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

Abstract

Recently, a new double progressive mean (DPM) control chart has been proposed in the literature of statistical process control. In the said proposal, an important term is missing in the variance expression of the DPM statistic that affects the detection ability of the proposed chart. In this study, we have derived and provided the correct version of the said variance along with its corresponding control limits. The run length profiles of the DPM chart are investigated, and the results are updated for the new version of the limits. Moreover, a sensitivity analysis between DPM and progressive mean charts based on the different choices of the design parameter is also included in this study. It is revealed that the revised version offers even more efficient outcomes than the previous ones. In addition, a real dataset application is also presented for practical considerations of the refined version.

Comparisons of Optimal Generally Weighted Moving Average and Exponentially Weighted Moving Average Charts

“…Abbas et al [14] proposed the progressive mean chart, which is based on the average of all data values collected since the start-up of the system. See also [15][16][17]. The progressive mean chart seems to detect changes in the process mean when the change occurs at system start-up.…”

Comparisons of Optimal Generally Weighted Moving Average and Exponentially Weighted Moving Average Charts

“…Abbas et al [14] proposed the progressive mean chart, which is based on the average of all data values collected since the start-up of the system. See also [15][16][17]. The progressive mean chart seems to detect changes in the process mean when the change occurs at system start-up.…”

The impracticality of homogeneously weighted moving average and progressive mean control chart approaches

“…For normal observations, Abbas et al 47 extended the analysis with the DPM chart, based on a PM of progressive means, which adds even more weight to the older observations (see Section 4). However, Riaz et al 48 found an error and corrected the DPM variance to improve its performance. Focusing on a different problem, Zafar et al 49 proposed a chart to monitor the variance.…”

“…Now, we want to compare the weights of the PM chart, the DPM chart introduced in Riaz et al, 48 and the HWMA chart with the weights of the EWMA chart, the DEWMA chart from Shamma et al 74 and more recently in Zhang et al, 75 and the TEWMA chart proposed in Alevizakos et al 76 . Next we provide illustrations for , and 100.…”

“…( 15) 47 ). In a more recent paper, Riaz et al 48 provided corrections to the variance formula of DPM. Alevizakos and Koukouvinos 45 extended the idea of the PM statistic introducing a second PM statistic for use with the Poisson distribution in Abbasi et al 43 They suggested the DPM and the optimal DPM charts for enhancing the detection ability of the PM chart.…”

Efficient GLM‐based control charts for Poisson processes

“…Subsequently, Abbas et al 45 suggested double progressive mean (DPM) control charts revamp the effectiveness of the PM chart. Further, a refined version of the DPM chart was discussed by Riaz et al 49 So, we evolved model based PM and DPM structures to supervise minor to moderate shifts in process location, which are explained in the following sections.…”

Comparisons of Optimal Generally Weighted Moving Average and Exponentially Weighted Moving Average Charts

“…Abbas et al [14] proposed the progressive mean chart, which is based on the average of all data values collected since the start-up of the system. See also [15][16][17]. The progressive mean chart seems to detect changes in the process mean when the change occurs at system start-up.…”

The impracticality of homogeneously weighted moving average and progressive mean control chart approaches

“…For normal observations, Abbas et al 47 extended the analysis with the DPM chart, based on a PM of progressive means, which adds even more weight to the older observations (see Section 4). However, Riaz et al 48 found an error and corrected the DPM variance to improve its performance. Focusing on a different problem, Zafar et al 49 proposed a chart to monitor the variance.…”

“…Now, we want to compare the weights of the PM chart, the DPM chart introduced in Riaz et al, 48 and the HWMA chart with the weights of the EWMA chart, the DEWMA chart from Shamma et al 74 and more recently in Zhang et al, 75 and the TEWMA chart proposed in Alevizakos et al 76 . Next we provide illustrations for , and 100.…”

“…( 15) 47 ). In a more recent paper, Riaz et al 48 provided corrections to the variance formula of DPM. Alevizakos and Koukouvinos 45 extended the idea of the PM statistic introducing a second PM statistic for use with the Poisson distribution in Abbasi et al 43 They suggested the DPM and the optimal DPM charts for enhancing the detection ability of the PM chart.…”

Efficient GLM‐based control charts for Poisson processes

“…Subsequently, Abbas et al 45 suggested double progressive mean (DPM) control charts revamp the effectiveness of the PM chart. Further, a refined version of the DPM chart was discussed by Riaz et al 49 So, we evolved model based PM and DPM structures to supervise minor to moderate shifts in process location, which are explained in the following sections.…”

Comparisons of Optimal Generally Weighted Moving Average and Exponentially Weighted Moving Average Charts

“…Abbas et al [14] proposed the progressive mean chart, which is based on the average of all data values collected since the start-up of the system. See also [15][16][17]. The progressive mean chart seems to detect changes in the process mean when the change occurs at system start-up.…”

The impracticality of homogeneously weighted moving average and progressive mean control chart approaches

“…For normal observations, Abbas et al 47 extended the analysis with the DPM chart, based on a PM of progressive means, which adds even more weight to the older observations (see Section 4). However, Riaz et al 48 found an error and corrected the DPM variance to improve its performance. Focusing on a different problem, Zafar et al 49 proposed a chart to monitor the variance.…”

“…Now, we want to compare the weights of the PM chart, the DPM chart introduced in Riaz et al, 48 and the HWMA chart with the weights of the EWMA chart, the DEWMA chart from Shamma et al 74 and more recently in Zhang et al, 75 and the TEWMA chart proposed in Alevizakos et al 76 . Next we provide illustrations for , and 100.…”

“…( 15) 47 ). In a more recent paper, Riaz et al 48 provided corrections to the variance formula of DPM. Alevizakos and Koukouvinos 45 extended the idea of the PM statistic introducing a second PM statistic for use with the Poisson distribution in Abbasi et al 43 They suggested the DPM and the optimal DPM charts for enhancing the detection ability of the PM chart.…”

Efficient GLM‐based control charts for Poisson processes

“…Subsequently, Abbas et al 45 suggested double progressive mean (DPM) control charts revamp the effectiveness of the PM chart. Further, a refined version of the DPM chart was discussed by Riaz et al 49 So, we evolved model based PM and DPM structures to supervise minor to moderate shifts in process location, which are explained in the following sections.…”