A control chart is considered for the problem of monitoring a process when
all items from the process are inspected and classified into one of two cat
egories. The objective is to detect changes in the proportion, p, of items
in the first category. The control chart being considered is a cumulative s
um (CUSUM) chart based on the Bernoulli observations corresponding to the i
nspection of the individual items. Bernoulli CUSUM charts can be constructe
d to detect increases in p, decreases in p, or both increases and decreases
in p. The properties of the Bernoulli CUSUM chart are evaluated using exac
t Markov chain methods and by using a corrected diffusion theory approximat
ion. The corrected diffusion theory approximation provides a relatively sim
ple method of designing the chart for practical applications. It is shown t
hat the Bernoulli CUSUM chart will detect changes in p substantially faster
than the traditional approach of grouping items into samples and applying
a Shewhart p-chart. The Bernoulli CUSUM chart is also better than grouping
items into samples and applying a CUSUM chart to the sample statistics. The
Bernoulli CUSUM chart is equivalent to a geometric CUSUM chart which is ba
sed on counting the number of items in the second category that occur betwe
en items in the first category.