Executive Summary : | The study of the reliability of k-out-of-n systems is interesting from a theoretical and practical point of view. From a theoretical point of view, this study offers a wide range of possibilities for new mathematical methods and applications. From a practical point of view, there are a number of investigations dedicated to the reliability-centric analysis of k-out-of-n systems. The application of such models can be seen in many real-world phenomena, including telecommunications, transmissions, transportation, construction, and service applications etc. In system design process, standby redundancy is a widely used technique to improve system reliability and availability. Typical standby techniques involve cold standby, hot standby, and warm standby. A recent paper by Min Gong et al. (2021) investigates the repairable K-out-of-N system with mixed standby strategy containing both warm and cold standby. The authors were assumed that, each component can be in failure, cold, warm, and active states and the components are assumed to be repairable. The proposed system is then modelled by continuous time Markov chain and the system long-run availability is derived. Furthermore, the optimal configuration of standby components in the system is studied considering both system availability and system running cost. Krishnamoorthy (2021) introduced into reliability literature a new concept called RELIABILITY-INVENTORY for the k-out-of-n system. Inventory appears in it through order placement at an appropriate epoch. Life times of components are assumed to be independent and identically distributed random variables. Lead time for order realization also has exponentially distributed duration, independent of the life times of the components, but having a different parameter. He obtains analytically the optimal order placement epoch for ensuring the reliability of the system manager’s choice. Thus his investigation is directed to continuous time Markov chains (CTMC). He considered COLD SYSTEM which means that the functional components do not deteriorate while the system is in down state. The result of Krishnamoorthy (2021) can be extended to WARM and HOT systems. There are several other extensions also possible. A few of such extensions are proposed to be considered in this project. Nevertheless, those are for discrete time processes. In this project we propose to analyse a similar situation in the case of discrete time life distributed units and also discrete time lead time distribution. The system is analyzed as a discrete time Markov chain. Thus the underlying distributions are assumed to be geometric distributed. Even if we assume arbitrary distribution, we can get a DTMC by taking into consideration appropriate supplementary variables. We concentrate on discrete-time system. Unlike the continuous case, this is much more complex. |