A Note on "Modified Tukey's Control Chart" - Lee, Pei-Hsi; Torng, Chau-Chen (Communications in statistics. Simulation and computation, 2015)
Tercero-Gomez et al. [Communications in Statistics - Simulation and Computation, 2012, 41(9), pp. 1566-1579] modified the Tukey's chart to improve the insensitivity of signaling mean shifts when the population is skewly distributed. They examine the efficiency for several skewed populations with the modified Tukey's chart (MTCC). The parameters of the MTCC were intuitively calibrated to fit several gamma distributions without following a specific mathematical procedure. Moreover, they performed no optimization for specific distributions. This study optimizes the MTCC with a statistical model for each skewed population and reexamines its efficiency. A numerical comparison shows that the optimal MTCC is sensitive to detect the shift of the means.