Performance Analysis of Bayesian Control Chart Under Variable Sample Size for Industrial Application With Measurement Error

This study introduces a Bayesian exponentially weighted moving average (EWMA) control chart with variable sample size (VSS), referred to as VEWMA, for monitoring process shifts in the presence of measurement errors (MEs). The chart incorporates two loss functions: the squared error loss function (SELF) and the linex loss function (LLF). To mitigate the impact of MEs, the method employs both a linear covariate model and a multiple measurement strategy. The performance of the proposed Bayesian VEWMA control chart is evaluated using two key metrics: average run length (ARL) and standard deviation of run lengths (SDRL). Monte Carlo simulations and data analysis demonstrate that MEs significantly influence the chart's performance. The results show that the Bayesian VEWMA control chart, particularly when using the multiple measurement approach, outperforms the traditional Bayesian FEWMA control chart in terms of monitoring effectiveness.