Analysis of Average Run Length of Extended and New Extended Exponentially Weighted Moving Average Control Charts Using Markov Chain Approach Under Symmetric Distribution

Statistical Process Control (SPC) plays a crucial role in monitoring and improving manufacturing processes to ensure product quality. Control charts using exponentially weighted moving averages (EWMA) and their extensions, including Extended EWMA (EEWMA) and New Extended EWMA (NEEWMA), have been developed to increase the sensitivity for detecting small to medium process changes. This research proposes a method for calculating the Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) of control charts under a symmetric distribution using the Markov Chain Approach (MCA). This method is based on the probability of state transitions between controlled and uncontrolled states. The MCA method is more efficient than the Monte Carlo Simulation Approach (MC) in terms of accuracy and significantly reduces processing time. This research also demonstrates the application of ARL and SDRL calculations using the MCA method in various studies. Firstly, the performance of control charts is compared using the Mean Percentage Error (MPE) and Mean Absolute Percentage Error (MAPE). Secondly, the impact of symmetrically distributed process parameters on the performance of control charts is examined. Thirdly, a practical application of the control charts is presented. This research applies the proposed method to detect changes in unemployment insurance claims (UI) using seasonally adjusted initial claims assessment (ICSA) and continuing claims assessment (CCSA) rates from 2021 to 2025. The results show that the MCA method is more efficient than the MC method in terms of accuracy and significantly reduces processing time.