Improved control charts for fraction non-conforming based on hypergeometric distribution

Abstract In this paper we introduce the control chart for fraction non-conforming based on the Hypergeometric distribution, and propose the exact Hypergeometric test for a population proportion to detect significant changes in the process quality level. In contrast to the common Binomial p-chart, which is especially suitable for sampling from continuous production processes, the Hypergeometric p-chart can be established also for periodical production processes, where sampled items successively produced during one period are not stochastically independent and the probability of a sampled item being non-conforming depends on the previous sampled item. Further, while the Binomial p-chart does not take the fluctuation of the production process into account, the Hypergeometric p-chart enables consideration of the population size of periodical production appropriately. The Hypergeometric p-chart leads in general to lower probabilities of the type I error, i.e. false rejection of the hypothesis of statistical control, to a considerably higher in-control ARL, and thus to a significantly lower frequency of false alarms. Moreover, it provides monitoring of a manufacturing process with a considerably lower inspection effort than its Binomial counterpart. Finally, the exact Hypergeometric test leads to more accurate test decisions in detecting process shifts compared with the common used approximate Binomial test.