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<p>In many fields, measurements are obtained in form of directions; such as wind directions or time of day when an event occur. Two-dimensional directional observations are known as circular data. Recently, control charts have been developed to monitor circular data. In this study, a Shewhart control chart is developed to monitor the variability of circular data through monitoring the concentration parameter of some well-known circular probability distributions. The presented chart is characterized by its applicability since it uses a simple chart statistic known as the sample mean resultant length. The performance of the chart is evaluated through a comprehensive simulation study. Finally, an application on a real data set in addition to an illustrative example on a simulated dataset are provided to demonstrate the applicability of the proposed chart.</p>

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Shewhart Control Chart for Monitoring Concentration of Circular Data

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Amani A. Ahmed,
  • Aya A. Aly,
  • Nesma A. Saleh

摘要

In many fields, measurements are obtained in form of directions; such as wind directions or time of day when an event occur. Two-dimensional directional observations are known as circular data. Recently, control charts have been developed to monitor circular data. In this study, a Shewhart control chart is developed to monitor the variability of circular data through monitoring the concentration parameter of some well-known circular probability distributions. The presented chart is characterized by its applicability since it uses a simple chart statistic known as the sample mean resultant length. The performance of the chart is evaluated through a comprehensive simulation study. Finally, an application on a real data set in addition to an illustrative example on a simulated dataset are provided to demonstrate the applicability of the proposed chart.