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Step-stress testing is a very common type of accelerated testing. It is a good way to obtain failures in a relatively short amount of time. There are many variations of step-stress testing. A common type is one in which the units are tested at a given stress level for a certain amount of time. At the end of that time, if there are units surviving, the stress level is increased and held for another amount of time. The data that result from such tests can be analyzed using the cumulative damage model, which computes the degradation (damage accumulated through time and through the increase of stress), in ReliaSoft's ALTA software. Click here for more information about this type of step-stress testing.
Alternatively, there are step-stress tests in which the degradation or performance data that can be directly related to the presumed failure of the product in question are monitored over the duration of the test. This test is essentially a degradation test in time-varying conditions. In this case, the "cumulative damage" (degradation) is measured over time and there is no need to use the complex cumulative damage model to estimate the reliability of the product. This article suggests an approach for using Weibull++ to estimate reliability from degradation data of a product tested using step-stress accelerated testing.
A semiconductor company is studying the reliability of Light Emitting Diodes
(LEDs) using a step-stress accelerated temperature test to estimate the
reliability at the normal conditions of
The following is the test procedure. A sample
of 15 units are tested in a temperature bath. Each unit is tested under the
designated test profile independently from the other units. The luminous
flux degradation is monitored for every unit in the test. The test's
temperature is initially set at
Because the change of temperature is decided
based on degradation, the duration of testing at a specific temperature
level might be different for every tested unit. Also, for a given test unit,
the amount of time it spends in a specific temperature level might be
different for every temperature level. The following are the test results,
showing the duration each unit spent at each temperature level before the
luminous flux dropped an additional 50 lm. The units were monitored until
the failure threshold value of 50% degradation (
To better explain the test profile, the following figures show the test profile and its corresponding luminous flux curve for one of the test units (Unit1) in a cumulative time line.
The purpose of this test is to estimate the
reliability of the LEDs at the normal continuous usage conditions of
For illustration purposes, let us assume that
the luminous flux decreases linearly over time at a certain temperature
level, L) and time (t) can be
described as follows:
where λ
is the degradation rate. Note that
other models could be considered._{i }
Table 1 can be used to estimate degradation
rate at a certain temperature value. The degradation rate,
In the studied experiment, the temperature is
changed once a drop of 50 lm has been observed, therefore
From Table 2, we obtain the following table
that uses Eqn. (2) to estimate the degradation rate, T. Note that in this case the degradation rate is a
random variable, therefore each unit's data set enables us to estimate a
possible value of degradation for a certain temperature level._{i}
We now use the Equation Fit Solver in Weibull++ to fit a model that describes the degradation rate versus
temperature. To add an Equation Fit Solver folio to a project, choose
Enter the temperature data in the
where
Note that other types of models (such as
exponential) can be used. The following shows an example using Unit 1 data.
The range of possible parameter values and initial guesses are specified in
the
The folio is now ready to
estimate the parameter of the degradation rate model. Click
A plot of the fitted model can also be
obtained by clicking the
Repeat the above procedure for all the units' data sets to obtain the degradation rate model parameters for every unit in the test.
The degradation model can
Using the Equation Fit Solver,
we can estimate the degradation rate for a certain temperature value. In the
The estimated degradation rate at
By repeating this process for all of the
tested units, the projected normal degradation rates, can be derived._{
}_{
}The following table summarizes the results.
With the degradation rate at normal condition,
the failure time for each unit can be estimated. Modifying Eqn. (1) to solve
for the failure time
Using Eqn. (3) and Table 4, the estimated
failure times for each unit had they been continuously tested under the
normal condition,
Using the data in Table 5, the reliability estimation using life data analysis becomes straightforward. The lognormal distribution and regression (RRX) are used to fit the failure data.
The reliability plot is as follows:
The reliability at t=400h of normal LEDs operation is estimated using the QCP as follows:
C. Chiao, M. Hamada, "Robust Reliabilty For
Light Emitting Diodes Using Degradation Measurements" |
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