Guaranteed In‐Control Performance Design of a Variable Sampling Interval Exponentially Weighted Moving Average Control Chart under Parameter Estimation

ABSTRACT

This study aims to adapt the Guaranteed In‐Control Performance (GICP) approach to the Exponentially Weighted Moving Average (EWMA) control chart with Variable Sampling Intervals (VSIs) in order to maintain a predetermined false alarm risk when process parameters are unknown and must be estimated. In such cases, control chart performance may vary across practitioners due to estimation‐related uncertainty. It is assumed that subgroup means of size n, obtained at VSIs, are independent and identically distributed, and that the process mean and variance are estimated from Phase I in‐control data. A standardized EWMA statistic is adopted to construct the VSI EWMA chart under unknown parameters, and a Markov chain approach is used to evaluate its performance measures. The GICP methodology is integrated into the VSI EWMA chart to guarantee a desired in‐control performance level with high reliability. The critical design parameters of the chart are obtained through constrained optimization models. The results show that the proposed GICP‐based VSI EWMA design effectively reduces practitioner‐to‐practitioner performance variability caused by parameter estimation, guarantees a specified in‐control performance level, significantly lowers the false alarm risk, and enables more reliable process monitoring.