Attribute Charts for Monitoring the Mean Vector of Bivariate Processes

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.