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Statistical quality control based on ranked set sampling

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  • Hassen Muttlak
  • Walid Al-Sabah

Abstract

Different quality control charts for the sample mean are developed using ranked set sampling (RSS), and two of its modifications, namely median ranked set sampling (MRSS) and extreme ranked set sampling (ERSS). These new charts are compared to the usual control charts based on simple random sampling (SRS) data. The charts based on RSS or one of its modifications are shown to have smaller average run length (ARL) than the classical chart when there is a sustained shift in the process mean. The MRSS and ERSS methods are compared with RSS and SRS data, it turns out that MRSS dominates all other methods in terms of the out-of-control ARL performance. Real data are collected using the RSS, MRSS, and ERSS in cases of perfect and imperfect ranking. These data sets are used to construct the corresponding control charts. These charts are compared to usual SRS chart. Throughout this study we are assuming that the underlying distribution is normal. A check of the normality for our example data set indicated that the normality assumption is reasonable.

Suggested Citation

  • Hassen Muttlak & Walid Al-Sabah, 2003. "Statistical quality control based on ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(9), pages 1055-1078.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:9:p:1055-1078
    DOI: 10.1080/0266476032000076173
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    References listed on IDEAS

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    1. Sinha Bimal K. & Sinha Bikas K. & Purkayastha Sumitra, 1996. "On Some Aspects Of Ranked Set Sampling For Estimation Of Normal And Exponential Parameters," Statistics & Risk Modeling, De Gruyter, vol. 14(3), pages 223-240, March.
    2. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
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    Cited by:

    1. Razmkhah Mansooreh & Ahmadi Jafar & Sadeghpour Gildeh Bahram, 2017. "An Economic Design of Rectifying Double Acceptance Sampling Plans via Maxima Nomination Sampling," Stochastics and Quality Control, De Gruyter, vol. 32(2), pages 99-104, December.
    2. Muhammad Abid & Hafiz Zafar Nazir & Muhammad Tahir & Muhammad Riaz, 2018. "On designing a new cumulative sum Wilcoxon signed rank chart for monitoring process location," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-18, April.
    3. Al-Omari Amer Ibrahim & Al-Nasser Amjad D., 2011. "Statistical Quality Control Limits for the Sample Mean Chart Using Robust Extreme Ranked Set Sampling," Stochastics and Quality Control, De Gruyter, vol. 26(1), pages 73-89, January.
    4. Abdul Haq & Amer Al-Omari, 2015. "A new Shewhart control chart for monitoring process mean based on partially ordered judgment subset sampling," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1185-1202, May.

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