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It is not rare for engineering systems exhibiting binaryor even multi-dimensional lifetimes. The life of an airplane can be described by both calendar time and the total flight hours; the life of rail track life can be described according to both age and the total gross load it has carried [2], while an automobile’s usage also corresponds with calendar time and distance travelled [12]. Binary-dimensional or multi-dimensional failure times are also practical when a system comprises several dependent components. For example, for the railway bogie, the failures of a wheel, an axle or a spring are essentially dependent on each other. The reliability of the bogie should address the dependency of the load, torque or other mechanic measurement on each other. Each measurement is a dimension corresponding to the lifetime. Multi-dimensional distribution is also practical when a system has multiple dependent failure modes. Each failure mode corresponds one dimension in the lifetime. Classic life-data analysis in reliability considers only one dimension [4, 24, 26, 28]. A typical example is Weibull analysis, which considers time as the sole variate. The covariate-based model, such as the Proportional Hazard Model (PHM), can accommodate multi-dimensional variates to some extend [3, 7, 14, 15]. The main dimension, usually calendar time, is in the baseline function. The other dimensions are accommodated in the covariate function. However, covariates are not one dimension of the distribution. The PHM is essentially a one-dimensional model. It is thus necessary to develop multivariate lifetime distribution model, applicable for reliability analysis. In the desired multi-dimensional model, each dimension of the lifetime is considered equal, instead of as covariate as in the PHM model. In order to apply the model to reliability analysis, the corresponding parameter estimation and goodness of fit test method should also be proposed. This paper is organized as follows: Section 2 presents the literature survey and discusses some properties of the bivariate Weibull model concerned with reliability. Section 3 presents the methods for parameter estimation and the reliability evaluation, while Section 4 discusses the case of the mining transportation truck and the application of the Bivariate Weibull model to the case. Finally, Section 5 presents the discussion and conclusion of the paper. Yuan Fuqing Abbas BArABAdi Lu Jinmei

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