Attribute charts for monitoring the mean vector of bivariate processes

Abstract

This article proposes two Shewhart charts, denoted np(xy) and np(w) charts, which use attribute inspection to control the mean vector ((x); (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+2N(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 (c) 2014 John Wiley &Sons, Ltd.