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A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules

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  • Chakraborti, S.
  • Eryilmaz, S.
  • Human, S.W.

Abstract

Nonparametric control charts do not require knowledge about the shape of the underlying distribution and can thus be attractive in certain situations. Two new Shewhart-type nonparametric control charts are proposed for monitoring the unknown location parameter of a continuous population in Phase II (prospective) applications. The charts are based on control limits given by two specified order statistics from a reference sample, obtained from a Phase I (retrospective) analysis, and using some runs-type signaling rules. The plotting statistic can be any order statistic in a Phase II sample; the median is used here for simplicity and robustness. Exact run length distributions of the proposed charts are derived using conditioning and some results from the theory of runs. Tables are provided for practical implementation of the charts for a given in-control average run length between 300 and 500. Comparisons of the average run length ARL, the standard deviation of run length (SDRL) and some run length percentiles show that the charts have robust in-control performance and are more efficient when the underlying distribution is t (symmetric with heavier tails than the normal) or gamma (1, 1) (right-skewed). Even for the normal distribution, the new charts are quite competitive. An illustrative numerical example is given. An added advantage of these charts is that they can be applied before all the data are collected which might lead to savings in time and resources in certain applications.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1054-1065
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    References listed on IDEAS

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    1. Fu, James C. & Spiring, Fred A. & Xie, Hansheng, 2002. "On the average run lengths of quality control schemes using a Markov chain approach," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 369-380, February.
    2. S. Chakraborti & P. van der Laan & M. A. van de Wiel, 2004. "A class of distribution‐free control charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 443-462, August.
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    1. Human, S.W. & Chakraborti, S. & Smit, C.F., 2010. "Shewhart-type control charts for variation in phase I data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 863-874, April.
    2. 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.
    3. Nikolaos I. Panayiotou & Ioannis S. Triantafyllou, 2023. "A Class of Enhanced Nonparametric Control Schemes Based on Order Statistics and Runs," Stats, MDPI, vol. 6(1), pages 1-14, February.
    4. 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.
    5. F.S. Makri & Z.M. Psillakis, 2017. "On Limited Length Binary Strings with an Application in Statistical Control," The Open Statistics and Probability Journal, Bentham Open, vol. 8(1), pages 1-6, February.
    6. Qiu, Peihua & Li, Zhonghua, 2011. "Distribution-free monitoring of univariate processes," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1833-1840.

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