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

There is growing literature on new versions of “memory‐type” control charts, where deceptively good zero‐state average run‐length (ARL) performance is misleading. Using steady‐state run‐length analysis in combination with the conditional expected delay (CED) metric, we show that the increasingly discussed progressive mean (PM) and homogeneously weighted moving average (HWMA) control charts should not be used in practice. Previously reported performance of methods based on these two approaches is misleading, as we found that performance is good only when a process change occurs at the very start of monitoring. Traditional alternatives, such as exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, not only have more consistent detection behavior over a range of different change points, they can also lead to better out‐of‐control zero‐state ARL performance when properly designed.

Section: Pm Approachmentioning

confidence: 99%

“…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

t = 2, 5, 10

, and 100.…”

Section: Weighting Patternsmentioning

confidence: 99%

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

Knoth

Tercero-Gómez

Khakifirooz

et al. 2021

“…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.…”

Section: Proposed Poisson Model-based Schemesmentioning

confidence: 99%

“…In literature, several researchers discovered that DPM structure has excellent identification power as compared to PM structure. [45][46][47][48][49][50] Furthermore, we have assessed the recommended techniques with respect to run length properties and contrasted them with existing SR-EWMA chart. Also, the proposed structures are executed on the number of 3D defective products in an additive manufacturing process.…”

Section: Introductionmentioning

confidence: 99%

Efficient GLM‐based control charts for Poisson processes

Mahmood

Iqbal²,

Amin

2021

The control charts are essential instruments that can impart crucial insights to quality controllers for maintaining the productivity of manufacturing processes. The conventional charting designs are based on a single study variable without exerting auxiliary information. Control charts derived from simple linear regression, generally with normality assumption, are one straightforward way of overcoming this difficulty. But, for a count distributed process, the generalized linear model (GLM) based strategy yields better outcomes. Hence, this study presents GLM-based progressive mean (PM) and double progressive mean (DPM) charting structures by employing the standardized residuals of the Poisson regression model. The functioning of the suggested and existing schemes (i.e., SR-EWMA) is investigated in the matter of run length distributions. The comparative analysis demonstrated that PM structures based on standardized residuals (i.e., SR-PM and SR-DPM) outperform the existing counterpart (i.e., SR-EWMA). Specifically, the SR-DPM chart is found to be more productive in identifying increasing alterations in the process mean. Finally, a case study about a 3D manufacturing procedure is presented to accentuate the significance of the suggested methods.

“…Unfortunately,

Var (P D P M_{t})

provided in (3) is not correct and we derive its correct version. The correct variance of the

P D P M_{t}

statistic following Riaz et al 9 is derived as follows:…”

Section: Derivation Of the Variance Of Double Progressive Mean Statisticmentioning

confidence: 99%

On correct expression of variance of double progressive mean statistic for monitoring Poisson observations

Abbas¹,

Nazir

Riaz

2021

Self Cite

Control charts play a vital role in tracing unfavorable changes in the ongoing process parameters to enhance the quality of the output. Attribute charting schemes are commonly utilized for tracing shifts in fraction nonconforming and number of nonconformities per unit in any production process. A double progressive mean charting structure for monitoring Poisson observations (PDPM) is recently proposed by Alevizakos and Koukouvinos 1 for efficient monitoring of the average number of nonconformities in the production unit. Unfortunately, the variance expression used in the charting statistic of the said article needs correction. The focus of this study is to provide correct derivation and expression of the variance of the PDPM statistic.