Table 1

Chart formulae and settings used in chart comparisons

 Shewhart p-chart g-chart EWMA CUSUM Chart statistic  where pj is the proportion in the jth reporting period, nj is the volume and xij is the ith observation in the jth period  where sk is the number of observations between events, ik is the sequence number of the kth event  where si is the ith value of the trace, xi is the ith observation and λ is the weighting parameter  where    where si is the ith value of the trace, xi 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.