Gumbel mixture modelling for multiple failure data

The Gumbel mixture model is a popular tool for modeling extreme events with mixed formation mechanisms. lack of shape parameter in the distribution makes it somewhat less practical compared to Weibull distribution, which widely used structural reliability and safety applications. Since has two forms (i.e., left- right-skewed), we describe as three-parameter distribution. additional ξ ∈ { − 1 , } control skewness maximum likelihood estimation procedure proposed derived. Based on simulation study, confirmed that 1) can successfully estimate parameters model, 2) advantages over state art using different parametric families. An illustrative real-world example also considered. Climbing rope failure was observed function random variables, competing modes were found. experiment subsequent provided further insight into degradation climbing ropes. Finally, proposal implemented freely available R package rebmix. • introduced. software implementation provided. novel provides better results than models. In an failure, types offers interesting insights mechanisms failure.