# A New Approach to Production Process Capability Assessment for Non-Normal Data
## 1 Introduction
The multitude of applications shows that there is a need to develop and improve the method itself as well, so that its application is also possible for less typical enterprises or processes whose characteristics differ from the classic assumptions of the method. Six Sigma projects typically involve an interdisciplinary team of employees [31; 32] who work together to identify and resolve process inefficiencies, eliminate waste and improve quality. Six Sigma methodology is based on decision-making using data extracted from the process, its statistical analysis and continuous improvement. It can be used in two varieties: DMAIC (an acronym from the first letters of the words Define--Measure--Analyze--Improve--Control), which aims to improve the performance of business processes and will be discussed in more detail below, and DMADV (an acronym from the first letters of the words Define--Measure--Analyze--Design--Verify), to design new objects [33; 34; 35]. The DMAIC methodology involves a structured approach with five phases: defining, measuring, analyzing, improving and control. Defining the problem is the first and crucial step for the success of the project. It requires defining the relevant issue for the company and type of business in a clear way, including its current and desired value, as well as ways to verify (measure) the results. In doing so, it is worth noting the nature of the variable under study--better results are provided by continuous rather than discrete variables. The measurement phase involves a numerical characterization of the current performance of a process, product or service and allows the current state to be determined, especially from the customer's perspective. In the analysis phase, the product or service is considered to determine the source or sources of variability that are causing the problem. This provides an opportunity to make sure that the true root cause is identified, not just the symptom. In this regard, process capacity indicators are used to identify whether the produced goods are within the accepted specification limits defined by the customer. The last two phases are improvement, which involves the presentation of implementable changes to the process, product or service to ensure the desired outcome of the project; and control, where the proposed changes are implemented, the supporting systems are updated, and the process, product or service, is audited--usually a statistical control of the process--to ensure that the solution is fully implemented in a sustainable manner [36; 37]. The key assumption of the presented method Is the postulate that the random variables under study, such as the number of products produced, working time, etc., are described by a normal distribution. This is justified because, in practice, most business processes tend to follow a normal distribution. In the Six Sigma method, the normal distribution is used to define specification limits and control process quality. It defines the variability expressed in standard deviation \(\sigma\), meaning that no more than 3.4 defects/errors per million possibilities of occurrence can be expected in a process. Thus, the basic assumption of the Six Sigma method is to achieve production correctness of 99.997%. The remaining 0.003% is 6\(\sigma\), which is six times the standard deviation [38; 39]. Normal distribution is therefore a key condition for using the Six Sigma method. Moreover, research indicates that abandoning this assumption leads to erroneous results [29]. If this postulate is not met, alternative statistical tools and methods, based on appropriate nonparametric tests, can be used to analyze the data and make improvements [40]. An example of such a method is an approach that focuses on ranking data and comparing the distribution of different groups using, for example, the Wilcoxon rank-sum test, which can be used to compare the distribution of a process before and after an improvement initiative [41; 42]. Another approach is to transform the data to obtain a more normal distribution.