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Optimal Design of VSI ―X Control Charts for Monitoring Correlated Samples
Author(s) -
Chen YanKwang,
Chiou KuoChing
Publication year - 2005
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.684
Subject(s) - control chart , statistics , interval (graph theory) , sample size determination , sampling (signal processing) , mathematics , multivariate statistics , computer science , process (computing) , filter (signal processing) , combinatorics , computer vision , operating system
This paper develops an economic design of variable sampling interval (VSI)― X control charts in which the next sample is taken sooner than usual if there is an indication that the process is off‐target. When designing VSI― X control charts, the underlying assumption is that the measurements within a sample are independent. However, there are many practical situations that violate this hypothesis. Accordingly, a cost model combining the multivariate normal distribution model given by Yang and Hancock with Bai and Lee's cost model is proposed to develop the design of VSI charts for correlated data. An evolutionary search method to find the optimal design parameters for this model is presented. Also, we compare VSI and traditional ― X charts with respect to expected cost per unit time, utilizing hypothetical cost and process parameters as well as various correlation coefficients. The results indicate that VSI control charts outperform the traditional control charts for larger mean shift when correlation is present. In addition, there is a difference between the design parameters of VSI charts when correlation is present or absent. Copyright © 2005 John Wiley & Sons, Ltd.