The I'-chart: a preliminary investigation of an improved individuals chart for quality improvement and control

Statistical Process Control (SPC) charts are widely used in healthcare to monitor and improve quality. Selecting the appropriate chart can be challenging because healthcare data often comprise subgroup summary measures derived from varying numbers of observations. The traditional Individuals (I-) chart is popular because of its simplicity but assumes constant subgroup sizes, an assumption frequently violated in practice. This can lead to inappropriate control limits and misleading interpretation. We describe the I'-chart, an extension of the traditional I-chart that accommodates varying subgroup sizes while remaining applicable to both measurement and attribute data and present a preliminary evaluation of its performance.

The I'-chart was evaluated using a range of simulated and real-world healthcare datasets to address three practical questions: (a) How does the I'-chart compare with the traditional I-chart when subgroup sizes are constant? (b) How does the I'-chart accommodate varying subgroup sizes? (c) How does the I'-chart compare with other established SPC charts?

(a) The I'-chart produced identical results to the traditional I-chart when subgroup sizes were constant, confirming that it generalises the conventional I-chart. (b) When subgroup sizes varied, the I'-chart adjusted the control limits according to subgroup size, making differences in data precision explicit and, in a healthcare example, changing an apparent special-cause signal into expected common-cause variation. (c) The control limits produced by the I'-chart using simulated data were broadly comparable with those from established SPC charts, including the Xbar-chart for measurement data and Laney's P'- and U'-charts for attribute data.

The I'-chart has superior design properties to the traditional I-chart while retaining its simplicity and ease of interpretation. By explicitly accounting for varying subgroup sizes, it addresses an important limitation of the traditional I-chart. Our findings support replacing the traditional I-chart whenever subgroup summary data with varying subgroup sizes are analysed. Although further methodological and empirical evaluation is required to establish its operating characteristics and define its role alongside other SPC charts, the examples presented suggest that the I'-chart produces results comparable with established SPC methods while providing a single, generalisable framework for analysing subgroup summary data.