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Shewhart type simultaneous univariate control chart based on ranked set sampling scheme.

Sukma Adi Perdana1,2, Muhammad Mashuri1, Muhammad Ahsan1

  • 1Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia.

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|July 30, 2025
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Summary
This summary is machine-generated.

Ranked Set Sampling (RSS) enhances control charts for detecting process shifts. A novel Max Chart using RSS and an improved bootstrap method offers superior performance over traditional Simple Random Sampling (SRS) charts.

Keywords:
Control chartsImproved bootstrap control chartMax chartRanked set sampling

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Area of Science:

  • Statistical Process Control
  • Quality Management
  • Industrial Engineering

Background:

  • Traditional control charts using Simple Random Sampling (SRS) have limitations in detecting process shifts.
  • Ranked Set Sampling (RSS) offers potential improvements in statistical efficiency.

Purpose of the Study:

  • To develop a novel Shewhart type simultaneous univariate control chart (Max Chart) utilizing the Ranked Set Sampling (RSS) scheme.
  • To enhance the detection capabilities of control charts for process mean and variance shifts.

Main Methods:

  • Development of a Max Chart based on RSS, addressing the unknown distribution of its statistics.
  • Implementation of an improved bootstrap method to establish control limits for the RSS-based Max Chart.

Main Results:

  • Monte Carlo simulations demonstrated the superiority of the Improved Bootstrap Max Chart (RSS) over the conventional Max Chart (SRS).
  • The proposed chart exhibited a superior Average Run Length (ARL1) in detecting shifts in process mean and variance.

Conclusions:

  • The novel Max Chart based on RSS, constructed with an improved bootstrap method, significantly improves process shift detection.
  • The proposed control chart provides a more effective tool for quality control and process monitoring.