The dual CUSUM charts with auxiliary information for process mean

Haq, Abdul; Bibi, Lubna

doi:10.1080/03610918.2019.1648824

Cited by 8 publications

(2 citation statements)

References 19 publications

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“…Also, Aslam et al [11] suggested mixed chart using EWMA statistic. On similar lines, Haq and Bibi [12] suggested the dual CUSUM charts with the help of auxiliary information to improve the process mean monitoring. Similarly, Anwar et al [13] suggested AIB-mixed EWMA-CUSUM and AIB-mixed CUSUM-EWMA charts for efficient monitoring of process location.…”

Section: Introductionmentioning

confidence: 98%

Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

Arslan

Ashraf

Anwar

et al. 2022

Mathematical Problems in Engineering

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The classical cumulative SUM (CUSUM) chart is commonly used to monitor a particular size of the mean shift. In many real processes, it is assumed that the shift level varies within a range, and the exact level of the shift size is mostly unknown. For detecting a range of shift size, the dual-CUSUM (DC) and dual-Crosier CUSUM (DCC) charts are used to provide better detection ability as compared to the CUSUM and Crosier CUSUM (CC) charts, respectively. This paper introduces a new mixed exponentially weighted moving average (EWMA)-DCC (EDCC) chart to monitor process mean. In addition, AIB-based EWMA-DC (EDC) and EDCC charts (namely, AIB-EDC and AIB-EDCC charts) are suggested to detect shifts in the process mean level. Monte Carlo simulations are used to compute the run length (RL) characteristics of the proposed charts. A detailed comparison of the proposed schemes with other competing charts is also provided. It turns out that the proposed chart provides better performance than the counterparts when detecting a range of mean shift sizes. A real-life application is also presented to illustrate the implementation of the existing and proposed charts.

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Section: Introductionmentioning

confidence: 98%

Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

Arslan

Ashraf

Anwar

et al. 2022

Mathematical Problems in Engineering

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“…11 Haq 12 suggested the AIB maximum EWMA chart for a simultaneous monitoring of the process mean and dispersion, while Haq 13 constructed an AIB adaptive EWMA chart to monitor the process mean. In a multivariate setting, Haq and Khoo 14 presented the AIB multivariate EWMA (MEWMA), double MEWMA, and multivariate CUSUM charts for monitoring the process mean, while Haq and Bibi 15 considered the AIB dual CUSUM charts for the process mean. Abbasi and Haq 16,17 introduced the AIB optimal CUSUM and AIB adaptive CUSUM charts for the process mean.…”

Section: Introductionmentioning

confidence: 99%

Memory‐type t charts with multiple auxiliary information for the process mean

Haq

Khoo

Brown

2021

Quality & Reliability Eng

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Multiple auxiliary information‐based (MAIB) memory‐type t charts are proposed with fixed and variable sampling intervals for an improved monitoring of the process mean, which include adaptive/nonadaptive cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) t charts. These control charts are constructed based on a unique uniformly minimum variance unbiased estimator of the process mean that requires information on a study variable as well as on several correlated auxiliary variables. The Monte Carlo simulation technique is used to compute the run length characteristics of the proposed charts when sampling from a multivariate normal distribution. The run length comparisons show that the proposed MAIB‐t charts outperform their existing auxiliary information based (AIB) and non‐AIB t charts, where the normalizing transformation is used for all considered t charts in order to have uniformity in the comparisons. A real data application is also given to support the proposed theory.

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New CUSUM and dual CUSUM mean charts

Haq

Syed

2020

Quality & Reliability Eng

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The CUSUM (C) charts are well recognized as a potentially advanced process monitoring tools because of their sensitivity against small and moderate shifts. In this paper, we first improve the sensitivity of the Brownian motion–based C (BC) chart with an appropriate transformation, named new BC (NBC) chart, for monitoring moderate and large shifts in the mean of a normal process. Then, using the control charting structure of the Crosier C (CC) chart, we propose the NBCC (NBC with CC structure) chart. In addition, for efficiently detecting a mean shift within an interval, dual version of these control charts are also proposed, named the dual NBC (DNBC) and dual NBCC (DNBCC) charts. Moreover, the fast initial response feature is also incorporated into the proposed charts. Using the Monte Carlo simulation, the run length properties of the proposed charts are computed. The run length performances of the existing and proposed charts are compared using the extra quadratic loss and integral relative average run length as performance criterion. It turns out that the NBC and NBCC (DNBC and DNBCC) charts are uniformly more sensitive than the C, CC, and NBC (dual C and dual CC) charts when detecting the mean shifts in small, moderate, and large intervals, where the DNBCC chart outperforms all considered charts. The proposed charts are also applied on real data sets to support the proposed theory.

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The dual CUSUM charts with auxiliary information for process mean

Cited by 8 publications

References 19 publications

Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

Memory‐type t charts with multiple auxiliary information for the process mean

New CUSUM and dual CUSUM mean charts

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