A triple exponentially weighted moving average control chart for monitoring time between events

Time between events (TBE) charts are used in high-yield processes where the rate of occurrences is very low. In the current article, we propose a triple exponentially weighted moving average control chart to monitor TBE (regarded as triple exponentially weighted moving average TEWMA-TBE chart) modeled by a gamma distribution. One- and two-sided schemes of the proposed chart are designed and compared with the double EWMA DEWMA-TBE and EWMA-TBE charts. It is shown that the lower- and two-sided TEWMA-TBE charts outperform its competitors, especially for small to moderate downward shifts, while the upper-sided TEWMA-TBE chart has very good detection ability for small shifts. We also study the robustness of the proposed chart when the true distribution is a Weibull or a lognormal and it is found that the TEWMA-TBE chart has better robustness properties than its competitors, especially for small shifts. Two illustrative examples from airplane accidents and earthquakes are also provided to display the application of the proposed chart.