###### Abstract
Another important category of prognostic methods is the model-based approach. Here, models are created using a mathematical approach, the physical installation of the equipment, or a combination of both [14]. This approach views faults as continuous variables, following either a definite or random rule in their development. Models such as the Time-Dependent Dielectric Breakdown (TDDB) model and the Hot Carrier model play crucial roles in estimating the lifespan of semiconductor devices [15]. Batteries also use these models to determine their state of charge. Another significant approach to fault prognosis is through the use of Hidden Markov Models (HMMs). These statistical models are highly effective due to their inherent dual statistical nature. HMMs have widespread applications across various fields, including speech recognition, hand gesture recognition, and text segmentation [16]. Moreover, they are instrumental in tasks like detecting and predicting tool wear, as well as monitoring bearing faults. HMMs also play a crucial role in classifying structural damage and tracking the wear of machine tools. Transitioning from the discussion on fault prognosis, recent advancements in fault diagnosis methodologies have introduced innovative approaches to address challenges in prognostics. A multihop graph pooling adversarial network based on distributed federated learning (MHGPAN-DFL) is one such approach that aims to accurately predict the remaining useful life (RUL) in complex systems [17]. Multihop graph pooling and adversarial transfer learning are two strategies that MHGPAN-DFL uses to deal with data dispersion and domain drift issues in a good way. The weighted modified conditional variational autoencoder (WM-CVAE) is a new tool that was created to help with class imbalance problems in data-driven methods. This method improves the quality of the data and the ability of fault diagnosis modelsto learn, as demonstrated by tests on real-world industrial datasets [18]. The method also created health indicators and predictions for the remaining useful life (RUL) of systems with few failures, changing operating conditions, and little labeled data. This was made possible by using an LSTM autoencoder [19]. DC machines, valued for their simple operation and control, are widely used across various operations, including within the auxiliary systems of automobiles [20]. Despite not being directly involved in the traction system, their malfunction can lead to the overall failure of the vehicle. Over the past century, researchers have extensively studied DC motors, but only recently have they focused on diagnosing and predicting faults in these machines. Such research aims to ensure the continuous operation of these machines and estimate their remaining useful life (RUL). This study proposes an innovative prognosis method that uses weak classifiers in AdaBoost to predict future fault severity conditions in automotive starter DC machines with gear faults. Unlike traditional approaches, this method utilizes a combination of weak classifiers to enhance predictive accuracy and robustness. AdaBoost enables the effective integration and iterative performance improvement of multiple weak classifiers, leading to more accurate fault severity condition predictions. The primary contributions of this research lie in the novel methodologies developed for computing the parameters of the weak classifiers and devising the prediction algorithm. This approach provides a more reliable and effective tool for prognosticating faults in DC machines, thereby enhancing the reliability and longevity of automotive systems. The problem of training weak classifiers with Adaboost becomes more difficult when limited data is available. This paper explores the complexities of computing weak classifier parameters with sparse training data. An algorithm is suggested to determine the next most likely fault severity condition, addressing an important part of fault prognosis when limited data is available.