An ARL-unbiased design of Gamma control chart

Gamma charts based on time-between-events (TBE) data are very useful for process monitoring in the manufacturing industry. The average run length (ARL) is widely adopted as a criterion to evaluate the performance of Gamma charts. The traditional equal-tail probability limits are often used to provide the control limits of Gamma charts, however their ARL curves will not approach their maximum values at their in-control occurrence rates. To overcome the above problem, an ARL-unbiased design for Gamma charts with known parameters is proposed. The comparison result shows that the ARL-unbiased Gamma control charts are more sensitive to systematic deterioration than the traditional charts with the equal-tail probability limits. Finally, a real example is illustrated to demonstrate the implementation of the proposed approach.