ORIGINAL ARTICLE Modelling and simulation of repairable mechanical systems reliability and availability Girish Kumar 1 • Vipul Jain 2 • Umang Soni 3 Received: 2 May 2019 / Revised: 29 July 2019 Ó The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019 Abstract Markov approach is applicable for reliability and availability modelling when time to failure and repair follow an exponential distribution. Since failure time of mechanical components follows Weibull distribution, Markov approach cannot be employed to these systems. In present work, Semi-Markov model, which is appro- priate for repairable mechanical systems, is considered. In structural dependency, once a unit of a repairable system is failed due to one or more of its constituent components, the entire unit is taken for repair. Therefore, the repairs are considered at the unit level. This feature of structural dependency in the proposed approach addresses the problem of larger state space. The states at the unit level are derived from the component states to develop the system model. The solutions for reliability and availabil- ity are obtained using the Monte Carlo simulation. The suggested approach is realistic than the existing soft- ware’s such as Rapid Algorithmic Prototyping Tool for Ordered Reasoning, Blocksim, etc., as failures and repairs are considered at different hierarchical levels. The rec- ommended approach is illustrated for a centrifugal pumping system. Keywords Weibull  Reliability  Semi Markov  Simulation  Mechanical systems 1 Introduction Higher system availability and reliability are desirable in many industries where downtime adversely affects the production cost. In the past, the reliability and the avail- ability models with various features such as imperfect repairs, common cause failure, human error, etc., are mostly analysed using the Markov approach (Hajeeh 2012). However, the Markov process can be used if the time to failure and repair follows an exponential distribu- tion. System reliability is overestimated when structural dependency is not considered (Dao and Zuo 2017). Therefore, such dependency features should be incorpo- rated in modelling for a realistic assessment of reliability. In general, for mechanical components, failure rates are not constant. Hence, it is appropriate to use a general proba- bility distribution that better represents the stay time behaviour in a state-space model (Kumar et al. 2013a). The model so obtained follows a Semi-Markov process (Semi- MP) and its analytical solution is difficult (Welte 2009). The failure process of mechanical systems is better mod- elled with Weibull distribution (Fricks and Trivedi 1997). The Semi-MP that allows non-exponential distributions offers a more appropriate model (Perman et al. 1997). There is no closed form transient solution method for the Semi-MP model. However, some researchers attempted the & Girish Kumar girishkumar@dce.ac.in Vipul Jain vipul.jain@vuw.ac.nz Umang Soni umang.soni@nsut.ac.in 1 Department of Mechanical Engineering, Delhi Technological University, Bawana Road, New Delhi 110042, India 2 School of Management, Victoria Business School, Victoria University of Wellington, Wellington 6140, New Zealand 3 Department of Manufacturing Process and Automation Engineering, Netaji Subhas University of Technology, Sector 3, Dwarka, New Delhi 110078, India 123 Int J Syst Assur Eng Manag https://doi.org/10.1007/s13198-019-00852-3