Maintaining high efficiency of using the fleet of public mass transport vehicles puts many challenges ahead of the operator. Among them, when planning periodic operational activities, the operator should take into account the assessment of possible unexpected vehicle failures and the costs of their removal under the so-called corrective maintenance. Due to the random nature of vehicle breakdowns, knowledge about stochastic processes is necessary to maintain their efficient and safe operation. The research problem formulated in the title meets these needs. Therefore, the costs of corrective maintenance of vehicles are modelled, i.e. the costs that are not included in the scheduled maintenance costs and are not related to preventive maintenance. The costs of corrective maintenance and the costs of replacement of damaged parts are unexpectedly created at random moments of operating means of transport, usually between scheduled maintenance. Due to the variety of failure processes of individual parts of the vehicle, the methods and applications of stochastic modelling for simple failures modelled by the Poisson process are presented in this paper. The basis for the application of the presented methods is to identify those parts of the vehicle that are damaged in accordance with this process. The assessment of parameters of failure processes of individual vehicle parts is made on the basis of the operational database of a homogeneous fleet of vehicles operated for 5 years. The operational database is dynamically updated with new events. On the basis of actual data on corrective maintenance of a distinguished group of damaged parts of vehicles, the possibilities and limitations of practical applications of the Poisson process to assess the risk of incurring costs in the further process of fleet operation were shown.

The aim of this paper is to develop a quantile method of cost analysis allowing identification of the most cost-generating malfunctions occurring in a fleet of public transport vehicles. The exemplification of this method has been performed for a fleet of a specified type of trams. The idea behind the quantile method of public transport vehicle operating cost analysis is the reversing of the accumulated function of costs, for the determination of which a cost database from a given operating time of a public transport vehicle fleet has been used. The paper presents data on the malfunctions from the first five years of operation of trams in a large transport company. The assumed time of five years results from the warranty period provided by the manufacturer. The recorded number of indexes of replaced parts was 547. The group contained inoperative parts that were renewed several times.

A ratio of the thermal expansion coefficient in a liquid (or high-elastic) state α 2 to that in a glassy state α 1 could be accepted as a measure of whether the substance is in an amorphous or crystalline state. Amorphous materials are characterised by a ratio α 2 / α 1 6.24 or >5.12. However, the lower magnitude of this limit (5.12) is better founded.

All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.