Design of Gamma control charts based on the narrowest confidence interval

In statistical process control, Gamma control charts are often designed for time-between-events (TBEs) monitoring. For Gamma distribution, the traditional equal-tail probability limits lead to the problem that some out-of-control events may occur in higher probability than in-control events. To overcome this problem, Gamma control limits with known parameters are proposed based on the narrowest confidence interval. Simulation and case study show that the proposed Gamma control limits outperform the conventional equal-tail probability limits, since the proposed Gamma control charts have shorter width and are more sensitive to detect the increase of parameter θ than the traditional ones.