The one-sided variable sampling interval exponentially weighted moving average X̅ charts under the gamma distribution

Abstract

Recently, adaptive quality control charts have been frequently utilised in diverse production and manufacturing industries to ensure process stability and maintain a desirable level of product quality. Among these charts, the variable sampling interval (VSI) exponentially weighted moving average (EWMA) X̅ chart is known for its sensitivity and efficiency in monitoring the process mean shifts. However, the existing literature on the design of the VSI EWMA X̅ chart is predicated on the presumption that the underlying process adheres to a normal distribution. This normality assumption is often violated in manufacturing settings, where many practical processes tend to follow non-normal or skewed distributions. Therefore, this paper investigates the performance of one-sided VSI EWMA X̅ charts designed under the normal distribution model, when the quality characteristics of interest follow a gamma distribution. Our findings indicate that the in-control average time to signal and the standard deviation of the time to signal for the one-sided VSI EWMA X̅ charts are significantly deteriorated under the gamma distribution. To tackle this problem, this paper proposes new charting parameters specifically derived for the one-sided VSI EWMA X̅ charts under the gamma distribution. Besides, comparative analyses show that the proposed one-sided VSI EWMA X̅ charts exhibit the best detection speed compared to the one-sided Shewhart X̅ and EWMA X̅ charts, when the process follows a gamma distribution. An illustrative application of the one-sided VSI EWMA X̅ chart for monitoring the weight of bias tires in scooter manufacturing is provided at the end of this paper.