Estimating X¯ Statistical Control Limits for Any Arbitrary Probability Distribution Using Re-Expressed Truncated Cumulants

Shewhart X¯ control charts commonly used for monitoring the mean of a process may be inaccurate or perform poorly when subgroup size is small distribution variable skewed. Truncated saddlepoint distributions can increase accuracy estimated limits by including higher order moments/cumulants in their approximation, yet this not exist lower tail, and thus limit exist. We introduce novel modification which some usually truncated higher-order cumulants are re-expressed as functions lower-order from data manner that ensures existence over complete domain random variable. The approach tested cases where assumed either known sample data, demonstrated healthcare application.