Many stochastic models of equipment deterioration have been proposed based on the physics of failure and the characteristics of the operating environment. The fundamental theme of these models is that they are derived by describing the underlying failure-causing mechanisms, such as degradation and wear, using suitable stochastic processes. The formulation and analysis of these stochastic deterioration models are critical to the development of a unified theory of predictive maintenance. These models lead to time to failure and residual life distributions that are quite complex mathematically. The objective of our study is to investigate the potential for approximating the time to first failure distributions resulting from stochastic deterioration models with traditional time to failure distributions (e.g., the Weibull). We first constructed a discrete-event simulation model that mimics the stochastic deterioration and failure of the system of interest: a single-unit system subject to a random operating environment such that its instantaneous rate of degradation depends on the state of the environment. The state of the environment is modeled as a continuous-time Markov Chain. A methodology is then defined for fitting a traditional time to failure distribution to the simulated data. A large numerical experiment is used to evaluate the quality of this fit under a wide range of system parameters. The goodness-fit tests results show that a truncated, three-parameter Weibull distribution is a reasonable estimate for the case described in the paper.