They also investigated circular out-of-r-from-n (\(k_{1},k_{2},\ldots,k_{n}\)) problems, which involve selecting \(F\) systems out of a total of \(n\), with \(r\) being the number of systems chosen in each selection. They collected numerical data on the reliability of different combinations of \(k\), \(r\), and \(n\) values using the MATLAB program, version 2021. [PERSON] [10] undertook a thorough investigation into the dynamics of collaboration within the framework of Software-Defined Networking (SDN). This study explored different dimensions such as the dependability of SDN, the typical duration until failure (MTTF), a comparison of costs and benefits, the evaluation of availability using copula distribution, and an analysis of how implementing reduction strategies influenced overall system performance. [PERSON] et al. [11] examined how a multi-faceted system was constructed, comprising three separate subsystems. [PERSON] et al. [5] and their colleagues utilized copula repair techniques to analyze the system's performance. [PERSON] [12] conducted research investigating the accessibility and dependability of a parallel system when subjected to imperfect repair and replacement methods. The study also delved into analyzing the associated costs and optimizing them. [PERSON] et al. [13] conducted a study examining the reliability, availability, and consistency of solar systems. [PERSON] et al. [14] evaluated the performance of a repairable system that consisted of two subsystems connected in series using a 2-out-of-4: G approach. The research conducted by [PERSON] et al. [15] delved into and analyzed numerous computer networking systems and their associated components. [PERSON] and colleagues [16] conducted an assessment to determine the effectiveness of a sophisticated repairable system. This system consisted of two subsystems operating simultaneously connected by a single faulty switch. [PERSON] et al. [17] conducted a study examining the cost assessment of a complex repairable system consisting of two subsystems connected in series. [PERSON] and [PERSON] [18] investigated the reliability metrics to determine the strength of a six-subsystem reverse osmosis system using the Gumbel-Hougaard family copula. The study provides graphical representations of the results over time and failure rates, offering insights to improve water treatment systems in harsh or contaminated environments. [PERSON] and [PERSON] [19] analyzed the reliability of an engine assembly system with an inspection facility, comprising nine main units. The system can fail due to individual unit failures or catastrophic failure. Using the supplementary variable method and Gumble-Hougaard copula, various reliability metrics are obtained. [PERSON] et al. [20] studied a reduced-order observer-based reset output feedback controller designed to address the output synchronization challenge in linear heterogeneous clustered multi-agent system (CMAS). [PERSON] et al. [21] introduced an optimal controller designed to minimize the expected value of a function influenced by random disturbances. [PERSON] and [PERSON] [22] analyzed the system reliability of a computer network that features the delayed reporting of non-fatal faults. The network is structured into four subsystems: a router, a gateway switch, two identical load balances, and a group of \(n\) similar applications or web servers operating under a \(k\)-out-of-\(n\): \(G\) policy with a standby arrangement, all connected in series. In this paper, a novel model is introduced for an Apache Kafka system, which is composed of three interconnected subsystems arranged in series: a producer group, an Apache Kafka cluster, and a consumer group (see Figure 1). Each subsystem consists of three identical units operating in parallel, employing a 1-out-of-3 redundancy strategy for robust performance. The units within subsystem 2 are linked to ZooKeeper to ensure the smooth functioning of the overall system. The failure rates of the units in each subsystem are assumed to be constant and follow exponential distributions.