reading
The samples are distributed in a 4:2:1 ratio from the
lowest to highest stress chamber deliberately to increase the
likelihood of detecting current draw changes at the lowest
Figure 42-year storage life CDF plot for thermal cycling
stress. The timing of the measurements are based on the
Using the fitted model parameters with time set to 2 assumed (some prior evidence from environmental testing)
years, we can calculate with 95% confidence that the units time to failure distribution. Previous experimentation to
have at least 98.3% reliability, based only on the current determine the rate of current draw change at 60°C provided a
draw test parameter. rough estimate of the timing to current draw degradation to
Finally, since none of the 60 samples that operated near the failure threshold as approximately a week.
over the two year simulated storage period failed any 5.2 Determination of thermal set points
performance test, the test demonstrated at least 95%
reliability with 95% confidence. The difference in the The chamber set points are set using the guidelines for
results between the models is the GLL-Weibull model is ALT design in the Meeker and Hahn monograph [4] using the
using the current draw readings to fit the data, whereas, following information:
the binomial model is using only the count of units tested. TH = 60°C, the glass transition temperature of the epoxy
is 70°C which limits the high temperature exposure.
TD = 25°C, the 90th percentile of storage temperature.

5. p = 0.05, the assumed probability of failure at the design Figure 8 shows formula 3 with the planning values. It
temperature over the 2 year storage life period. highlights the tradeoff between sample size, precision, and
pH = 0.90, the assumed probability of failure when confidence.
exposed at high test temperature over planned duration of test.
6 THERMAL EXPOSURE ALT RESULTS
pD = 0.001, the assumed probability of failure when
exposed to the nominal temperature over duration of test. The results of thermal aging of the units in the ALT
τ = 3 months, expected test duration indicate at least a 95% confidence of 99.41% reliability over
n = 200, expected total sample size available. the two year storage period. The units appear to be stable over
The Meeker and Hahn guideline assumes the units are the entire two-year period.
only measured before and after the testing period. The The current draw limit is 68mA during functional testing
guideline expects the testing to permit at least five failed units of the unit. In this paper we are not discussing the other testing
per test temperature. Given this test benefits from the parameters used to fully evaluate the units.
monotonic degradation of current draw we expect to be able to The post testing determined all units operated within
project each sample to estimate the time to failure. The specifications. The thermal aging expected during storage
guideline provides a convenient means to balance the appears to have a minor effect of product performance.
acceleration temperature range and the sample size
6.1 Hypothesis
distribution across the chambers to permit a statistically
efficient design. We expect a change in current draw corresponding to the
amount of thermal aging experienced.
5.3 Determination of sample size
Considering the readings are destructive each unit was
Formula 3 is based on the Weibull distribution and measured once. Samples were drawn at random from the
assuming at least 25% of units show failures permits the chamber for readings for each scheduled test point.
determination of the sample size for a given confidence and
6.2 Analysis for stability
precision.[5]
(3)
where, Current Draw 45°C Samples
R′ is the ratio of the compromise variance over the
optimum variance - calculated.
V is the variance factor for the optimum plan - calculated.
Kγ is the standard normal 100(1+γ)/2 percentile.
60
w is the bound about the true value (precision about true
value is +/- w)
50
40
30
20
TP0 TP1 TP2 TP3 TP4 TP5
Figure 6 Box plot of 45°C current draw results
For each of the three test temperatures, 45°C, 52.5°C and
Figure 5Sample sizegiven precision and confidence level 60°C we first plot the data in a boxplot. Figure 9has an
example boxplot showing the results for the 45°C group. The
The second element of the sample size estimate is the vertical axis is Current (mA) and the upper specification for
estimate of the Weibull distribution. Assuming the unit will current draw is 68 mA. The highest value of any unit is 67
have a probability of failure of 0.001 at 24 months. And, the mA. Given the relative small sample size per TP1 though TP5
failure rate increases over time with a slope of 1.5 (beta value there is insufficient evidence the spread (variance) is different
for Weibull distribution). This is a rough estimate based on or related to time. The boxplots for the 52.5°C and 60°C were
very limited prior experimental data. similar and no samples were outside specifications.

6. Next a plot (figure 6) with the linear regression fit of the 60 0.12
measurements at each test point. Again using testing days Table5Slopes of fitted line for each temperature
rather than TPs in order to plot and fit with a continuous
variable. Therefore, we are concluding the units exhibit stability
based on the assumed model relating test temperature
Aged at 45°C Current Draw acceleration will cover at least two years of storage at 25°C.
6.3 Analysis for reliability
The data used in ALTA Pro included three columns,
Current in mA, Age in days, and Temperature in Kelvin. Age
60
is the period of time in days the unit was within the aging
chamber. Temperature was converted from °C to K by adding
217.15.
50
The data is fit to a Temperature-NonthermalWeibull
Current
model. It uses an Arrhenius model for the effects of
temperature, and an inverse power law model for the effects of
40
time, that enables us to model the destructive measurement,
degradation accelerated life test data.
The likelihood function for the model is in equation 4.
30
(4)
Where, t is the age or time in days; T is temperature in
20
Kelvin: and, B, C, and n are the model parameters to estimate.
0 10 20 30 40 Using ALTA Pro to perform the maximum likelihood
Days estimator fit on the 219 data points (a total of 220 units tested
with one unit removed after being dropped and damaged)
Figure 7Linear regression plot of 45°C current draw provided the results shown in figure 13.
The coefficients of the fitted line are in Table 4.
Lower Estimated Upper
bound bound
Estimate Std. t Pr(>|t|)
Beta, 7.0 7.6 8.3
Error value
B -382 -35.7 311
Intercept 48.5 0.61 78.5 <2e-16
Significant
C 21.4 60.8 172
Slope 0.015 0.03 0.50 0.614
Not
Significant n -0.01 0.01 0.03
Table 4Linear regression coefficients of 45°C current draw Table 6Fitted Parameters for Temperature-
NonthermalWeibull model
The slope is not different than zero and therefore the units
exhibit stability over the duration of the exposure to 45°C. A The C parameter is the y-intercept and is approximately
check of the regression residuals (plots not shown) did not the mean value of the data, which is true. With B and n not
reveal any anomalies or concerns. different than zero (90% confidence), it indicates there is not a
Each test temperature group revealed similar results with conclusive effect of time or temperature on the performance of
not showing a significant slope. Table 5 shows the results of the units.
the three regressions. While there appears to be a relationship Using the fitted data as the best available estimate, one
between the stress and the slope, none of the fitted slopes were can use the use the natural log of the likelihood function to
statistically significantly different than zero. plot that expected life distribution at 25°C at 2-years (730
days) of use. Equation 5 has the natural log of the likelihood
function in equation 4.
Aging Temperature (°C) Slope
45 0.02 (5)
52.5 0.09 And Figure 8 has the resulting plot.

7. http://www.weibull.com/acceltestwebcontents.htm,
accessed April 3-8, 2012.
4. William Q. Meeker and Gerald J. Hahn, How to Plan an
Accelerated Life Test, ASQC, Milwaukee, WI, 1985.
5. Wayne Nelson, Accelerated Testing: Statistical Models,
Test Plans, and Data Analysis, New York, John Wiley &
Sons, 1990, p. 348.
6. Accelerated Life Testing Reference, ReliaSoft Alta Pro
software manual, etextbook,
http://www.weibull.com/acceltestwebcontents.htm,
accessed April 3-8, 2012.
BIOGRAPHY
Fred Schenkelberg
Figure 8 2-year storage life CDF plot for thermal aging 15466 Los Gatos Blvd #109-371
Los Gatos, CA, 95032, USA
Based on the fitted model and calculating the probability
of having a value above 68 mA at 25°C and 2 years results in e-mail: fms@opsalacarte.com
a value of 0.0058% or very low. The lower 95% confidence Fred Schenkelberg is a reliability engineering and
bound on this value is 0.59%, still only about a half percent management consultant with Ops A La Carte, LLC, with areas
chance of being out of spec. The test results demonstrate of focus including reliability engineering management training
TCAG (current draw) will survive 2 years of storage and accelerated life testing. Previously, he co-founded and
temperature stress with at least 99.41% reliability with 95% built the HP corporate reliability program, including
confidence. consulting on a broad range of HP products. He is a lecturer
with the University of Maryland teaching a graduate level
REFERENCES course on reliability engineering management. He earned a
Master of Science degree in statistics at Stanford University in
1. National Climatic Data Center, U.S. Department of 1996. He earned hisbachelor’s degrees in Physics at the
Commerce, as of July 6, 2012, United State Military Academy in 1983. Fredis the immediate
http://www7.ncdc.noaa.gov/CDO/cdoselect.cmd?dataseta Past-Chair of the American Society of Quality Reliability
bby=GSOD&countryabby=&georegionabby= Division, active with IEEE and IEC reliability standards
2. Gary S. Wasserman,Reliability Verification, Testing, and development teams. Fred is also the founder of the No MTBF
Analysis in Engineering Design, New York, Marcel movement and website nomtbf.com. He is a Senior Member of
Dekker, 2003, p. 209. ASQ and IEEE. He is an ASQ Certified Quality and
3. Accelerated Life Testing Reference, ReliaSoft Alta Pro Reliability Engineer.
software manual, etextbook,