An Improved p Chart for Monitoring High Quality Processes Based on Cornish-Fisher Quantile Correction

The conventional Shewhart 3-sigma p control chart constructed by the normal approximation for the binomial data suffers a serious inaccuracy in the modeling process and control limits specification when the true rate of nonconforming items is small. We offer an improved p chart which can provide a large improvement over the usual p chart for attributes. This new chart, based on the Cornish-Fisher expansion, is corrected to order $n^{-3/2}$, where $n$ is the sample size of inspections units. This chart is also better than the modified p chart corrected only to order $n^{-1}$, especially in thesense that it allows monitoring lower values of p. We compare our improved p chart with both and show the benefits of including a new term of correction in the Cornish-Fisher expansion of quantiles for monitoring high-quality processes.