A new memory-type monitoring technique for count data

•A new control scheme with memory is proposed and studied.•It can be used for monitoring count data of any type.•Its theoretical properties can be exactly derived.•It has an increased sensitivity in the detection of small and moderate shifts.•It can be used for monitoring industrial and non-industrial processes. The monitoring of count data arise in several industrial applications in which quality characteristics cannot be measured on a continuous numerical scale. Usually, in such cases the interest is on the number of defects or nonconformities that are produced from a manufacturing process. In this work, a new control scheme with memory, suitable for monitoring discrete data, is proposed and studied. It only uses integer-valued weights in the recent as well as in the past observations, while the plotted statistic is also a positive integer. An appropriate Markov chain technique is used for the determination of the entire run-length distribution of the proposed chart. Also, practical guidelines and comparisons with other competitive schemes are provided, demonstrating an increased sensitivity in the detection of small magnitude shifts, especially the decreasing ones. Finally, the practical application of the proposed scheme is illustrated with two numerical examples.