The Ornstein-Uhlenbeck-process, a stochastic process describing a particle in a harmonic potential subject to thermal noise, finds application in many different areas of research. We use simple and coupled Ornstein-Uhlenbeck processes to model lifetimes of cellular junctions in biological tissue to understand how mechanical properties such as elasticity of a tissue depend on external parameters. Therefore, we studied the first-passage-time-problem of the Ornstein Uhlenbeck process, i.e. the probability distribution of the time it takes the particle to travel from A to B, in the limit of small distances. We apply different analytical methods to show that the probability distribution is governed by one dimensionless parameter that interpolates between two different regimes (spring-driven, noise-driven) and validate this finding with numerical simulations. We then discuss exact and effective models for non-harmonic and coupled systems and difficulties that arise in each case.