InfraTech Journal of Sustainable Architecture and Civil Engineering
History is written by the winners. Reflections on Control Charts for Process Control
Abstract
Fausto Galetto
We use the Jarrett (1979) data from “A Note on the Intervals Between Coal-Mining Disasters” and the analysis by Kumar et al., and by Zhang et al. From the analysis we get different results: the cause is that they use the Probability Limits of the PI (Probability Interval) as they were the Control Limits (so they name them) of the Control Charts (CCs): those authors do not extract the complete information from the statistical data of CCs for TBE (Time Between Events) data exponentially distributed or not normally distributed. The Control Limits in the Shewhart CCs are based on the Normal Distribution (Central Limit Theorem, CLT) and are not valid for non-normal distributed data: consequently, the decisions about the “In Control” (IC) and “Out Of Control” (OOC) states of the process are wrong. The Control Limits of the CCs are wrongly computed, due to unsound knowledge of the fundamental concept of Confidence Interval. Minitab and other software (e.g. JMP, SAS) use the “T Charts”, claimed to be a good method for dealing with “rare events”, but their computed Control Limits of the CCs are wrong. We will show that the Reliability Integral Theory (RIT) is able to solve these problems.
