A Note on the Lower-Sided Synthetic Chart for Exponentials

Abstract

The synthetic control chart for exponential data is discussed and an expression is derived for its average run length, as well as its design parameters. The synthetic control chart for exponentials is shown analytically to be a two-in-a-row rule. This chart is compared with the Shewhart chart for individuals and with the worst-case, lower-sided exponential EWMA and CUSUM charts. While the synthetic control chart for exponentials outperforms the Shewhart chart for individuals, the EWMA and CUSUM charts are shown to be far superior in detecting decreases in the exponential mean.

Keywords:

• Shewhart chart
• Synthetic control chart
• EWMA
• CUSUM
• Conforming run length
• Average run length
• Exponential data

Acknowledgments