The lifetime data observed from one-shot devices are all either left- or right-censored. For this reason, data analysis of one-shot device lifetimes poses a real challenge in developing efficient inferential methods. When a flexible lifetime distribution with more model parameters is considered for modeling the data, the likelihood function becomes quite complicated, with its maximization becoming a complex numerical problem. To model dependence among multiple failure modes of one-shot devices, the authors used the theory of copulas. The selection of suitable link functions to relate stress levels to specific parameters of a lifetime distribution is quite critical for accurate estimation of reliability and mean lifetime under normal operating conditions. In reliability studies, it may be often reasonable to assume that there is a nonzero origin below which no event can occur; in such situations, the Weibull distribution with an unknown location (threshold) parameter will be more suitable for the analysis.