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 Weibull++'s Accelerated Life Testing module.
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 T_{N}= 200K. For LEDs, failure has traditionally been defined in terms of the amount of degradation in luminosity or luminous flux (in lumens per radiated watt). For this particular LED product, the industry defines failure as 50% degradation from the original luminous flux of 700 lm.
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 T_{1 }= 300K and is then increased by 50K for every 50 lm drop in luminous flux.
The purpose of this test is to estimate the reliability of the LEDs at the normal continuous usage conditions of T_{N}=200K.
For illustration purposes, let us assume that the luminous flux decreases linearly over time at a certain temperature level, T_{i} (Chiao, Hamada, 1996). Therefore, the relationship between luminous flux (L) and time (t) can be described as follows:
Eqn. (1)
where L_{0 }= 700 lm is the initial luminous flux and λ_{i }is the degradation rate. Note that other models could be considered.
Table 1 can be used to estimate degradation rate at a certain temperature value. The degradation rate, λ_{i}, can be estimated by calculating the drop of luminous flux over a certain change of time. Therefore:
Eqn. (2)
In the studied experiment, the temperature is changed once a drop of 50 lm has been observed, thereforeΔLi = 50 lm consistently.
From Table 2, we obtain the following table that uses Eqn. (2) to estimate the degradation rate, λ_{i}, at a certain temperature level, T_{i}. 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.
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 Home > Insert > Equation Fit Solver.
Enter the temperature data in the X column and the degradation rate data in the Y column. Create an equation that defines degradation rate versus temperature by entering the equation in the Formula field and giving it a name. The assumed equation shape is a linear shape (i.e., degradation rate vs. temperature is considered to be a linear relation):
where T_{i} is temperature level.
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 Function Parameters area.
The degradation model can help in understanding what the degradation rate would be if a unit were tested under normal conditions of T_{N}= 200K.
Using the Equation Fit Solver, we can estimate the degradation rate for a certain temperature value. In the Calculate Y given X section, enter the X=200 value and click
to obtain the estimated degradation rate value for TN= 200K.
Eqn. (3)
Using Eqn. (3) and Table 4, the estimated failure times for each unit had they been continuously tested under the normal condition, TN, are: