This paper classifies the causes of cable failures according to two types: unpredictable random causes; and predictable ageing effects. A piecewise power-law non-homogeneous Poisson process and a stochastic electro-thermal model are proposed to predict total annual failures and failures due specifically to ageing, respectively. An amalgamation of the two models is then used to estimate the number of failures attributable to random causes or ageing. The proposed method is successfully applied to real data of vintage unjacketed XLPE cables. The results show that these cables have an expected lifespan of 39 years based on ageing effects alone; however, failure of these cables is dominated by random failure modes such as manufacturing defects, sudden shock, or water and electrical tree, which cause many of these cables to fail earlier in their life.