This paper focuses on companies that have both a fleet to serve customers and depots for vehicle maintenance. When management of such a vehicle fleet is considered, one of the most important problems is the computation (estimation) of the reliability and the availability of the vehicles. What often makes this computation difficult is the insufficient data for statistical inference or total lack of data (such an aggravating circumstance arises, for example, whenever the fleet is renewed). Concentrating on such a case, this paper presents some analytical formulae based on the Bayesian approach to uncertainty that contribute to the solution of the problem.