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This paper develops a truncated saddlepoint (TS) control chart for the mean of a population with a skewed density. This chart requires the estimation of only a few population cumulants from sample data and is relatively straightforward in construction. Performance is assessed at various levels of truncation in terms of type 1 and 2 error rates and compared with other heuristic control charts via the Monte Carlo simulation. The truncated saddlepoint (TS) chart is shown to generally outperform these charts, especially in cases with small sample sizes or high levels of population skewness.

Compliance to evidenced-base practices, individually and in 'bundles', remains an important focus of healthcare quality improvement for many clinical conditions. The exact probability distribution of composite bundle compliance measures used to develop corresponding control charts and other statistical tests is based on a fairly large convolution whose direct calculation can be computationally prohibitive. Various series expansions and other approximation approaches have been proposed, each with computational and accuracy tradeoffs, especially in the tails. This same probability distribution also arises in other important healthcare applications, such as for risk-adjusted outcomes and bed demand prediction, with the same computational difficulties. As an alternative, we use probability generating functions to rapidly obtain exact results and illustrate the improved accuracy and detection over other methods. Numerical testing across a wide range of applications demonstrates the computational efficiency and accuracy of this approach.

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