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A nonparametric exponentially weighted moving average signed-rank chart for monitoring location

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  • Graham, M.A.
  • Chakraborti, S.
  • Human, S.W.

Abstract

Nonparametric control charts can provide a robust alternative in practice to the data analyst when there is a lack of knowledge about the underlying distribution. A nonparametric exponentially weighted moving average (NPEWMA) control chart combines the advantages of a nonparametric control chart with the better shift detection properties of a traditional EWMA chart. A NPEWMA chart for the median of a symmetric continuous distribution was introduced by Amin and Searcy (1991) using the Wilcoxon signed-rank statistic (see Gibbons and Chakraborti, 2003). This is called the nonparametric exponentially weighted moving average Signed-Rank (NPEWMA-SR) chart. However, important questions remained unanswered regarding the practical implementation as well as the performance of this chart. In this paper we address these issues with a more in-depth study of the two-sided NPEWMA-SR chart. A Markov chain approach is used to compute the run-length distribution and the associated performance characteristics. Detailed guidelines and recommendations for selecting the chart's design parameters for practical implementation are provided along with illustrative examples. An extensive simulation study is done on the performance of the chart including a detailed comparison with a number of existing control charts, including the traditional EWMA chart for subgroup averages and some nonparametric charts i.e. runs-rules enhanced Shewhart-type SR charts and the NPEWMA chart based on signs. Results show that the NPEWMA-SR chart performs just as well as and in some cases better than the competitors. A summary and some concluding remarks are given.

Suggested Citation

  • Graham, M.A. & Chakraborti, S. & Human, S.W., 2011. "A nonparametric exponentially weighted moving average signed-rank chart for monitoring location," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2490-2503, August.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:8:p:2490-2503
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    References listed on IDEAS

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    1. Knoth, Sven, 2006. "Computation of the ARL for CUSUM-S2 schemes," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 499-512, November.
    2. Huwang, Longcheen & Huang, Chun-Jung & Wang, Yi-Hua Tina, 2010. "New EWMA control charts for monitoring process dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2328-2342, October.
    3. Chakraborti, S. & Eryilmaz, S. & Human, S.W., 2009. "A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1054-1065, February.
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    Cited by:

    1. Lianjie Shu & Jinyu Fan, 2018. "A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 317-330, June.
    2. Khanittha Talordphop & Yupaporn Areepong & Saowanit Sukparungsee, 2023. "Design and Analysis of Extended Exponentially Weighted Moving Average Signed-Rank Control Charts for Monitoring the Process Mean," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    3. Shu, Lei & Chen, Yu & Zhang, Weiping & Wang, Xueqin, 2022. "Spatial rank-based high-dimensional change point detection via random integration," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Graham, M.A. & Mukherjee, A. & Chakraborti, S., 2012. "Distribution-free exponentially weighted moving average control charts for monitoring unknown location," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2539-2561.
    5. Saber Ali & Zameer Abbas & Hafiz Zafar Nazir & Muhammad Riaz & Xingfa Zhang & Yuan Li, 2020. "On Designing Non-Parametric EWMA Sign Chart under Ranked Set Sampling Scheme with Application to Industrial Process," Mathematics, MDPI, vol. 8(9), pages 1-20, September.

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