Analysis of Light Utility Vehicle Readiness in Military Transportation Systems Using Markov and Semi-Markov Processes

Abstract

This paper presents the issues of modeling the operation process of light utility vehicles operating in military transport systems. The required condition for the effective operation of the system is to maintain the means of transport at the appropriate level of technical readiness. For this purpose, it is necessary to equip the technical system with appropriate resources enabling the efficient implementation of fuel refilling, maintenance and repair processes. Each failure of the means of transport causes a significant reduction in transport capacity, which then results in the inability to perform the planned tasks. Quality control and vehicle operation process management require advanced mathematical methods and tools. Three indicators have been proposed as quantitative characteristics for assessing and optimizing the availability of military vehicles: functional readiness, technical efficiency and airworthiness. To determine their value, a stochastic exploitation model was developed based on the application of the theory of Markov processes. Based on the collected empirical data, a nine-state phase space of the studied process was identified. Operating states were distinguished relating to the implementation of the transport task, refueling, parking in the garage, as well as maintenance and repairs. As part of the considerations for the continuous time, verification of the distributions of time characteristics led to the development of a semi-Markov model. The ergodic probabilities calculated based on the conditional probability matrix of interstate transitions and the expected values of the time spent in the states were used to determine the indicators of functional availability, efficiency and technical suitability. In order to determine the possibility of optimizing the process, a sensitivity analysis was performed. Reducing the amount of time the vehicles must wait for repair by about 50% can improve the values of the indexes from 0.91 to 0.95.

Semi-Markov approach for reliability modelling of light utility vehicles

“…At any time t, an object is only in one of the states identified within the phase space S = X(t). This assumption requires a precise identification of all possible operational states in which vehicles may remain during the operation process [33]. Stochastic processes that satisfy the Markov property are important in terms of applicability.…”

“…Therefore, the authors of this paper developed a specialized semi-Markov model to analyse the reliability of light utility vehicles. Based on assumptions adopted in military technical systems and the 9-state model [33] developed for a detailed analysis of vehicle readiness. The phase space aggregation was carried out in 3 main operational states.…”

“…Markov models assume exponential distributions of transition times between individual states within the phase space, which significantly narrows down their applicability when modelling reliability. Furthermore, their use without verifying the adopted assumptions may lead to significant errors in the obtained results [33,48]. Semi-Markov models are a solution to this problem.…”

“…In turn, the variable Tij determines the sojourn time in the Si state before the direct transition to the Sj state. If at time t = 0, the object is in the state Si ∊ A', then the sum of the times Tij until the transition to the state Sk ∊ A is equal to the value of ΘA, as described by the formula (33):…”

“…The duration during which these vehicles remain in these states is strictly correlated with the capacities of a technical subsystem that supports the transport system and the effectiveness of logistics processes associated with the supply chain of consumables and spare parts. In the case of many technical systems, due to the unavailability of fast and flexible material requirements, the unsuitability time of faulty means of transport constitutes a significant factor reducing the values of readiness indices [33].…”