Accelerated Test Planning in ALTA
[Editor's Note: This article has been updated
since its original publication to reflect a more recent
version of the software interface.]
In today’s highly competitive environment, companies
are pressured to shorten their development cycles,
reduce development costs and produce highly reliable
products. Accelerated tests are a very powerful tool
in achieving these goals, providing the means to
observe failures more rapidly under higherstress
operating conditions while accurately predicting
reliability under normal operating conditions. However,
when performing an accelerated test, it is critical to do
enough preparation and planning up front, as poorly
planned accelerated tests can result in wasted time,
effort and money — and may not even yield the desired
information.
In this article, we will present the accelerated test
plan methods that are available in
ALTA and illustrate the
process of generating a test plan through an example.
Note that the math behind these plans is beyond the
scope of the article. For more details on the theory,
please refer to [1].
Introduction
ALTA provides a number of different test plans for
tests with one or two stresses. The purpose of these
plans is to determine the appropriate stress levels that
should be used for each stress type and the number of
test units that should be allocated to different stress
levels.
As with any test plan, some initial assumptions have
to be made in order to design the test. For the test
plans in ALTA, the required inputs are:
 The
lifestress relationship.
 The use stress and the highest possible stress (design
limit).
 The test duration.
 The probability of failure at the test duration under
use conditions.
 The probability of failure at the test duration under
the highest possible stress.
Plans for SingleStress Tests
The available test plans for the case of a single
stress are:
 The
2 Level Statistically Optimum Plan. The plan will
recommend two stress levels. One will be the maximum
allowable stress and the second will be computed so that
the variance of the B(X) life is minimized.
 The 3 Level Best Standard Plan. The plan will recommend
three equally spaced stress levels with equal
allocations. One stress will be the maximum allowable
stress and the other two stresses will be computed so
that the variance of the B(X) life is minimized.
 The 3 Level Best Compromise Plan. The plan will
recommend three equally spaced stress levels using the
same approach as the 3 Level Standard Plan. The
difference is that the proportion of the
units to be allocated to the middle stress level is defined
by the user.
 The 3 Level Best Equal Expected Number Failing Plan. The
plan will recommend three equally spaced stress levels
using the same approach as the 3 Level Standard Plan.
The difference is that the proportion of units allocated
to each stress level is calculated such that the number
of units expected to fail at each level is equal.
 The 3 Level 4:2:1 Allocation Plan. The plan will
recommend three equally spaced stress levels using the
same approach as the 3 Level Standard Plan. The
difference is that the allocation of test units from the
lowest to the highest stress level is a 4:2:1 ratio.
This plan also gives the option to specify a reduction
factor in order to keep the low stress level closer to
normal stress conditions.
Plans for TwoStress Tests
The available test plans for the case of two stresses
are:
 The
3 Level Optimum Plan. The plan will recommend three
stress level combinations. The proportion of units
allocated at each stress level combination is such that
the variance on the B(X) life is minimized.
 The 5 Level Best Compromise Plan. The plan will
recommend five stress level combinations. The proportion
of units allocated at each stress level combination is
such that the variance on the B(X) life is minimized.
Example
Andrew is a reliability engineer for a computer
manufacturer. He wants to plan an accelerated life test for
a new design of an electronic component. Some initial
HALT tests have indicated that temperature is the major
stress of concern. The temperature at use conditions is
300 K, while the design limit was found to be 380 K.
Looking at historical data of the previous design, he
finds that after 2 years of operation (which translates
to 6,000 hours of actual usage) approximately 1% of the
units had failed and that the beta parameter of the
Weibull distribution was 3. Given that the failure mode
of the new design is expected to be similar, Andrew
feels that this is a good approximation of the beta.
Finally, previous accelerated tests have indicated that
an acceleration factor of 30 can be achieved at
temperature levels close to the design limit.
The available resources that Andrew has at this point
are three test chambers, 100 test units and a test time of 2
months or 1,440 hours. He wants to determine
the appropriate temperature that should be set at each
test chamber and the number of units that should be
allocated at each chamber, so he decides to use the test
plans utility in ALTA.
In order to generate a test plan, he needs to
determine the probabilities of failure at the end of the
test at the usage temperature and at the design limit
temperature, something that can be accomplished in
Weibull++. The first step is to use the
Quick Parameter Estimator (QPE) tool in order to determine the eta
parameter of the Weibull distribution at the normal use
temperature, as shown in Figure 1.
Figure 1: Parameter Experimenter
Knowing that the beta parameter of the Weibull
distribution is 3 and that at 6,000 hours approximately
1% of the units will fail, he finds that the eta is
27,803 hours. Having that, he adds a standard folio in
Weibull++ and clicks the Calculate icon without
entering any data in order to define the calculated
Weibull parameters, as shown in Figure 2.
Figure
2: The parameters of the Weibull distribution at the
normal use
temperature
He can now calculate the probability of failure at
the end of the test using the Quick Calculation Pad (QCP), as
shown in Figure 3.
Figure 3: Probability of failure at the end of the test at
the normal use temperature
Next, he needs to estimate the probability of failure
at the end of the test at the design limit temperature
of 380 K. Given the fact that the acceleration factor at
that condition is expected to be 30, the eta parameter
at 380 K will be equal to the eta at usage temperature
divided by 30, or equal to 926.8 hours.
Following the same steps as before, he adds another
standard folio and enters the following Weibull
parameters.
Figure 4: The parameters of the Weibull distribution at the
design limit temperature
He then calculates the probability of failure at the end of the test at
the design limit in the QCP, as shown in Figure
5.
Figure 5: Probability of failure at the end of the test at the
design limit temperature
Having these two probabilities of failure, Andrew can
now generate a test plan. Given that he has three
test chambers available, he decides to use a 3level
plan. In this case, he generates a 3 Level Best Standard
Plan using the initial assumptions that were made, the
available resources and the calculated probabilities of
failure. Figure 6 shows the inputs for the test plan utility.
Figure 6: Test plan setup window
Note that the
Arrhenius lifestress relationship was chosen because the
stress is temperature. The BX% Life Estimate Sought is the BX life metric that the selected test
plan will attempt to minimize the variance for. In this
case, the company’s reliability requirements are in the
form of a B10 life, so Andrew has chosen a value of 10.
Figure 7 shows the output of the test plan.
Figure 7: Output of the test plan
The 3 Level Best Standard Plan has
determined that the temperatures for the three
chambers should be 349 K, 364 K and 380 K. The test units
should be allocated equally across all three chambers.
Andrew wants to compare these results with the other
test plan methods, so he follows the same steps to
generate test plans using the rest of the available 3level methods. Table 1 summarizes the results of these
test plans. Note that the expected number of failures in
the table is the probability of failure at each
temperature level multiplied by the number of units
allocated at that level.
Table 1:
Results of different 3level test plans


Best Standard Plan 
Best Compromise Plan 



349 K 
364 K 
380 K 
354 K 
367 K 
380 K 


Units on Test 
33.3333 
33.3333 
33.3333 
50.7 
20 
29.3 


Probability of Failure 
0.1032 
0.4723 
0.9765 
0.1767 
0.5743 
0.9765 


Expected Failures 
3.44 
15.7433 
32.55 
8.9587 
11.486 
28.6115 












Equal Expected Number Failing 
4:2:1 Allocation 



356 K 
368 K 
380 K 
352 K 
366 K 
380 K 


Units on Test 
62.7992 
22.6909 
14.5099 
57.1429 
28.5714 
14.2857 


Probability of Failure 
0.2256 
0.6244 
0.9765 
0.1415 
0.5307 
0.9765 


Expected Failures 
14.1675 
14.1682 
14.1689 
8.0857 
15.1628 
13.95 

Andrew sees that the temperature levels recommended by
all test plans are fairly similar and with the exception
of the Best Standard Plan, where the expected number of
failures at 349 K is low, the expected number of failures
at each temperature level is reasonable. Knowing that in
an accelerated test ideally the number of failures at
each level should be similar, he decides to use the
Equal Expected Number Failing Plan, where he expects to
observe approximately 14 failures in each chamber.
Finally, Andrew wants to evaluate his test plan.
Given a confidence level of 80% and his current sample
size of 100 units, the bounds ratio (which is the upper
confidence bound divided by the lower confidence bound)
is 3.3664, as shown in Figure 8.
Figure
8: Calculated bounds ratio
If he wanted to reduce the bounds ratio to 2 in order to
see tighter confidence bounds at the same confidence
level, his sample size should be increased from 100 test
units to 307 test units, as shown in Figure 9.
Figure
9: Calculated sample size
As with any sort of testing, the larger the sample
size, the more certain the results will be. Given the
information that Andrew has determined here, he can now
address the business decision of whether to accept these
bounds or to approach management and request more units
for testing.
References
[1]
http://ReliaWiki.org/index.php/Additional_Tools#Accelerated_Life_Test_Plans
