Shewhart p-chart | g-chart | EWMA | CUSUM | ||||||||

Chart statistic | where p _{j} is the proportion in the j^{th} reporting period, n_{j} is the volume and x_{ij} is the i^{th} observation in the j^{th} period | where s _{k} is the number of observations between events, i_{k} is the sequence number of the kth event | where s _{i} is the i^{th} value of the trace, x_{i} is the ith observation and λ is the weighting parameter | where where s _{i} is the ith value of the trace, x_{i} is the ith observation, p is the baseline event rate and OR is the OR corresponding to the minimum shift size the chart should detect | |||||||

Target line | Baseline event rate, p | Baseline mean number between events, or (1−p)/p | Baseline event rate, p | No target line. Trace moves between zero and the control limit | |||||||

Control limits | where L is the number of SEs (sigma) from the target line (see main text for runs rules) | Absolute value for limit | |||||||||

Chart settings | p | n per period | Only limits are altered | λ=0.01 | OR=2 for an increase and 0.5 for a decrease | ||||||

<0.02 0.02 to <0.1 0.1 to 0.5 | 200 100 50 | ||||||||||

In-control ARLs* | For L=3 with runs rules, n as above: | To detect a decrease: | For λ=0.01: | For OR=2: | |||||||

p | In-control ARL | p | L | In-control ARL | p | L | In-control ARL | p | Limit | In-control ARL | |

0.01 0.10 0.50 | 14 400 9 800 8 750 | 0.01 0.10 0.50 | 4.0 6.0 8.0 | 14 800 10 500 8 200 | 0.01 0.10 0.50 | 4.3 3.3 2.9 | 15 250 10 050 8 460 | 0.01 0.10 0.50 | 3.5 3.5 6.0 | 14 290 9 300 8 900 |

*In-control ARLs are given for specified values of control limits. Control limits were more finely adjusted to achieve in-control ARLs for comparisons in table 2.

ARL, average run length; CUSUM, cumulative sum; EWMA, exponentially weighted moving average.