Process Capability Indices Optimized via Classical and Metaheuristic Algorithms: An Application of the Natural Discrete Lindley Distribution

Process capability indices are accepted indispensable tools for evaluating process performance and supporting purchasing decisions in the manufacturing industry and supply chain. Meanwhile technological advances have increased the efficiency of industrial systems, they have also increased their complexity, making precise modeling more difficult. To overcome this problem, a generalized process capability index, Cpyk, for discrete processes has been developed. In this study, the natural discrete Lindley distribution is chosen to estimate Cpyk because it can flexibly model discrete data structures and is compatible with a wide variety of data sets. The performance of metaheuristic and classical optimization methods is evaluated with maximum likelihood estimation and the obtained results are analyzed using metrics such as bias and mean square error. Six different real data sets are analyzed to validate the simulation results. These results show that classical and metaheuristic methods exhibit comparable accuracy. However, considering the demands of the technological era, metaheuristic algorithms are found to be significantly faster, with this speed advantage proving critical for industrial process analysis and decision-making. This study is expected to make a significant contribution to the field of process capability analysis for discrete data structures and to provide a robust framework for further exploration across various data structures and industrial applications.