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Attribute Charts for Monitoring the Mean Vector of Bivariate Processes
Author(s) -
Lee Ho Linda,
Costa Antonio
Publication year - 2015
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.1628
Subject(s) - bivariate analysis , control chart , mathematics , statistic , statistics , \bar x and r chart , chart , x bar chart , multivariate normal distribution , control limits , covariance matrix , combinatorics , computer science , multivariate statistics , process (computing) , operating system
This article proposes two Shewhart charts, denoted np xy and np w charts, which use attribute inspection to control the mean vector (μ x ; μ y )′ of bivariate processes. The units of the sample are classified as first‐class, second‐class, or third‐class units, according to discriminate limits and the values of their two quality characteristics, X and Y . When the np xy chart is in use, the monitoring statistic is M = N 1 + N 2 , where N 1 and N 2 are the number of sample units with a second‐class and third‐class classification, respectively. When the np w chart is in use, the monitoring statistic is W = N 1 + 2 N 2 . We assume that the quality characteristics X and Y follow a bivariate normal distribution and that the assignable cause shifts the mean vector without changing the covariance matrix. In general, the synthetic np xy and np w charts require twice larger samples to outperform the T 2 chart. Copyright © 2014 John Wiley & Sons, Ltd.