## 1 Introduction  
In recent years, machine learning has been increasingly used in various fields and has become an indispensable part of our daily lives. In the field of machine learning, two key roles are data owners and developers. As developers aim to improve models, they often need large amounts of diverse data. To achieve this goal, they sometimes ignore data privacy, aggregating datasets from multiple data owners for training, sharing these data with each other and even third parties. However, this does not mean that all customers also trust or are willing to hand over their information to third parties. Therefore, how data owners can jointly train models without sharing private data with third parties has become an important issue. To address privacy issues related to data exchange, Google proposed federated learning (FL) [1, 2] as a solution in 2016. Federated learning is a decentralized form of distributed learning where users locally train models using their own data. After completing this training, they upload their respective model parameters to a central aggregator. The central aggregator integrates these parameters and then returns the aggregated model to all users. Through federated learning, users can collectively train a model without having to hand over their individual data. However, recent studies show that gradients contain sensitive private information from the original data. Thus, attackers can potentially exploit gradients to compromise individuals' privacy [3, 4, 5, 6]. To address these issues, many studies have employed techniques such as secure multiparty computation, homomorphic encryption, and differential privacy to prevent privacy leaks. However, because homomorphic encryption increases the operational costs and differential privacy adds noise to the model that impacts on the overall accuracy, we have chosen additive secret sharing to ensure that gradients cannot be easily obtained by attackers. In the past research on using additive secret sharing to protect model parameters [7,8], the methods are \(n\)-out-of-\(n\). We considered the real-world risk of server failure and devised a solution that can aggregate the gradients of all clients by selecting \(t\) servers from \(n\) servers, given certain prerequisites. This \(t\)-out-of-\(n\) concept not only ensures the security of the gradients but also allows for a certain probability of server failure without affecting overall operations. In addition to ensuring the availability of the mechanism, we also propose a quality of service (QoS)-enabled federated learning mechanism. We want the trained models to provide different accuracy levels for users according to their attributes. The concept of providing a less accurate model may seem counterintuitive but is not uncommon in the real world. For example, in 1983, the United States opened the Global Positioning System (GPS) for civilian use. However, for reasons related to national security, the United States used Selective Availability (SA) to add errors to civilian GPS, reducing its accuracy, while the U.S. military and its allies were able to use highly accurate GPS systems. It was not until May 2000 that the United States announced it would stop using SA and thus allow civilian agencies to obtain accurate GPS systems. We incorporate the concept of SA into our proposed distributed federated learning scheme to provide different service level models to various customers, applying a membership hierarchy. By modifying gradients on each server, which can affect the model parameters, it is possible to derive various models with different accuracies. Finally, each client is provided with a model of different accuracy depending on their service level. The contributions of our work are summarized as follows:  
* We construct a threshold additive secret sharing scheme and propose a reliable distributed federating learning system. The model can be aggregated even when some servers are offline or not functioning.