Cornish–Fisher-Based Control Charts Inclusive of Skewness and Kurtosis Measures for Monitoring the Mean of a Process

In this paper, we propose control limits for monitoring the mean of a process variable based on a first and second order Cornish–Fisher expansion, which limits are inclusive of its skewness and kurtosis measures, respectively. These are shown to have better in-control error performance than other limits that were similarly derived from this expansion with smoothing functions, both when these measures are assumed to be known and estimated from sample data. The range of measure specifications where the underlying Cornish–Fisher function is monotonic is derived. Operating characteristic curves for select cases demonstrate the associated out-of-control error performance. The Cornish–Fisher limits are applied to a real-life dataset in developing a control chart for monitoring the mean lifetime of car brake pads, wherein they are compared to other limit approximations.