Hybrid EWMA Control Chart under Bayesian Approach Using Ranked Set Sampling Schemes with Applications to Hard-Bake Process

Abstract

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.

Keywords

• Bayesian approach
• loss function
• RSS schemes
• HEWMA
• average-run-length
• control charts