The aim of this paper is to assist deeper understanding of the value of reliability, as it relates to the users of transport systems. The approach is theoretical, and follows the precedent of Noland & Small (1995) and Bates et al. (2001) in couching the scheduling model of Small (1982) within an objective problem of expected utility maximisation (von Neumann & Morgenstern, 1947; Savage, 1954). In contrast to these earlier works on reliability, the paper adopts a discrete representation of time; this appeals both to the context of scheduled public transport services, and implementation within Stated Preference and the Random Utility Model. The paper applies this representation to further theoretical exposition, in the following respects. The implications of Small’s utility function for travellers’ attitudes to unreliability are considered, finding that travellers would tend to exhibit risk aversion. Following from this observation, the paper considers the associated risk premium, i.e. the delay in arrival time that a risk-averse traveller would be willing-to-accept in exchange for eliminating unreliability in arrival time. The risk premium is then converted from time to money, thereby arriving at the ‘true’ value of reliability. Following from the properties of Small’s function, the theoretical analysis yields two policy implications. First, a public transport operator might feasibly increase the timetabled journey time, whilst maintaining market share, provided full reliability of service is ensured. Second, some departure times carry a value of reliability, whilst others do not.