## 1 Introduction  
The main requirement for the efficient and effective operation of a technical system is the durability and reliability of the system. According to refs. [1, 2], durability represents the period in which a technical system is kept in operation under well-established conditions and the materials, even after operation, keep their initial properties. Instead, reliability concerns the operational safety of the technical system, with the latter not breaking down over the working process time, according to the prescribed norms [2, 3, 4], thus being a quality characteristic. A modern description of durable and reliable technical systems is systemically presented in Figure 1.  
Figure 1: General systemic description of a technical system. Mathematically, the essential components that define safety in the exploitation of a system, under known working conditions (the availability, reliability, and maintenance of the system), i.e., without failures, are presented below. Reliability, \(R(t)\), as a function of time (\(t\)--operation time, of variable size), represents the operation probability in a time range [0, \(t\)] [4] with predetermined parameters and without failures and has values between 0 and 1. Practically, reliability is determined by calculation (established during product design [5; 6]), followed by verification in the laboratory, and in system operation, the effective reliability is confirmed. For each product/element of the technical system, the reliability of each element resulting from series production can be determined [7], even with the start of the system's operation, and so can its experimental reliability. Therefore, reliability is the main component of total quality control. This paper's theoretical notions refer only to dental bur active part wear, which is verified through a practical application. Thus, dental bur active part failure will be analyzed together with its wear, also experimentally [6; 7; 8]. The active part is the element of a dental bur that cannot be restored (which loses working capacity due to failure or wear [6; 7; 8]), i.e., it is not repairable but needs to be replaced/changed. The defect of the dental bur active part, in the studied case, represents a deviation from quality, and it assumes operation interruption in the set time range or the inability to function with the parameters imposed by the designer. According to [8], defects are physical imperfections, material inconveniences, etc., that can appear during the execution phase, due to the material, the user, the equipment used, etc., and during operation, due to the working environment, wear, shocks, deformations, etc. Thus, by summing up the operation times of the system, the quantitative failures can be determined [6; 9]. Dental burs are fine mechanics tools made of expensive materials and used for delicate operations from a technical point of view, so their rapid wear requires studies and research to extend their lifetime or even optimize their operation. This involves a detailed analysis of the working process based on the calculation of wear, which limits dental bur lifetime (durability and reliability) [9; 10]. Understanding the advances in medical research in general [11; 12; 13; 14] and in the field of dental applications in particular [10] is crucial to the appropriate interpretation of statistical results. Thus, the state of uncertainty and apparent chaos from nature can be transformed into measurable parameters, which is also applicable in dental practice, with the help of statistical tools. At the same time, understanding the meaning and actual extent of these instruments is essential and of great importance for researchers, practitioners, and users, who, based on evidence close to reality, constantly require up-to-date information and support for decision-making [15]. The various aspects of statistical analysis and results are reviewed, and their comprehension is then attempted based on common but not-yet-in-depth knowledge to obtain non-exhaustive, constructive, and realistic insights.