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Semi-Markov approach for reliability modelling of light utility vehicles
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Institute of Mechanics & Computational Engineering, Military University of Technology, Faculty of Mechanical Engineering, Poland
Submission date: 2023-01-19
Final revision date: 2023-02-07
Acceptance date: 2023-03-03
Online publication date: 2023-03-05
Publication date: 2023-03-05
Corresponding author
Jerzy Małachowski   

Institute of Mechanics & Computational Engineering, Military University of Technology, Faculty of Mechanical Engineering, 2 Gen. Sylwestra Kaliskiego Street, 00-908, Warsaw, Poland
Eksploatacja i Niezawodność – Maintenance and Reliability 2023;25(2):161859
Vehicles are important elements of military transport systems. Semi-Markov processes, owing to the generic assumption form, are a useful tool for modelling the operation process of numerous technical objects and systems. The suggested approach is an extension of existing stochastic methods employed for a wide spectrum of technical objects; however, research on light utility vehicles complements the subject gap in the scientific literature. This research paper discusses a 3-state semi-Markov model implemented for the purposes of developing reliability analyses. Based on an empirical course of the operation process, model was validated in terms of determining the conditional probabilities of interstate transitions for an embedded Markov chain, as well as parameters of time distribution functions. The Laplace transform was used to determine the reliability function, failure probability density function, failure intensity, and expected time to failure. Readiness index values were calculated based on ergodic probabilities.
Alkaff A, Qomarudin M N, Purwantini E, Wiratno S E. Dynamic reliability modeling for general standby systems. Computers & Industrial Engineering 2021; 161: 1–21,
Bai B, Zhang J, Wu X et al. Reliability prediction-based improved dynamic weight particle swarm optimization and back propagation neural network in engineering systems. Expert Systems with Applications 2021; 177: 1–13,
Barbu V S, D’Amico G, Gkelsinis T. Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems. Mathematics 2021; 9(16): 1997,
Blasi A, Janssen J, Manca R. Numerical Treatment of Homogeneous and Non-homogeneous Semi-Markov Reliability Models. Communications in Statistics - Theory and Methods 2004; 33(3): 697–714,
Borucka A, Niewczas A, Hasilova K. Forecasting the readiness of special vehicles using the semi-Markov model. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2019; 21(4): 662–669,
Brayer E F. Calculating the Standard Error of a Proportion. Applied Statistics 1957; 6(1): 67–68,
Chang K-H. A novel reliability allocation approach using the OWA tree and soft set. Annals of Operations Research 2016; 244(1): 3–22,
Chryssaphinou O, Limnios N, Malefaki S. Multi-State Reliability Systems Under Discrete Time Semi-Markovian Hypothesis. IEEE Transactions on Reliability 2011; 60(1): 80–87,
D’Amico G. Single-use reliability computation of a semi-Markovian system. Applications of Mathematics 2014; 59(5): 571–588,
Dobrzinskij N, Fedaravicius A, Pilkauskas K, Slizys E. Impact of climatic conditions on the parameters of failure flow of military vehicles. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 2021; 236(4): 753–762,
Du Y, Wu G, Tang Y, Liu S. A two-stage reliability allocation method for remanufactured machine tools integrating neural networks and remanufacturing coefficient. Computers & Industrial Engineering 2022; 163: 1–12,
Fang L, Tarasiuk T, Xia J, Xu X-Y. Reliability assessment of the port power system based on integrated energy hybrid system. Bulletin of the Polish Academy of Sciences: Technical Sciences 2022; 70(2): e140372.
Grabski F. Semi-Markov failure rates processes. Applied Mathematics and Computation 2011; 217(24): 9956–9965,
Guo J, Wilson A G. Bayesian Methods for Estimating System Reliability Using Heterogeneous Multilevel Information. Technometrics 2013; 55(4): 461–472,
Gurland J, Tripathi R C. A Simple Approximation for Unbiased Estimation of the Standard Deviation. The American Statistician 1971; 25(4): 30–32,
Hao S, Yang J, Ma X, Zhao Y. Reliability modeling for mutually dependent competing failure processes due to degradation and random shocks. Applied Mathematical Modelling 2017; 51: 232–249,
Hong L, Zhai Q, Wang X, Ye Z-S. System Reliability Evaluation Under Dynamic Operating Conditions. IEEE Transactions on Reliability 2019; 68(3): 800–809,
Hu J, Shen J, Shen L. Periodic preventive maintenance planning for systems working under a Markovian operating condition. Computers & Industrial Engineering 2020; 142: 106291,
Ivanchenko O, Kharchenko V, Moroz B et al. Semi-Markov availability model considering deliberate malicious impacts on an Infrastructure-as-a-Service Cloud. 2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET), 2018: 570–573,
Iversen E B, Morales J M, Madsen H. Optimal charging of an electric vehicle using a Markov decision process. Applied Energy 2014; 123: 1–12,
Karakaya E, Vinel A, Smith A E. Relocations in container depots for different handling equipment types: Markov models. Computers & Industrial Engineering 2021; 157: 1–18,
Kou L, Chu B, Chen Y, Qin Y. An Automatic Partition Time-Varying Markov Model for Reliability Evaluation. Applied Sciences 2022; 12(12): 5933,
Li X, Zhao X, Pu W. Knowledge-oriented modeling for influencing factors of battle damage in military industrial logistics: An integrated method. Defence Technology 2020; 16(3): 571–587,
Liu P, Wang G. Optimal periodic preventive maintenance policies for systems subject to shocks. Applied Mathematical Modelling 2021; 93: 101–114,
Lolas S, Olatunbosun O A. Prediction of vehicle reliability performance using artificial neural networks. Expert Systems with Applications 2008; 34(4): 2360–2369,
Lyu H, Yang Z, Wang S et al. Reliability modeling for multistage systems subject to competing failure processes. Quality and Reliability Engineering International 2021; 37(6): 2936–2949,
Macheret Y, Koehn P, Sparrow D. Improving reliability and operational availability of military systems. 2005 IEEE Aerospace Conference, Big Sky, Montana, USA, IEEE Operations Center: 2005: 3948–3957,
Mengistu T M, Che D, Alahmadi A, Lu S. Semi-Markov Process Based Reliability and Availability Prediction for Volunteer Cloud Systems. 2018 IEEE 11th International Conference on Cloud Computing (CLOUD), San Francisco, CA, USA, IEEE: 2018: 359–366,
Migawa K. Availability control for means of transport in decisive semi-markov models of exploitation process. Archives of Transport 2012; 24(4): 497–508,
Migawa K, Borowski S, Neubauer A, Sołtysiak A. Semi-Markov Model of the System of Repairs and Preventive Replacements by Age of City Buses. Applied Sciences 2021; 11(21): 10411,
Miziuła P, Navarro J. Birnbaum Importance Measure for Reliability Systems With Dependent Components. IEEE Transactions on Reliability 2019; 68(2): 439–450,
Oniszczuk W. Loss tandem networks with blocking - a semi-Markov approach. Bulletin of the Polish Academy of Sciences: Technical Sciences; 2010; 58; No 4; 673-681 2010; 58(4): 673–681,
Oszczypała M, Ziółkowski J, Małachowski J. Analysis of Light Utility Vehicle Readiness in Military Transportation Systems Using Markov and Semi-Markov Processes. Energies 2022; 15(14): 5062,
Oszczypała M, Ziółkowski J, Małachowski J. Reliability Analysis of Military Vehicles Based on Censored Failures Data. Applied Sciences 2022; 12(5): 1–25,
Papadopoulos C T, Li J, O’Kelly M E J. A classification and review of timed Markov models of manufacturing systems. Computers & Industrial Engineering 2019; 128: 219–244,
Park M, Jung K M, Park D H. Optimization of periodic preventive maintenance policy following the expiration of two-dimensional warranty. Reliability Engineering & System Safety 2018; 170: 1–9,
Rafiee K, Feng Q, Coit D W. Reliability assessment of competing risks with generalized mixed shock models. Reliability Engineering & System Safety 2017; 159: 1–11,
Rajarshi M B. Statistical Inference for Discrete Time Stochastic Processes. India, Springer India: 2013. doi:10.1007/978-81-322-0763-4,
Rosychuk R J, Sheng X, Stuber J L. Comparison of variance estimation approaches in a two-state Markov model for longitudinal data with misclassification. Statistics in Medicine 2006; 25(11): 1906–1921,
Roy V, Tan A, Flegal J M. Estimating standard errors for importance sampling estimators with multiple markov chains. Statistica Sinica 2018; 28(2): 1079–1101,
Rychlicki M, Kasprzyk Z, Rosiński A. Analysis of Accuracy and Reliability of Different Types of GPS Receivers. Sensors 2020; 20(22): 6498,
Şahin İ. Markov chain model for delay distribution in train schedules: Assessing the effectiveness of time allowances. Journal of Rail Transport Planning & Management 2017; 7(3): 101–113,
Selech J, Andrzejczak K. An aggregate criterion for selecting a distribution for times to failure of components of rail vehicles. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2019; 22(1): 102–111,
Shepero M, Munkhammar J. Spatial Markov chain model for electric vehicle charging in cities using geographical information system (GIS) data. Applied Energy 2018; 231: 1089–1099,
Soltanali H, Rohani A, Abbaspour-Fard M H, Farinha J T. A comparative study of statistical and soft computing techniques for reliability prediction of automotive manufacturing. Applied Soft Computing 2021; 98: 106738,
Song S, Coit D W, Feng Q. Reliability for systems of degrading components with distinct component shock sets. Reliability Engineering & System Safety 2014; 132: 115–124,
Stawowy M, Rosiński A, Siergiejczyk M, Perlicki K. Quality and Reliability-Exploitation Modeling of Power Supply Systems. Energies 2021; 14(9): 2727,
Świderski A, Borucka A, Grzelak M, Gil L. Evaluation of Machinery Readiness Using Semi-Markov Processes. Applied Sciences 2020; 10(4): 1541,
Wang J, Miao Y. Optimal preventive maintenance policy of the balanced system under the semi-Markov model. Reliability Engineering & System Safety 2021; 213: 1–10,
Wang L, Cui L, Zhang J, Peng J. Reliability evaluation of a Semi-Markov repairable system under alternative environments. Communications in Statistics - Theory and Methods 2016; 45(10): 2938–2957,
Wang Y, Xie B, E S. Adaptive relevance vector machine combined with Markov-chain-based importance sampling for reliability analysis. Reliability Engineering & System Safety 2022; 220: 1–11,
Warr R L, Collins D H. A comprehensive method for solving finite-state semi-Markov processes. International Journal of Simulation and Process Modelling 2015; 10(1): 89–99,
Wawrzyński W, Zieja M, Tomaszewska J, Michalski M. Reliability Assessment of Aircraft Commutators. Energies 2021; 14(21): 7404,
Wu B, Cui L. Reliability of multi-state systems under Markov renewal shock models with multiple failure levels. Computers & Industrial Engineering 2020; 145: 106509,
Wu B, Cui L. Reliability of repairable multi-state two-phase mission systems with finite number of phase switches. Applied Mathematical Modelling 2020; 77: 1229–1241,
Wu B, Cui L, Fang C. Reliability analysis of semi-Markov systems with restriction on transition times. Reliability Engineering & System Safety 2019; 190: 106516,
Zhang T, Liu T, Liu D, Sun F. Reliability Evaluation of Modular Multilevel Converter System Based on Semi-markov Model. 2021 IEEE 4th International Conference on Electronics Technology (ICET), 2021: 513–517,
Zhao L, Li K, Zhao W et al. A Sticky Sampling and Markov State Transition Matrix Based Driving Cycle Construction Method for EV. Energies 2022; 15(3): 1057,
Ziółkowski J, Małachowski J, Oszczypała M et al. Modelling of the Military Helicopter Operation Process in Terms of Readiness. Defence Science Journal 2021; 71(5): 602–611,
Żyluk A, Kuźma K, Grzesik N et al. Fuzzy Logic in Aircraft Onboard Systems Reliability Evaluation—A New Approach. Sensors 2021; 21(23): 7913,
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