This paper considers a comprehensive study of the parallel system, accounting for repairing failed components and order for replenishment. Accordingly, the system under consideration forms a Reliability-Queueing-Inventory system. The system consists of identical components whose lifetimes are independent. The parallel system is studied under three cases, considering the stages at which the repair of failed components and order for replenishment realizations. Using the difference-differential equations, we derive the steady-state probabilities explicitly. We calculate various significant performance metrics of the system and compare the corresponding numerical results to analyze the most reliable system. We examine additional reliability measures like the distribution of the duration until the first failure and the distribution of time during which the repair facility is continuously available for all the cases. Further, we explore optimization problems in detail and then compare the results to identify a cost-effective system with high reliability.

This paper presents an integrated system for ensuring uninterrupted power supply to tethered high-altitude platform systems (HAPS) by strategically managing the repair and replenishment of batteries in a k-out-of-n:G, COLD system. We assume that the batteries are identical and their lifetimes are independent of each other and exponentially distributed. The batteries deteriorate independently due to failures and await repair. The repair facility is activated when the number of working batteries decreases to L (L<n), and a replenishment order for n-k+1 batteries is placed when the number of operational batteries falls to N (N<L). We derive an explicit solution for the system-state probability and analyze key performance measures. Furthermore, we employ the particle swarm optimization (PSO) algorithm to determine the optimal cost for the proposed optimization problem and use the Morris method for sensitivity analysis. The results provide insights into efficient battery management strategies for HAPS, ensuring reliable power supply while minimizing costs.

In this paper, we study the so-called k-out-of-n queueing-inventory system with a single repair unit, identical elements that are subject to failure, stock of spare elements, and state-dependent replenishment policy. The finite state space Markov chain model is described, and key stationary performance measures are defined. The key focus of this research is on the non-Markov case, in which the random repair and replenishment times may have infinite means, which may affect the positive recurrence of the states of the model. This case is investigated numerically.

This paper investigates the reliability of a multi-cell battery system used in the Ground Control Station (GCS) of tethered High-Altitude Platform Systems (tHAPS), assuming the battery cells are series-connected. The model integrates repair and replenishment strategies to enhance battery reliability and ensure uninterrupted power supply to tHAPS. We analyze four practical variants, deriving explicit steady-state probabilities, which offer critical insights into system performance. Despite the inherent lower reliability of series-connected cells, our results demonstrate that effective management of repairs and replenishment significantly improves overall reliability. Additionally, the cost analysis indicates that increasing repair and replenishment rates reduces system costs by minimizing battery failures. The model underscores the importance of proper resource allocation and optimizing costs while maintaining high system reliability.