Time to Failure Behavior under a Stochastic Deterioration Model

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.