Weibullness test and parameter estimation of the three-parameter Weibull model using the sample correlation coefficient

Chanseok Park

Abstract


In reliability engineering, the Weibull distribution is one of the most widely used distributions for modelling lifetime data. Often when analyzing experimental data, it is important to determine whether the underlying distribution is Weibull. To this end, the Weibull plot is often recommended for visually assessing whether the underlying distribution is Weibull or not. Unfortunately, this visual assessment is subjective.

In this paper, using the sample correlation coefficient from the Weibull plot, we propose a method for objectively assessing the goodness of fit of the Weibull distribution by using a formal hypothesis test. In order to construct a critical region for the proposed hypothesis test for Weibullness, one needs the distribution of the sample correlation coefficient from the Weibull plot. However, it is impossible or extremely difficult to obtain the explicit distribution of the sample correlation coefficient. Extensive Monte Carlo simulations are carried out to obtain the empirical distribution of the sample correlation coefficient and the critical values. These critical values can then be used to construct a critical region for the proposed hypothesis test for Weibullness. Illustrative examples with real data sets are provided.


Keywords


Weibull distribution, Sample correlation, Weibull plot, Weibullness

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