Enhanced Monitoring Using Multiscale Exponentially Weighted Moving Average Control Charts

Abstract

The exponentially weighted moving average (EWMA) method is a widely used univariate process monitoring technique. This conventional EWMA technique is normally designed to optimize the out of control average run length (ARL1) specific to a fixed in control average run length (ARL0). This design procedure of EWMA technique is based on some assumptions – the evaluated process residuals are Gaussian, independent and contain moderate level of noise. Violation of these assumptions may adversely affect its fault detection abilities. Wavelet based multiscale representation of data is a powerful data analysis tool and has inherent properties that can help deal with these violations of assumptions, which thus improve the performance of EWMA through satisfying its assumptions.

The main purpose of this work is to develop a multiscale EWMA technique with improved performance over the conventional technique and establish a design procedure for this method to optimize its parameters by minimizing the out of control average run length for different fault sizes and using a specified in control average run length assuming that the residuals are contaminated with zero mean Gaussian noise.

Through several comparative studies using Monte Carlo simulations, it has been shown that the multiscale EWMA technique provides a better performance over the conventional method. Multiscale EWMA is shown to provide smaller ARL1 and missed detection rate with a slightly higher false alarm rate compared to the conventional EWMA technique not only when both the techniques are designed to perform optimally but also when data violate the assumptions of the EWMA chart. The advantages of the multiscale EWMA method over the conventional method are also illustrated through their application to monitor a simulated distillation column.