## 1 Introduction  
The growing demand for effective and secure systems has led to the development of operational maintenance processes to improve system availability and operational safety while achieving cost effectiveness. Predictive maintenance is one such process, which utilizes data analytics and machine-learning algorithms to predict potential failures before they occur [1, 2]. This approach has widespread adoption in the manufacturing, energy, and transportation industries. Predictive maintenance can identify patterns and anomalies indicative of impending issues by analyzing real-time data obtained from sensors and other sources. This enables maintenance teams to take proactive measures, such as replacing faulty components or adjusting operating conditions, thereby preventing failures [3, 4]. Unexpected and untimely failures remain a significant challenge for maintenance practices today. Depending on the severity of the failure, it can disrupt the proper functioning of a manufacturing line or, in more severe cases, lead to a complete shutdown, resulting in substantial expenses ranging from the procurement of spare components to equipment replacement. Hence, it becomes crucial to comprehend the behavior of equipment [5]. Such understanding forms a solid foundation for determining optimal maintenance policies tailored to each piece of equipment and its components. This leads to significant cost savings by optimizing inspection frequencies, reducing component replacements and stocking, improving pre-maintenance work, and minimizing repair times. To predict the future behavior of equipment and components, it is valuable to employ a tool, which fits theoretical models to the dataset to identify potential failures accurately and rapidly. Analysis and estimation processes are supported by statistical techniques, methods, and procedures, which facilitate modeling the system by adjusting predefined distributions or calculating customized distribution functions [6; 7]. These statistical techniques offer valuable tools for data-driven decision making, enabling the identification of underlying patterns and trends in complex systems. Statistical techniques prove beneficial in predicting future trends and outcomes. Analyzing historical data allows statisticians to develop models and predictions for strategic decision making. By leveraging statistical techniques, it becomes possible to forecast when the equipment will require repair or replacement and allocate resources accordingly, thus saving time, money, and preventing unplanned downtime. Furthermore, statistical analysis can optimize maintenance schedules and identify opportunities for improving maintenance processes [8; 9]. In some cases, estimating statistical distribution parameters can be challenging to solve [10; 11; 12]. This article presents a procedure for resolving such difficulties, employing the expectation maximization (EM) algorithm. The proposed procedure offers a structured and practical approach to estimating Weibull distribution parameters, even in challenging scenarios, where conventional methods may fail. By leveraging the EM algorithm, the estimation process becomes more precise and reliable, enhancing decision-making capabilities. This method helps estimate distribution parameters in realistic situations. The remainder of this paper is organized as follows. Section 2 highlights the main practical problems, which are generally associated with the analysis of data from the historical record of mechanical equipment failures, namely the existence of censored data. Section 3 provides an overview of the concepts and theoretical foundations underlying the method for determining Weibull distribution parameters. Since maximum likelihood equations often lack analytical solutions due to their complexity, the expectation maximization (EM) algorithm is presented as a resolution technique. The EM algorithm analysis is performed in the presence of censored data, aligning with their application in the case study.