Ocena zmožnosti proizvodnega procesa za poljubno zvezno porazdeljene podatke

This thesis addresses the challenge of assessing process capability in manufacturing when data deviate from normal distribution assumptions , a common scenario that complicates traditional quality control methods. Introduction of Shewhart’s control charts in 1924 enabled quality monitoring by identifying random and assignable causes of variability, allowing for early detection of process issues. However, control charts rely on assumptions of normality that do not hold in all the cases. To overcome limitations in arbitrary continuous data, this research investigates novel approaches in capability estimation designed for skewed or kurtotic data. Three primary methodological categories are explored: transformationbased methods, percentile-based methods, and adjusted indices. Notably, the thesis proposes a new power transformation technique, which shows superior performance in reducing data skewness compared to traditional Box-Cox and Johnson transformations, offering enhanced interpretability and practical application. The thesis further introduces the Marshall-Olkin family of distributions for capability index estimation, demonstrating that Marshall-Olkin indices consistently outperform conventional methods like Burr’s and Clements’ indices across various simulated non-normal datasets. A robust estimator approach is also evaluated, proving effective in maintaining stability under high outlier contamination. The thesis offers structured guidelines for process capability assessment that adapt to data characteristics, including skewness, kurtosis, and sample size. Simulation studies validate the proposed methods, confirming that the Marshall-Olkin indices and proposed power transformation are robust across diverse distributions, making them highly applicable in real-world manufacturing contexts.