Given the joint distribution of cause of failure and system lifetime of a series system in which components fail simultaneously with probability 0, it is possible (under mild regularity conditions) to assume a model for the system in which component lifetimes are independent.
"A Note on Independence of Multivariate Lifetimes in Competing Risks Models." Ann. Statist. 5 (3) 576 - 579, May, 1977. https://doi.org/10.1214/aos/1176343859