Comparison of out-of-control ARLs, in number of observations, for the Shewhart p-chart*, the EWMA† the CUSUM‡ and the g-chart
| Baseline event rate | In-control ARL | Size of Shift | Out-of-control ARL | ||||
| Absolute shift | OR | p-chart | EWMA | CUSUM | g-chart | ||
| 1% | 14 400 | −0.5% | 0.5 | N/A§ | N/A§ | 1 500 | 2 400 |
| +1% | 2.0 | 1 000 | 990 | 750 | N/A§ | ||
| +2% | 3.1 | 600 | 350 | 320 | N/A§ | ||
| 10% | 14 600** | −5% | 0.5 | 500 | 520 | 270 | 690 |
| 9 800 | +5% | 1.6 | 400 | 400 | 330 | N/A§ | |
| 9 800 | +10% | 2.3 | 200 | 170 | 70 | N/A§ | |
| 50% | 8 750 | −15% | 0.5 | 200 | 250 | 110 | 500 |
| +15% | 1.9 | 200 | 250 | 110 | N/A§ | ||
| +25% | 3.0 | 100 | 160 | 50 | N/A§ | ||
*3-sigma limits and supplementary runs rules. Reporting periods=200, 100 and 50 cases for 1%, 10% and 50% baseline event rates.
†Value of λ=0.01.
‡OR=2 to detect increases and ½ to detect decreases in rates.
§The lower-limit of the chart is at zero for the selected in-control ARL and chart settings, such that decreases in rates cannot be detected by the p-chart or EWMA, and increases in rates cannot be detected by the g-chart.
**In-control ARLs for a chart set up to detect a decrease can differ from those for a chart set up to detect an increase because the exact binomial probability of crossing the upper limit will not always be the same as the exact binomial probability of crossing the lower limit.
ARL, average run length; CUSUM, cumulative sum; EWMA, exponentially weighted moving average.