Analysis Method

With our current understanding of the principles behind accelerated life testing analysis, we will continue with a discussion of the steps involved in analyzing life data collected from accelerated life tests like those described in the Quantitative Accelerated Life Tests section.

Select a Life Distribution

The first step in performing an accelerated life data analysis is to choose an appropriate life distribution. Although it is rarely appropriate, the exponential distribution has in the past been widely used as the underlying life distribution because of its simplicity. The Weibull and lognormal distributions, which require more involved calculations, are more appropriate for most uses. The underlying life distributions available in ALTA are presented in detail in the Life Distributions chapter of this reference.

Select a Life-Stress Relationship

After you have selected an underlying life distribution appropriate to your data, the second step is to select (or create) a model that describes a characteristic point or a life characteristic of the distribution from one stress level to another.

Fig. 7: Selecting a model.

The life characteristic can be any life measure such as the mean, median, R(x), F(x), etc. This life characteristic is expressed as a function of stress. Depending on the assumed underlying life distribution, different life characteristic are considered. Typical life characteristics for some distributions are shown in the next table.

*Usually assumed constant

For example, when considering the Weibull distribution, the scale parameter, η, is chosen to be the life characteristic that is stress dependent, while β is assumed to remain constant across different stress levels. A life-stress relationship is then assigned to η. Eight common life-stress models are presented later in this reference. Click a topic to go directly to that page.

Parameter Estimation

Once you have selected an underlying life distribution and life-stress relationship model to fit your accelerated test data, the next step is to select a method by which to perform parameter estimation. Simply put, parameter estimation involves fitting a model to the data and solving for the parameters that describe that model. In our case, the model is a combination of the life distribution and the life-stress relationship (model). The task of parameter estimation can vary from trivial (with ample data, a single constant stress, a simple distribution and simple model) to impossible. Available methods for estimating the parameters of a model include the graphical method, the least squares method and the maximum likelihood estimation method. Parameter estimation methods are presented in detail in Appendix B: Parameter Estimation of this reference. Greater emphasis will be given to the MLE method because it provides a more robust solution, and is the one employed in ALTA.

Derive Reliability Information

Once the parameters of the underlying life distribution and life-stress relationship have been estimated, a variety of reliability information about the product can be derived such as:

Warranty time.
The instantaneous failure rate, which indicates the number of failures occurring per unit time.
The mean life which provides a measure of the average time of operation to failure.
B(X) life, which is the time by which X% of the units will fail.

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