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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.

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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.

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

Details

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.

References:

[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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