Univariate fast initial response statistical process control with taut strings.

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.