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Univariate fast initial response statistical process control with taut strings.

Michael Pokojovy1, J Marcus Jobe2

  • 1Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX, USA.

Journal of Applied Statistics
|June 27, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new taut string (TS) monitoring scheme for detecting process mean shifts. The TS chart significantly reduces detection time compared to CUSUM FIR methods, especially for early process changes.

Keywords:
Fast initial response CUSUM chartindividuals chartnonparametric statisticstaut stringtotal variation

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Area of Science:

  • Statistical Process Control
  • Quality Management

Background:

  • Real-time monitoring is crucial for detecting deviations in process means.
  • Existing methods like CUSUM FIR have limitations in detecting early or sustained process shifts.

Purpose of the Study:

  • To introduce a novel real-time univariate monitoring scheme using a nonparametric taut string estimator.
  • To compare the performance of the proposed taut string (TS) scheme against the CUSUM fast initial response (FIR) methodology.

Main Methods:

  • Development of a stopping rule based on the total variation of a nonparametric taut string estimator.
  • Implementation of a two-sided TS scheme designed for a specific average run length under in-control conditions.
  • Comparison with CUSUM FIR, considering restarts after false alarms.

Main Results:

  • The proposed TS scheme demonstrates a significant reduction in average run length for detecting mean shifts.
  • This improvement is particularly notable for changes occurring early in the process monitoring.
  • A decision rule is proposed to guide the choice between TS and CUSUM FIR charts based on false alarm rates and detection times.

Conclusions:

  • The taut string monitoring scheme offers superior performance in detecting sustained process mean departures compared to CUSUM FIR.
  • The proposed scheme is effective in reducing average run length, enhancing early detection capabilities.
  • The decision rule aids practitioners in selecting the optimal monitoring strategy for their specific quality control needs.