Measuring the performance improvement of a double generally weighted moving average control chart

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%

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

Alevizakos

Koukouvinos

Lappa

2018

“…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%

“…The DGWMA charts are more sensitive and detect a shift quicker than its main time‐weighted counterpart the GWMA chart in the case of a small or tiny shift, see for example, Sheu and Hsieh, Huang et al, Lu, and the references therein. It is therefore logical to compare the OOC performance of the proposed DGWMA‐EX chart with the DGWMA‐

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, GWMA‐

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, GWMA‐EX, and EWMA‐EX charts under the normal and a number of non‐normal distributions when parameter of interest is unknown (Case U).…”

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%

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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.

“…As an alternative method to improve the performance of control charts, Sheu and Lin added design and adjustment parameters to expand the EWMA control chart, called the generally weighted moving average (GWMA) chart, which was shown to be more effective than the EWMA, CUSUM, and Shewhart charts in detecting very small shifts. Sheu and Yang, Sheu and Chiu, Sheu and Lu, Chiu, Sheu and Hsieh, Teh et al, Huang et al, Huang, Lu, Aslam et al, and Chakraborty et al provide more details on recent developments in GWMA charts.…”

Section: Introductionmentioning

confidence: 99%

Novel design of composite generally weighted moving average and cumulative sum charts

2017

Self Cite

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts are popular statistical tools to improve the performance of the Shewhart chart in detecting small process shifts. In this study, we propose the mixed generally weighted moving average (GWMA)‐CUSUM chart and its reverse‐order CUSUM‐GWMA chart to enhance detection ability compared with existing counterparts. The simulation revealed that the mixed GWMA‐CUSUM and mixed CUSUM‐GWMA charts have the sensitivity to detect small process shifts and efficient structures compared with the mixed EWMA‐CUSUM and mixed CUSUM‐EWMA charts, respectively. Moreover, the mixed GWMA‐CUSUM chart with a large design parameter has robust performance, regardless of the high tail t distribution or right skewness gamma distribution.