Fitting Lifetime Data to a Weibull Model

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Reliability analysis (or survival analysis) is a branch of statistics that deals with death in biological organisms and failure in mechanical or electronics systems, which may be within a localized test time. This topic is called reliability theory or reliability analysis in engineering, and duration analysis or duration modeling in economics or sociology.


This Demonstration shows how to analyze lifetime test data from data-fitting to a Weibull distribution function plot. The data fit is on a log-log plot using a least-squares fitting method. The results are presented as Weibull distribution CDF and PDF plots.


Contributed by: Frederick Wu (March 2011)
Open content licensed under CC BY-NC-SA


The top-left table shows initial test data: is lifetime and is a simplified percentile as median rank.

The top-right graphic shows the data fit on a log-log plot with a least-squares fitting method.

The bottom-left and bottom-right graphics show the lifetime result on a CDF and PDF of a Weibull distribution plot.


[1] W. Weibull, "Fitting of Curves to Observations," Fatigue Testing and Analysis of Results, New York: Pergamon Press, 1961 pp. 201–203.

[2] B. L. Vlcek, R. C. Hendricks, E. V. Zaretsky, "Monte Carlo Simulation of Sudden Death Bearing Test," NASA Technical Memorandum, NASA/TM-2003-212506, STLE-2003-121, p. 7.


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