Table 3

Comparison of out-of-control ARLs, in number of observations, for Shewhart p-chart with 3-sigma limits with different reporting periods

Volume per period:			30		50		100		200		500
Baseline event rate	Absolute shift	OR	In-control ARL	Out-of-control ARL	In-control ARL	Out-of-control ARL	In-control ARL	Out-of-control ARL	In-control ARL	Out-of-control ARL	In-control ARL	Out-of-control ARL
1%	−0.5%	0.5	N/A*	N/A*	N/A*	N/A*	N/A*	N/A*	N/A*	N/A*	61 000	5 000
	+1%	2.0	840	270	2 150	400	3 200	600	14 400	1 000	48 500	1 500
	+2%	3.1	840	150	2 150	200	3 200	300	14 400	600	48 500	1 000
10%	−5%	0.5	2 700	330	6 150†	500	14 600†	500	38 800†	600	1 15 000†	1 000
	+5%	1.6	2190	270	5 850	400	9 800	400	29 000	600	94 500	1 000
	+10%	2.3	2 190	120	5 850	150	9 800	200	29 000	400	94 500	1 000
50%	−15%	0.5	4 710	180	8 750	200	16 000	200	43 000	400	1 09 500	1 000
	+15%	1.9	4 710	180	8 750	200	16 000	200	43 000	400	1 09 500	1 000
	+25%	3.0	4 710	60	8 750	100	16 000	200	43 000	400	1 09 500	500

*Lower-limits of chart are at zero so decreases cannot be detected.
†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.