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A Weibull-Exponential Distribution Hypothesis and Derivative Fitting Method: A Case Study on Accelerated Life Data Statistics

Wang Li, Wan Bo


This paper improved the point estimate of characteristic life at the normal stress and enhanced the estimate precision based on the relationship lemma between Weibull distribution and exponential distribution. The derivative fitting method and extrapolation method based on gray theory was used in the fitting and extrapolation of the accelerated model, to fit the test data and the model derivative and describe the development trend of the model curve well, and to make the extrapolation result more reasonable than the direct extrapolation. The method also improved the precision of reliability assessment. An example of the mechanical and electrical product’s constant-stress accelerated life test was given and proved that the proposed approach is accuracy. The method should be valuable for implement of engineering.


Weibull Distribution; Exponential Distribution; Derivative Fitting; Statistics; Hypothesis.

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