Integration of Bayesian Adaptive Exponentially Weighted Moving Average Control Chart and Paired Ranked-Based Sampling for Enhanced Semiconductor Manufacturing Process Monitoring

Exponentially weighted moving average (EWMA) and Shewhart control charts are commonly utilized to detect the small to moderate and large shifts in the process mean, respectively. This article introduces a novel Bayesian AEWMA control chart that employs various loss functions (LFs), including square error loss function (SELF) and LINEX loss function (LLF). The control chart incorporates an informative prior for posterior and posterior predictive distributions. Additionally, the control chart utilizes various paired ranked set sampling (PRSS) schemes to improve its accuracy and effectiveness. The average run length (ARL) and standard deviation of run length (SDRL) are used to evaluate the performance of the suggested control chart. Monte Carlo simulations are conducted to compare the performance of the proposed approach to other control charts. The results show that the proposed method outperforms in identifying out-of-control signals, particularly under PRSS schemes compared to simple random sampling (SRS). The proposed CCs effectiveness was validated using a real-life semiconductor manufacturing application, utilizing different PRSS schemes. The performance of the Bayesian AEWMA CC was evaluated, demonstrating its superiority in detecting out-of-control signs compared to existing CCs. This study introduces an innovative method incorporating various LFs and PRSS schemes, providing an enhanced and efficient approach for identifying shifts in the process mean.