Neutrosophic X-bar EWMA control chart: a novel framework for addressing uncertainty in statistical process control

Control charts are widely used statistical tools for monitoring process quality, even when data is imprecise or uncertain. Traditional approaches, however, often struggle to adequately represent the ambiguity present in such data. This research introduces a novel X-bar exponentially weighted moving average (EWMA) control chart based on Neutrosophic Random Variables (NRVs) - an extension of classical stochastic variables that incorporates degrees of truth, indeterminacy, and falsity. Unlike conventional probabilistic or fuzzy models, NRVs provide a more comprehensive framework for representing uncertainty, especially when faced with incomplete, inconsistent, or ambiguous information. Monte Carlo simulations were employed to generate normally distributed random data, facilitating the evaluation of the proposed chart's performance under various process shift scenarios. Key neutrosophic measures were implemented to enhance the assessment of chart efficacy. A comparative analysis between the proposed neutrosophic X-bar EWMA chart and its traditional counterpart was conducted using average run length (ARL) metrics. Results demonstrate that the proposed chart offers greater adaptability and improved sensitivity in detecting process shifts, particularly in environments characterized by uncertain or indeterminate data. The practical utility of this approach is further illustrated through a real-world application involving quality characteristics in glass production.