This paper deals with reliability analysis of transformer using stochastic or random process through supplementary variable technique (SVT) and neural network approach. The failure of the considered complex system can occur due to the failure of breakdown voltage (BDV) and moisture content (MC) of insulating paper and oil. The repair rates for both insulation oil and insulation paper are presumed to be general, whereas for insulation, oil repair rates are exponentially distributed. Further, whenever there are two possibilities of repairs, it has been coupled using Gumbel–Hougaard copula. All types of failures and repair rates are treated as weights while analyzing with the help of neural network approach which are governed by exponential distribution. System state probabilities, up and down states probabilities and reliability are evaluated for the proposed model by using Markovian process with the help of Laplace transforms. Numerical examples are included to illustrate the results.