EWMA Control Chart for Rayleigh Process With Engineering Applications

Abstract

Process monitoring is typically performed with quality control charts. The normality assumption is often taken into consideration for the development of control charts. However, this assumption may not hold in many real-life situations. One such circumstance is utilizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {V}_{\mathrm {SQR}}$ </tex-math></inline-formula> chart to track the process variability of Rayleigh distributed processes. The structure of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {V}_{\mathrm {SQR}}$ </tex-math></inline-formula> chart follows the basic design of the Shewhart-type chart, which is not sensitive mainly for smaller to moderate shifts in monitoring parameter. In this paper, an enhanced approach, namely Rayleigh exponential weighted moving average (REWMA) is introduced. The suggested REWMA scheme aims to significantly improve the detection capabilities of the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {V}_{\mathrm {SQR}}$ </tex-math></inline-formula> chart. Designated limits, along with charting parameters, are evaluated for different sample sizes. The effectiveness of the suggested REWMA control chart is assessed in terms of run length distributional parameters. Moreover, the Monte Carlo simulations are made to compare the run length properties of the proposed REWMA chart with the existing competitor design. The comparative assessment demonstrates that the suggested offers a considerable enhancement relative to the competing design. An application of the REWMA chart on simulated data also reveals that the proposed chart is highly sensitive to smaller and persistent shifts in the scaling parameter of Rayleigh distribution. Finally, an example from real-life has been presented to illustrate the importance of the suggested chart.