$q$-Weibull Applied to Brazilian Hydropower Equipment

The socioeconomic development of a nation depends, among other factors, on the ability of electrical power sector growth in order to satisfy an increasing demand. The suitable level of hydropower installations system reliability requires reliable power generation and transmission systems. This paper presents a comparison between the Weibull and q-Weibull reliability models, through a practical example, and the main reliability parameters of some Brazilian hydropower equipment. The application of the models to a practical example is done with parameters estimation by using probability plotting method. R
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, Akaike information criterion, and mean squared error were calculated to verify the suitability of the model for the sample data and to compare the distributions adjustments. The maximum likelihood method was applied to determine the parameters of the q-Weibull distribution and the results were compared with those of the probability plotting method. An analysis using 3-D contour plots for the likelihood function was performed for four types of equipment. The results were analyzed by reliability and failure rate plots. The failure rate plots were grouped according to their shapes. The modeling of the failure phenomenon done by q-Weibull is closer to reality and allows better planning of maintenance and replacement policies. Hydropower data bank q-Weibull parameters have not been introduced in the literature.