Advances in sensor technology have led to an increased interest in using degradation-based sensory information to predict the remaining lives of partially degraded components and systems. This paper presents a stochastic degradation modeling framework for computing and continuously updating remaining life distributions (RLDs) using in situ degradation signals acquired from individual components during their operational lives. Unfortunately, these sensory-updated RLDs cannot be characterized using parametric distributions and their moments do not exist. Such difficulties hinder the implementation of this sensor-based framework, especially from the standpoint of computational efficiency of embedded algorithms. In this paper, we identify an approximate procedure by which we can compute a conservative mean of the sensory-updated RLDs and express the mean and variance using closed-form expressions that are easy to evaluate. To accomplish this, we use the first passage time of Brownian motion with positive drift, which follows an inverse Gaussian distribution, as an approximation of the remaining life. We then show that the mean of the inverse Gaussian is a conservative lower bound of the mean remaining life using Jensens inequality. The results are validated using real-world vibration-based degradation information.