# A New Approach to Production Process Capability Assessment for Non-Normal Data
## 1 Introduction  
Six Sigma is a method of managing organizations with the goal of striving for excellence. This method evolved from the Total Quality Management (TQM) theory and is seen as the most modern stage in the evolution of quality management [1, 2]. It is defined as a management system that aims to improve process efficiency and reduce defects [3, 4]. It is a business strategy enabling identification and later elimination of the causes of problems, errors or anything that can lead to customer dissatisfaction. Numerous scientific considerations indicate that Six Sigma implementation is an effective way to improve processes and reduce costs, contributing to significantly better results [5]. The origins of Six Sigma date back to the 1980s. Its forerunner was Motorola, and the premise was to reduce the number of errors in the manufacturing process and the cost of poor-quality products, which at the time accounted for 15-20% of revenue from all sales [6, 7]. The low efficiency of production processes and the high proportion of products that did not meet customer requirements required radical changes. Since then, Six Sigma methodology has been successfully applied in a multitude of organizations, primarily in the production industry, to improve customer satisfaction, reduce costs and increase productivity and competitiveness. It is used by large corporations suchas Sony, Texas Instruments, Honeywell, Kodak, Allied Signal, Du Pont, Boeing and General Electric [8; 9; 10]. Its effectiveness caused its rapid spread into other areas and industries as well. It is implemented for a number of business processes, products and services. It is used, for example, in the medical industry, primarily to improve patient treatment results, reduce medical errors and increase the efficiency of the treatment process [11; 12]. It is used to improve the quality of healthcare services by identifying factors that contribute to patient satisfaction, including in the administrative area [10; 13; 14]. It is used in areas such as pharmaceutics, internal logistics, equipment maintenance and medical records [15; 16]. It has been successfully employed in the field of education to improve the methods used by improving the process of designing, developing and implementing curricula and conducting courses to ensure the desired learning outcomes. Six Sigma can be used to improve student achievements by identifying factors that contribute to their potential success, measuring the effectiveness of teaching methods and implementing strategies to improve results. It also promotes the streamlining of administrative processes, such as registration, recruitment, and financial assistance. Identifying inefficiencies in these areas allows the development of strategies, reducing errors and increasing productivity [14; 17]. Six Sigma can be used to improve business processes, reduce costs and increase customer satisfaction in the financial industry. The method can be used to identify and eliminate inefficiencies in financial processes, improve compliance and ensure standards in accordance with requirements governing financial practices or profitability [18; 19; 20]. Six Sigma can be used to improve quality and increase efficiency in almost any process, including telecommunications (identifying and eliminating the source of network failures, reducing customer complaints and optimizing network capacity [21; 22]), in logistics (streamlining supply chain processes, reducing errors and increasing efficiency, reducing lead times and improving delivery performance [23; 24]) or in the service sector (improving service quality, reducing customer complaints, optimizing service delivery processes and increasing efficiency). This practice has been successfully used, for example, in the hotel industry [13; 25; 26], retail [27; 28] and banking [29; 30].