Binomial funnel control limits ($p_0\pm z_{1-\alpha /2}\sqrt{p_0(1-p_0)/n}$)

The displayed pointwise control limits follow from the normal approximation to an observed binomial proportion. Clip plotted limits to the probability range. Their nominal coverage is approximate and can be poor for small expected counts; exact binomial tails give a discrete alternative. Pointwise coverage does not provide simultaneous coverage of all hospitals; use Bonferroni correction or another familywise error rate procedure when that is the required guarantee.