Random vector approach to the calculation of the number of railway vehicles to hold in reserve

Abstract

The goal of every public transport operator is to not only provide high-quality service, but also to minimize investment and operating costs. A significant proportion of the costs are associated with the acquisition, operation and maintenance of reserve vehicles. If the number of vehicles held in reserve is too high, an operator will incur economic losses because vehicles are underused. Conversely, if the number of reserve vehicles is too low, the quality of service will be reduced due to disruptions in the timetable. To determine the number of vehicles to hold in reserve, a coefficient of availability is commonly used. The coefficient of availability is determined by two parameters: reliability and maintainability. Both parameters have the same physical dimensions, the mean time between failures (MTBF) and mean time to repair, and they are expressed in hours. Vehicle wear, which results during the emergence of failures, is not very dependent on the time of operation but is strongly dependent on the distance travelled. It is therefore appropriate to use mean distance between failures (MDBF) instead of MTBF, because it better describes the reliability of vehicles. Using MDBF, however, means that the coefficient of availability is not considered, because MDBF and MTTR have different physical dimensions. This problem is solved by using a random vector that makes it is possible to determine the number of vehicles to hold in reserve based on the distance travelled and maintenance time. This original approach allows the acquisition of better and more authentic data necessary for an operator's decision-making process. Therefore, the number of required reserve vehicles can be much better planned. Ultimately, this positively affects the quality of services and also the investment and operating costs of the operator.

Application of hardware reliability calculation procedures according to ISO 26262 standard

“…As the detected and the undetected multiple failures are mutually disjoint phenomena, it is possible to sum up the partial probability of failures, and the resulting failure probability F AVG,M is given by Equations (12) and (13).…”

“…Also, the utilization of random vector as a very suitable computational method for functional safety assessment is possible. 13 The utilization of FTA analysis leads to relatively simple computational formulas and simplifies the procedures required to perform a qualitative analysis of the assessed system. Especially in the early stages of hardware development, the simplicity of calculation is desirable, when frequent changes in hardware design and consequently changes in calculation will be expected.…”

The contribution to the modal analysis of the control system

“…where E k is the kinetic energy; E p is position energy; θ is the generalized coordinate (the angle of the rocker arm); generalized angular velocity and t is time, [17][18][19].…”