Design of Gamma Charts Based on Average Time to Signal

Gamma charts for time between events are very useful in the high-quality processes, which monitor the time until the rth event. The average time to signal (ATS) is adopted to evaluate the performance of Gamma charts, because it reflects both the number and the sampling interval of samples inspected until an out-of-control signal occurs. An ATS-unbiased design for Gamma charts with known parameters is proposed based on the hypothesis test of the scale parameter. For the phase I monitoring, a new ATS-unbiased design with unknown parameters is developed, and a sequential sampling scheme is adopted to start process monitoring as soon as possible. Some specific guidelines to stop updating the control limits are suggested from the convergence of the width between control limits with different phase I sample sizes. Finally, a real example is illustrated to demonstrate the implementation of the proposed approach.