Mean residual life (MRL) is important in reliability studies; it provides the engineer with an idea of how long a device of any particular age can be expected to survive. Components and systems are frequently characterized as having increasing or decreasing MRL. Over the past 10-15 years, several authors have discussed MRL for components or systems whose lifetimes are measured in discrete units (number of trials until failure). This paper establishes some simple bounds for residual life when the device has a monotonic hazard rate sequence (either increasing or decreasing) and provides examples. MRL is obtained in closed form for a particular family of decreasing failure-rate models.