Sequential Tests and Decisions. Application to Process Control

Abstract

Fausto Galetto

We use the data of three papers “Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution” (Zhuang et al.), “Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing” (Hu et al.) and “On Designing of Bayesian Shewhart-Type Control Charts for Maxwell Distributed Processes with Application of Boring Machine” (Alshahrani et al.) to compare the above authors findings with ours. 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 Confidence Limits (Control Limits of the Control Charts, CCs). 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. The same happens for the Confidence Limits of the parameters of the distribution involved in the papers (Weibull, Inverse Weibull, Gamma, Binomial, Maxwell). We will show that the Reliability Integral Theory (RIT) is able to solve these problems and the Sequential way of dealing with data.

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