## 1 Introduction  
The availability of the transport system in general depends on the reliability and serviceability of vehicles and the conditions of their use, as well as the quality of the technical service [1; 2; 3].  
\[AT=f\left(R_{v},M_{v},K,O_{ZM}\right) \tag{1}\]  
where \(AT\)--vehicle availability, \(R_{v}\)--vehicle reliability, \(M_{v}\)--vehicle serviceability, \(K\)--operating conditions, \(O_{ZM}\)--quality of technical services and repairs.  
The concept of availability is often used in rapid response systems when the moments of launching operational tasks are sudden (unplanned), e.g., in the air force, ambulance services or the fire brigade [4; 5; 6; 7; 8]. In recent years, the concept of using the availability criterion has gained wide recognition also in the management of public transport companies. In general, companies want to reduce costs while guaranteeing business continuity. According to Formula (1), an increase in the availability of the transport system can be ensured by:  
* using vehicles with higher reliability;
* maintaining proper standards of operation;
* improving organizational procedures and staff competences as well as technology of technical maintenance and repairs of the vehicle fleet.  
The analysis of methods to improve the availability of transport systems has been the subject of many scientific studies. The paper [9] presents various methods of estimating the relationship between the quality of transport services and selected quality factors, including the availability of the transport service, effectiveness of the offer information, the timeliness of the services, and customer service standards.  
In the works [10; 11], the problem of the relationship between the vehicle availability and maintenance costs was analyzed. The model of optimal inspections and technical service strategy, from the point of view of costs, was presented. Knowing the costs of operation, the operator can control those costs, and thus financial risk decreases, connected with planned and preventive as well as forced maintenance of vehicles, significantly limiting the risk of fleet availability and decreasing the risk related to safety of transport activities [12; 13]. The papers [14; 15] conducted analyses on the impact of bus reliability and the shift system of service operation on increasing the availability and reducing the costs of maintaining the transport system. The works [16; 17] present a model of urban transport enterprise management, taking into account the design of travel routes and the selection of transport means and timetables. In the papers [18; 19], the authors proposed the use of the semi-Markov model in relation to the selected example of public bus transport. The work [20] presents a method of continuous identification of the technical condition of city bus engines as the basis for optimizing the maintenance process.  
The papers [21; 22; 23; 24] describe the use of the availability index to improve city bus timetables and to monitor and maintain the punctuality of trips. The method of increasing the availability of the transport system by improving the efficiency of the repair subsystem is described by [25]. A queuing model with delayed repair and two maintenance phases was proposed. On the basis of this, the size of the queue of the vehicles waiting for repair was optimized. In the conclusion, it was emphasized that rationalizing the organization of the service process creates, in the long run, great opportunities to minimize the costs of maintaining high fleet availability.  
Guided by those assumptions, we undertook a study of the availability of buses during 12 years of their operation at a selected municipal transport company. The observations covered the operation process of 162 buses of 7 makes and model. The objective of the research was to analyze the relationship between availability and the category (type) of bus downtime and the time of their operation. This article is an extension of the previous studies presented by the authors in the papers [26; 27; 28; 29].