Economic-statistical design of multivariate control charts for monitoring the mean vector and covariance matrix

When a control chart is used to monitor a process, three test parameters should be determined: the sample size, the sampling interval between successive samples, and the control limits or critical region of the chart. In this paper, we present the procedure to conduct the economic-statistical design of multivariate control charts for monitoring the process mean vector and covariance matrix simultaneously; i.e. to economically determine the optimum values of the three test parameters such that the statistical constraints (including the type I error probability and power) of the control chart can be satisfied. The test statistic -2lnL is applied to develop this procedure and the cost model is established based on the function given by Montgomery and Klatt. A numerical example is provided to illustrate the solution procedure of the design and then the effects of cost parameters on the optimal design are examined. (C) 2003 Elsevier Science Ltd. All rights reserved.