Looking at a Single Constant Stress Accelerated Life Test

To understand the process involved with extrapolating from overstress test data to use level conditions, let's look closely at a simple accelerated life test. For simplicity we will assume that the product was tested under a single stress at a single constant stress level. We will further assume that times-to-failure data have been obtained at this stress level. The times-to-failure at this stress level can then be easily analyzed using an underlying life distribution. A pdf of the times-to-failure of the product can be obtained at that single stress level using traditional approaches. This pdf, the overstress pdf, can likewise be used to make predictions and estimates of life measures of interest at that particular stress level. The objective in an accelerated life test, however, is not to obtain predictions and estimates at the particular elevated stress level at which the units were tested, but to obtain these measures at another stress level, the use stress level.

To accomplish this objective, we must devise a method to traverse the path from the overstress pdf to extrapolate a use level pdf.

Figure 1 illustrates a typical behavior of the pdf at the high stress (or overstress level) and the pdf at the use stress level. To further simplify the scenario, let's assume that the pdf for the product at any stress level can be described by a single point. Figure 2 illustrates such a simplification. In Figure 2, we need to determine a way to project (or map) this single point from the high stress to the use stress.

Fig. 1: pdf at different stress levels.

Fig. 2: Projecting a single point from the high stress to the use stress.

Obviously, there are infinite ways to map a particular point from the high stress level to the use stress level. We will assume that there is some model (or a function) that maps our point from the high stress level to the use stress level. This model or function can be described mathematically and can be as simple as the equation for a line. Figure 3 demonstrates some simple models or relationships.

Fig. 3: Example of two simple life-stress relationships

Even when a model is assumed (i.e. linear, exponential, etc.), the mapping possibilities are still infinite since they depend on the parameters of the chosen model or relationship. For example, a simple linear model would generate different mappings for each slope value because we can draw an infinite number of lines through a point. If we tested specimens of our product at two different stress levels, we could begin to fit the model to the data. Obviously, the more points we have, the better off we are in correctly mapping this particular point or fitting the model to our data.

Fig. 4: Testing at two (or more) higher stress levels allows us to begin to fit the model.

Figure 4 illustrates that you need a minimum of two higher stress levels to properly map the function to a use stress level.

This subchapter includes the following topic:

Life Distribution and Life-Stress Models

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