On the conditional performance of the synthetic chart with unknown process parameters using the exceedance...

Area of Science:

• Statistical Process Control
• Quality Engineering

Background:

• Control charts with unknown parameters exhibit variable conditional in-control average run length (ARL).
• Estimating parameters from limited Phase I samples significantly impacts ARL performance.

Purpose of the Study:

• To investigate the conditional ARL performance of the synthetic chart using the exceedance probability criterion (EPC).
• To propose a method for adjusting control limits to improve conditional performance with limited Phase I data.

Main Methods:

• Simulation of the empirical distribution of conditional ARL.
• Application of the exceedance probability criterion (EPC) for control limit adjustment.
• Comparison with the bootstrap approach.

Main Results:

• A large number of Phase I samples are required for a specified EPC.
• Adjusted control limits improve conditional in-control performance for limited Phase I samples.
• A trade-off exists between in-control and out-of-control performance for small shifts.

Conclusions:

• The EPC method provides comparable conditional performance to bootstrap methods with less computational effort.
• Adjusted synthetic charts offer satisfactory conditional performance for moderate to large shifts.
• The proposed EPC adjustment is effective for improving synthetic chart performance with limited Phase I data.