| Multivariate quality control is used when the quality of a production process depends on several correlated variables. The object of the control procedure is to jointly use sample data from each variable to monitor the process. In other words, one statistic describes all of the variables of concern. The quality variable x is a vector of p quality characteristics; {dollar}x = (xsb1,xsb2,...,xsb{lcub}p{rcub}){dollar}; with mean vector; {dollar}mu = (musb1,musb2,...,musb{lcub}p{rcub}){dollar}; and covariance matrix {dollar}Sigma{dollar}.; Most of the research performed in this area assumes the variables that describe the quality characteristics have a joint normal distribution. Additionally, in much of the research it is assumed that the covariance matrix, {dollar}Sigma{dollar}, is known. When the sample statistics are sample averages and the sample size is at least as large as four to six, it has been shown that the assumption of normally distributed variables is usually reasonable. However, it is not always possible to obtain large sample sizes and the assumption of normally distributed quality characteristics may not be met. Nonparametric multivariate quality control methods are a means by which to control the error rate for any distribution of variables. Two classes of nonparametric multivariate quality control methods are developed along with a nonparametric multivariate exponentially weighted EWMA chart, nonparametric Phase I procedures, and methods of detecting the aberrant variables. Recommendations are also made concerning pool size and procedures for updating the data pool. |
