The Max EWMAMS control chart for joint monitoring of process mean and variance with individual observations

Abstract

A traditional approach to monitor both the location and the scale parameters of a quality characteristic is to use two separate control charts. These schemes have some difficulties in concurrent tracking and interpretation. To overcome these difficulties, some researchers have proposed schemes consisting of only one chart. However, none of these schemes is designed to work with individual observations. In this research, an exponentially weighted moving average (EWMA)-based control chart that plots only one statistic at a time is proposed to simultaneously monitor the mean and variability with individual observations. The performance of the proposed scheme is compared with one of the two other existing combination charts by simulation. The results show that in general the proposed chart has a significantly better performance than the other combination charts.

On the Effect of Measurement Error with Linearly Increasing-Type Variance on Simultaneous Monitoring of Process Mean and Variability

“…Hence, they are more sensitive to small shifts rather than Shewhart‐type control charts. In this section, we describe a simultaneous monitoring control scheme called MAX‐EWMAMS control chart proposed by Memar and Niaki based on two control charts including EWMA and exponential weighted mean square error (EWMS) control charts.…”

“…In order to derive MAX‐EWMAMS statistic, Memar and Niaki used EWMA and EWMS statistics for monitoring the process mean and process variability, respectively. Then, they transformed the distribution of both statistics to a similar distribution (standard normal distribution).…”

“…Memar and Niaki also used the following statistic with approximate standard normal distribution for monitoring the process variability according to Equation : where H { a ; d } is defined as the cumulative distribution function of a chi‐square distribution denoted by . The MAX‐EWMAMS statistic at sample point t ; t = 1, 2, … is defined as follows: …”

Multivariate variability monitoring using EWMA control charts based on squared deviation of observations from target

“…Then, Reynolds and Stoumbos 4 used a one-sided statistic based on the EWMS chart statistic to monitor variability of univariate processes. Recently, Memar & Niaki 5 presented a transformation of EWMA along with a transformation of EWMS to control simultaneous changes in process mean and variance.…”

Maximum Multivariate Exponentially Weighted Moving Average and Maximum Multivariate Cumulative Sum Control Charts for Simultaneous Monitoring of Mean and Variability of Multivariate Multiple Linear Regression Profiles

“…In recent years, joint monitoring of process mean and dispersion in both univariate and multivariate cases has been considered by some researchers. Simultaneous monitoring of the mean and variance in univariate process has been studied by Khoo et al [22], Zhang et al [23], Guh [24], Memar and Niaki [25], Teh et al [26], Sheu et al [27], Haq et al [28], and Prajapati and Singh [29]. The simultaneous monitoring of multivariate process mean vector and covariance matrix has also been addressed by several authors.…”