Adaptive EWMA control chart using Bayesian approach under ranked set sampling schemes with application to Hard Bake process

Abstract

The memory-type control charts, such as cumulative sum (CUSUM) and exponentially weighted moving average control chart, are more desirable for detecting a small or moderate shift in the production process of a location parameter. In this article, a novel Bayesian adaptive EWMA (AEWMA) control chat utilizing ranked set sampling (RSS) designs is proposed under two different loss functions, i.e., square error loss function (SELF) and linex loss function (LLF), and with informative prior distribution to monitor the mean shift of the normally distributed process. The extensive Monte Carlo simulation method is used to check the performance of the suggested Bayesian-AEWMA control chart using RSS schemes. The effectiveness of the proposed AEWMA control chart is evaluated through the average run length (ARL) and standard deviation of run length (SDRL). The results indicate that the proposed Bayesian control chart applying RSS schemes is more sensitive in detecting mean shifts than the existing Bayesian AEWAM control chart based on simple random sampling (SRS). Finally, to demonstrate the effectiveness of the proposed Bayesian-AEWMA control chart under different RSS schemes, we present a numerical example involving the hard-bake process in semiconductor fabrication. Our results show that the Bayesian-AEWMA control chart using RSS schemes outperforms the EWMA and AEWMA control charts utilizing the Bayesian approach under simple random sampling in detecting out-of-control signals.