The Combined Double Generally Weighted Moving Average Control Chart for Individual Observations

Monitoring of time between events (TBE) instead of the number of events is used in high‐quality processes where the events occur rarely. This article presents a double generally weighted moving average control chart with a lower time‐varying control limit to monitor the TBE (regarded as DGWMA‐TBE chart). The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the DGWMA‐TBE chart is more effective than the DEWMA and GWMA charts in detecting moderate to large shifts. Furthermore, the DGWMA‐TBE chart is very robust for the same range of shifts when the TBE observations follow a Weibull or a lognormal distribution. Finally, examples are also presented to enhance the performance of the proposed chart.

Section: Introductionmentioning

confidence: 99%

“…Sheu and Hsieh studied the DGWMA control chart for the normal distribution, and it was found more effective than the DEWMA and GWMA control charts in detecting moderate shifts of the process mean. Other studies about the DGWMA control charts are Tai et al, Sheu et al, Huang et al, Chiu and Lu, Chiu, and Lu …”

Section: Introductionmentioning

confidence: 99%

Monitoring of time between events with a double generally weighted moving average control chart

Alevizakos

Koukouvinos

Lappa

2018

“…Tai et al 74 proposed a DGWMA (

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S^{2}

) scheme and showed that, in many situations, it has a better OOC ARL performance as compared to the corresponding GWMA (

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S^{2}

) scheme by Sheu et al 45 . Next, Huang et al 75 proposed a DGWMA SoS scheme and showed that it has a better ARL and SDRL detection ability than the corresponding DEWMA and GWMA SoS schemes in many situations.…”

Section: Dgwma 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.

“…The IC design of the proposed DGWMA‐EX chart consists of obtaining the values for the charting constant, ie, L > 0 for chosen values of m (known as the reference sample size) and n (known as the test sample size) and a certain range of values for each ( q , α ) combination, so that the attained IC ARL is close to the desirable value ARL * which is typically 370 or 500. Sheu and Hsieh, Tai et al, and Huang et al noted that ( q , α ) combinations in the intervals 0.5 ≤ q ≤ 0.9 and 0.5 ≤ α ≤ 1.0 enhanced the sensitivity of the DGWMA‐

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chart and outperformed the GWMA‐

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, DEWMA‐

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, and EWMA‐

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charts for small shifts. Chakraborty et al considered m = 49 and 99 and n = 5 and 10 as the values for the reference sample and test sample sizes, respectively, and the following range of values for the GWMA‐EX parameters: q = 0.8, 0.9, 0.95 and α = 0.7, 0.8, 0.9, 1.0, 1.3.…”

Section: Implementation and Performancementioning

confidence: 99%

“…They have shown that the DGWMA‐

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chart is more sensitive in detecting minor shifts in the process. The interested reader is referred to the works by Tai et al and Huang et al In typical applications, Shewhart‐type and time‐weighted charts are based on the fact that the observations of the underlying process are assumed to follow a normal or specified probability distribution. However, in many situations, the assumption of normality may not be justified or valid when the observations are from a non‐normal or unknown distribution.…”

Section: Introductionmentioning

confidence: 99%

A double generally weighted moving average exceedance control chart

Karakani

Human

Niekerk

2018

Since the inception of control charts by W. A. Shewhart in the 1920s, they have been increasingly applied in various fields. The recent literature witnessed the development of a number of nonparametric (distribution‐free) charts as they provide a robust and efficient alternative when there is a lack of knowledge about the underlying process distribution. In order to monitor the process location, information regarding the in‐control (IC) process median is typically required. However, in practice, this information might not be available due to various reasons. To this end, a generalized type of nonparametric time‐weighted control chart labeled as the double generally weighted moving average (DGWMA) based on the exceedance statistic (EX) is proposed. The DGWMA‐EX chart includes many of the well‐known existing time‐weighted control charts as special or limiting cases for detecting a shift in the unknown location parameter of a continuous distribution. The DGWMA‐EX chart combines the better shift detection properties of a DGWMA chart with the robust IC performance of a nonparametric chart, by using all the information from the start until the most recent sample to decide if a process is IC or out‐of‐control. An extensive simulation study reveals that the proposed DGWMA‐EX chart, in many cases, outperforms its counterparts.