Run-length distributions of Q-chart schemes

This article studies the performance of the Shewhart chart of Q statistics in the detection of process mean shifts in start-up processes and short runs. We propose an accurate, analytic approximation of this chart's run-length distribution. Our study reveals that the chart has an early detection advantage in that it is more likely than other methods to detect a process mean shift within the first few observations following the shift. This is a desirable property because early detection should make it easier to identify the cause of the shift, increasing the rate of continuous quality improvement. In addition, our analysis illustrates the importance of reacting immediately to out-of-control signals from the chart as compared to waiting for subsequent observations to confirm the presence of a shift.

Acknowledgements

The author is grateful to the anonymous referees and the Department Editor for several constructive comments that have improved this article. He also thanks S. “Raghu” Raghavan for assistance with computing and Frank B. Alt, Michael C. Fu, Douglas M. Hawkins, S. Lele, Robert D. Plante, and Charles P. Quesenberry for helpful comments and suggestions related to this research.