Hypergeometric p-chart with dynamic probability control limits for monitoring processes with variable sample and population sizes

Abstract Control charts for monitoring fractions non-conforming are widely used in healthcare surveillance, industrial quality control, and service operations management. They are usually based on the assumption of Binomial-distributed variables, control limits approximated by the Normal distribution and infinitely large population size. However, there are many practical situations where the assumption of Binomial-distributed data is not satisfied, for instance when the underlying periodic population is of a finite size and random sampling complies with sampling without replacement. Moreover, the Normal approximation is often inappropriate and efficient monitoring requires control charts to be able to take varying population sizes into account. To overcome these drawbacks of the traditional p-chart, we present in this paper the Hypergeometric p-chart with probability control limits, where fraction data is assumed to follow the Hypergeometric distribution and control limits are calculated using exact Hypergeometric probabilities in compliance with time-varying sample and population sizes. This approach enables a dynamic and thus more general modelling of the control limits, i.e. the probability control limits are capable of accommodating more complex situations in practice in a natural way.