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The study of lengths of the lives of organisms, devices, materials, etc., is of major importance in the [[biological]] and [[engineering]] sciences. In general, the lifetime of a device is expected to exhibit decreasing failure rate (DFR) when its behavior over time is characterized by 'work-hardening' (in engineering terms) or 'immunity' (in biological terms).
The exponential-logarithmic model, together with its various properties, are studied by Tahmasbi and Rezaei (2008).<ref name="tahmasbi2008">Tahmasbi, R., Rezaei, S., (2008), "A two-parameter lifetime distribution with decreasing failure rate", ''Computational Statistics and Data Analysis'', 52 (8), 3889-3901. {{doi|10.1016/j.csda.2007.12.002}}</ref>
This model is obtained under the concept of population heterogeneity (through the process of
compounding).
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