Reliability modelling on two-dimensional life data using bivariate weibull distribution: with case study of truck in mines

Abstract

An engineering system can exhibit two- or multi-dimensions in its lifetime. As the classical univariate distribution cannot model this multi-dimensional characteristic, it is necessary to extend it to multivariate distribution in order to capture the multi-dimensional characteristics. This paper proposes a bivariate Weibull distribution that combines two classical Weibull models by a common exponent. The common exponent can represent the correlation between the two dimensions. A ratio likelihood test is proposed to test the significance of the correlation between the two dimensions. To solve the parameter estimation problem, this paper suggests a Bayesian method. Moreover, a goodness of fit test method is developed to visually check the fitness of the model. A case study considering mining trucks is presented to apply the bivariate Weibull distribution to model the two-dimensional life data.