## 1 Introduction  
Global competition requires automatic production systems that can be operated seamlessly, efficiently, and qualitatively. In an automatic system with multi-stage and quick manufacturing processes, sudden production machine failures can be expensive. A standard cause for production machine breakdowns is the failure of equipment to operate as needed. This instantly contributes to production waste such as waiting for unplanned downtime or product rejects [1]. Therefore, the extensive knowledge of reliability is crucial in predicting the unplanned downtime cost and the spare parts as well as recommending the optimal maintenance intervals [2; 3]. The use of an excellent reliability program will reassure the collection of vital information regarding the system's reliability performance right through the operation stage and direct the use of this information in the employment of analytical and management processes [4]. For valid effective reliability programs and maintenance development, proper data collection and analysis arerequired, together with the development of reliability models to aid in the decision-making procedures [5]. The greater part of industrial systems contains a high level of intricacy; however, they can be repaired in many cases. In those circumstances, it is obvious that excellent reliability, availability, and maintainability (RAM) study could play a vital role in the design stage and in any necessary modification to achieve the optimized performance of these systems. Nevertheless, it is effortful to evaluate the RAM parameters of such systems reaching up to a wanted degree of accuracy, utilizing information available and uncertain data [6]. A complex measure of reliability, availability, and maintainability in the mode of RAM-index for measuring the system performance was introduced by [PERSON] et al. [7]. RAM analysis is essential to increase the productivity, efficiency, and the quality of the products. In addition, the RAM methodology guides us to continuous improvement based on total quality management (TQM) principles. Reliability analysis is a crucial tool to determine how efficient a system is, and also to select a maintenance policy [8]. [PERSON] et al. [9] examined reliability of the shearer machine to identify urgent workstations. Subsequently, with a view to attaining a proper and practicable maintenance schedule, a task package for the drum shearer machine in the Tabas coal mine was recommended. [PERSON] et al. [10] assessed the reliability of 10 torries and the computed significance of each constituent was weighted by the importance measure method. The impact of critical items on the availability of machines was showed in this study. The dump truck is one of the major types of machineryin unenclosed pit mines and its downtime reduction has definite outcomes on the production plan. [PERSON] and [PERSON] [11] have recently approved a system reliability performance based on a reliant two-stage failure process, inclusive of the defect initialization stage and the defect development stage with competing failures. The reliance connecting both these stages was modeled by a statistical approach, specifically the non-homogeneous Poisson process (NHPP) model. RAM analysis of the system's vital performance metrics, such as mean-time-to-failure (MTTF), equipment down-time (EDT), and system availability values (Asys) can be determined. Development of a methodology by [PERSON] and [PERSON] [12] allows the system's reliability analysts/managers/engineers/practitioners to administer RAM analysis of the system to model, examine and predict the behavior of industrial systems in a greater pragmatic and consistent manner. They demonstrated that using RAM analysis of the system's vital performance metrics such as mean-time-between-failure (MTBF), mean-time-to-repair (MTTR), and system availability values are determined. Acquired information from analysis assists the management in assessment of the RAM needs of system [13]. [PERSON] et al.