A double homogeneously weighted moving average control chart for monitoring of the process mean

Abstract

In the service and manufacturing industry, memory‐type control charts are extensively applied for monitoring the production process. These types of charts have the ability to efficiently detect disturbances, especially of smaller amount, in the process mean and/or dispersion. Recently, a new homogeneously weighted moving average (HWMA) chart has been proposed for efficient monitoring of smaller shifts. In this study, we have proposed a new double HWMA (DHWMA) chart to monitor the changes in the process mean. The run length profile of the proposed DHWMA chart is evaluated and compared with some existing control charts. The outcomes reveal that the DHWMA chart shows better performance over its competitor charts. The effect of non‐normality (in terms of robustness) and the estimation of the unknown parameters on the performance of the DHWMA chart are also investigated as a part of this study. Finally, a real‐life industrial application is offered to demonstrate the proposal for practical considerations.

A mixed HWMA‐CUSUM mean chart with an application to manufacturing process

“…Another measure called the percentage decrease in is also used for comparison and is labeled as the (cf. Abbas et al 18 and Abid et al 23 ). The is calculated as .…”

“…In the SPCM literature, the homogeneously weighted moving average (HWMA) chart proposed by Abbas 19 became well known. The interested readers can see the work of the following researchers: Adegoke et al, 20,21 Nawaz and Han, 22 Abid et al, 23 and Abbas et al 24 on the HWMA chart under various directions. So, taking motivation from the structures of the HWMA chart, this article suggests a new CUSUM chart by using the statistic of the HWMA chart and from now labeled as the MHC chart.…”

An enhanced approach for the progressive mean control charts: A discussion and comparative analysis

“…This section presents the ARL-based graphical comparison of the DPM chart with its competitor's such as the exponentially weighted moving average (EWMA) chart suggested by Roberts, 12 the double EWMA (DEWMA) chart studied by Shamma and Shamma, 13 the PM chart designed by Abbas et al, 1 the homogenously weighted moving average (HWMA) chart proposed by Abbas, 14 and double HWMA (DHWMA) chart by Abid et al. 15 The ARL curves between proposed and its competitor's charts are presented in Figure 1A,B. It is obvious from these graphical displays that the DPM chart takes an edge over EWMA, DEWMA, PM, HWMA, and DHWMA chart.…”

Parameter Estimation Effect of the Homogeneously Weighted Moving Average Chart to Monitor the Mean of Autocorrelated Observations With Measurement Errors

“…Thereafter, [36] investigated the use of an auxiliary variable in the form of a regression estimator as an unbiased estimate of the process mean in Cases K and U; and robustness to normality is illustrated. Next, [37] and [38] proposed the double and hybrid HWMA schemes as well as robustness to normality, respectively. The double (hybrid) model entails using the same (different) smoothing parameters to design a monitoring scheme.…”

“…The double (hybrid) model entails using the same (different) smoothing parameters to design a monitoring scheme. While [37] studied both Cases K and U, [38] investigated Case K only. More recently, [39] proposed a bivariate HWMA scheme based on linear profiles to monitor the intercept, slope and variance parameters using the Bayesian estimation framework and illustrated its efficiency over a number of competitors in Case U.…”