## 1 Introduction  
Pumps are a common item of hydraulic equipment, used in both industrial and residential settings, and their primary function in high-volume fluid handling is to control oil-flow operations. Their areas of application include power plants, oil refineries, building services industry, water engineering, chemical and process industries, and biomedical applications, to mention a few [1]. However, the persistent use of high-speed pumps without maintenance causes serious damage to the entire assembly by destroying their mechanical components. Meanwhile, using classical models to predict reliability is no longer viable. A typical reliability evaluation methodology relies primarily on the pumps' lifespan data, and failure data may be challenging to obtain. Furthermore, prior lifespan statistics may not fully depict the pump's behavior in a specific application or environment [2]. As a result, studies reveal that maintenance expenditures account for over a third of overall operating costs in most cases. According to [PERSON] [3], maintenance costs account for about fifteen to seventy percent (15% to 70%) of the production. In another study by [PERSON], it was revealed that maintenance costs is about forty percent (40%) of the total cost [4]. The performance characteristics of most industrial pumps may be connected to their reliability estimations as they degrade over timeDue to this finding, degradation assessment methods have recently gained popularity due to their capability to monitor the operational status of a system over time. The traditional maintenance solutions usually applied are divided into two categories, namely, corrective and preventative maintenance. Corrective maintenance is used to fix complex systems and equipment only after they have failed, leading to an increase in the processes direct expenses. In contrast, preventive maintenance is carried out regularly to avoid equipment breakdowns. Thus, preventative repairs to machinery or components are performed when their remaining useful life is unknown, resulting in unplanned downtime and increased operating costs [5]. Consequently, a scheduled maintenance or preventive approach should be provided to enhance overall equipment condition while lowering the rate of equipment failure, reducing the cost of maintenance, and increasing the useful lifetime of equipment [6]. During the fourth Industrial Revolution (Industry 4.0), industries continuously seek ways to improve production processes while minimizing costs [7]. Besides these examples, various terminologies and categories of maintenance management strategies may be found in other research [8; 9; 20]. The study considered the categories provided by the research works of [PERSON] et al. [21; 22]. In their study, they categorized the maintenance procedures into three groups, compared with the existing researchers. These maintenance procedures can be described as follows. Run-to-Failure (R2F) maintenance, also known as corrective maintenance: this maintenance type occurs only when a piece of equipment fails to function correctly. It is the most basic maintenance method, as it necessitates a halt in production and the repair of the components to be replaced, both of which add a direct cost to the operation. On the other hand, preventive maintenance (PvM), often referred to as time-based maintenance (TBM) or scheduled maintenance (SMS) is a preventative maintenance approach that is conducted regularly, according to a predetermined schedule in time or process iterations, to anticipate equipment problems. It is a typically successful method of avoiding failures. Whilst, the predictive maintenance (PdM) method employs predictive technologies to identify when maintenance operations are required. It is based on the constant assessment of the reliability of a machine or process, allowing maintenance to be conducted only when necessary.