Adaptive EWMA control charts for the Rayleigh distribution

Abstract

Numerous supplementary Shewhart monitoring designs have emerged, customized to data that follows specific non-normal distributions like the Rayleigh distribution (RD). The Rayleigh distribution has a variety of applications in modeling theory of communication, physical sciences, diagnostic imaging, life testing, reliability analysis, applied statistics and clinical studies. The exponential weighted moving average (EWMA) design is frequently advocated in the literature because of its ability to swiftly detect smaller process alterations. However, the common EWMA chart may not perform optimally in detecting all changes in the process parameters. To address this limitation, this study introduces an adaptive EWMA structure for monitoring quality characteristics following the RD, called the adaptive Rayleigh EWMA (AREWMA) chart. To determine the design parameters of the AREWMA chart, a Markov chain model is utilized. Analytical results are then used to assess the performance of the AREWMA chart in comparison to existing competitors. The comparative analysis illustrates the strengths of the proposed AREWMA chart in detecting shifts of various magnitudes during parameter monitoring. Finally, we present a practical application of the proposed AREWMA chart in the manufacturing industry, utilizing real data on the time of failure eld-tracking of devices in a system. Our analysis demonstrates the effectiveness of the AREWMA chart in detecting a range of shifts in the manufacturing process, highlighting its utility for continuous monitoring and quality control.