Generally weighted moving average control chart for monitoring process variability

Control charts are widely known quality tools used to detect and control industrial process deviations in statistical process control. In the current paper, we propose a new single memory-type control chart, called the sum of squares triple exponentially weighted moving average control chart (referred as SS-TEWMA chart), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed SS-TEWMA control chart is compared with that of the sum of squares EWMA, sum of squares double EWMA, sum of squares generally weighted moving average, and sum of squares double generally weighted moving average, control charts, through Monte Carlo simulations. The comparisons indicate that the proposed chart is more efficient, than the competing ones, in detecting small shifts in the process mean and/or variability for most of the considered scenarios, while it has comparable performance for some others in identifying large shifts in the process mean and small to large shifts in the process variability. Finally, two illustrative examples are provided to explain the application of the SS-TEWMA control chart. K E Y W O R D S average run length (ARL), single control chart, SS-DEWMA chart, SS-DGWMA chart, SS-EWMA chart, SS-GWMA chart, SS-TEWMA chart, standard deviation of run length (SDRL)

Section: =1mentioning

confidence: 99%

A sum of squares triple exponentially weighted moving average control chart

Chatterjee

Koukouvinos

Lappa

2021

“…Sheu and Tai 41 proposed the GWMA

S^{2}

scheme and showed that it outperforms the corresponding EWMA scheme in detecting OOC observations especially for small shifts. Next, Sheu and Lu 42 used an unbiased estimator of the process variance to propose the one‐sided GWMA

S^{2}

scheme and showed that it yields better ARL s than the basic EWMA and exponential weighted mean square deviation schemes.…”

Section: Gwma Schemesmentioning

confidence: 99%

Generally weighted moving average monitoring schemes: Overview and perspectives

Mabude

Malela‐Majika

Castagliola

et al. 2020

An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution‐free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (ie, double GWMA, composite Shewhart‐GWMA, mixed GWMA‐CUSUM, and mixed CUSUM‐GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA‐related schemes (ie, 66 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.

“…Let { Y t } be an GWMA sequence based on { M t }, defined by

Y_{t} = W_{1} M_{t} + W_{2} M_{t - 1} + ⋯ + W_{t} M_{1},

where

W_{t} = false({\overset{P}{true}}_{t - 1} - {\overset{P}{true}}_{t} false)

is the weight—here expressed as a difference of 2 probabilities. Sheu and Tai suggested considering

\overset{P_{t}}{true} = q^{t^{α}}

, where α and q ∈[0,1) are 2 known constants. The control chart based on { Y t } is called the GWMA chart.…”

Section: The Proposed Chartsmentioning

confidence: 99%

“…Castagliola applied a 3‐parameter logarithmic transformation on S 2 to propose an S 2 ‐EWMA chart for monitoring the process variance. Sheu and Tai suggested a GWMA chart for monitoring the process variability. Castagliola et al suggested an S 2 ‐EWMA chart with the variable sampling interval for monitoring the process variance.…”

Section: Introductionmentioning

confidence: 99%

New memory‐type dispersion control charts

Ali

Haq

2017

The exponentially weighted moving average (EWMA) control chart is a memory‐type process monitoring tool that is frequently used to monitor small and moderate disturbances in the process mean and/or process dispersion. In this study, we propose 2 new memory‐type control charts for monitoring changes in the process dispersion, namely, the generally weighted moving average and the hybrid EWMA charts. We use Monte Carlo simulations to compute the run length profiles of the proposed control charts. The run length comparisons of the proposed and existing charts reveal that the generally weighted moving average and hybrid EWMA charts provide better protection than the existing EWMA chart when detecting small to moderate shifts in the process dispersion. An illustrative dataset is also used to show the superiority of the proposed charts over the existing chart.