A memory-type control chart is an important tool of statistical process control for monitoring small to moderate shifts in the manufacturing process. Using the prior information by the Bayesian approach is helpful in control charts. In this paper, a new hybrid exponentially weighted moving average (HEWMA) control chart is suggested under the Bayesian theory using ranked set sampling (RSS) schemes for posterior and posterior predictive distribution with informative prior and different loss functions (LFs). The extensive Monto Carlo simulation is conducted to evaluate the overall performance of the proposed Bayesian HEWMA control chart through average-run-length (ARL) and standard-deviation of the run-length (SDRL). Finally, a numerical example of the hard-bake process in semiconductor manufacturing is used to check the working and execution of the proposed Bayesian HEWMA control-chart under different RSS schemes. The results reveal that the suggested Bayesian HEWMA control-chart under RSS schemes is more sensitive in detecting out-of-control signals than the Bayesian HEWMA and Bayesian AEWMA control-charts under simple random sampling.

This study introduces a novel adaptive exponentially weighted moving average (AEWMA) control chart for monitoring process dispersion, employing adaptation to determine the smoothing constant. It is designed to effectively track shifts within expected ranges in process dispersion by computing the smoothing constant through a suggested adaptive approach. To determine its efficacy, the chart’s performance is evaluated by using smaller run-length profiles derived from Monte Carlo simulations. A key feature is the utilization of an unbiased estimator to calculate the smoothing constant via the proposed function, enhancing the chart’s ability to detect various magnitudes of decreasing and increasing process dispersion shifts. A comparison with an existing adaptive EWMA dispersion chart underscores the significant efficiency of the proposed chart across various types of process dispersion shift magnitudes. Moreover, the study encompasses a real-life dataset application, demonstrating the practical implementation and ease of use in real-world scenarios.

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.

Control charts are widely used to efficiently detect small to moderate shifts and they include exponentially moving average control charts, named memory type control charts. Today, memory type control charts are a significant tool to assure quality standards and monitor manufacturing goods. The proposed study suggests a novel Bayesian exponentially weighted moving average (EWMA) control chart design utilizing various pair ranked set sampling schemes for posterior and posterior predictive distributions given an informative prior. The proposed chart strategy is evaluated in terms of the small run length characteristic by using Monte Carlo simulation methods. The comparative analysis is also carried out by using a Bayesian EWMA control chart to apply simple random sampling for the respective average and standard deviation of the run length values in the both control chart designs. The results revealed efficient and rapid detection of shifts in process means which proves the success and superiority of the suggested design. A real-life data sets is used to elaborate the efficient application of the suggested Bay-EWMA-PRSS control chart design. The overall research findings support the theoretical and simulation results, which are provided in the form of extensive tables.