The mis-specification effects of stochastic process-based degradation models are rarely studied and mainly focus on linear models. This paper investigates two types of misspecification in inverse Gaussian (IG) processes, that is, a non-stationary IG process without random effects which is wrongly assumed to be a nonlinear Wiener process without random effects, and an IG process with a random effect which is wrongly assumed to be a simple IG process. In such situations, the distribution characteristics of quasi maximum likelihood estimation (QMLE) of the mean-time-to-failure (MTTF) are derived according to the theory of QMLE asymptotic normality. Through a case study about fatigue-crack-growth data, the effects of the corresponding model’s mis-specification on the MTTFs are compared and analyzed. The results also show that the effects of mis-specification become large under some settings of parameters, or combinations of the number of the sample size and measurements, which can be used as references to engineering applications.