An integral equation for the in-control average run length of a multivariate exponentially weighted moving average control chart

Abstract

An integral equation is given for the in-control average run length of a multivariate exponentially weighted moving average control chart. This integral equation is used to determine the appropriate upper control limits for various values of the smoothing constant r, the dimension p of the measured quality characteristic, and the desired in-control average run length L _o Tables are given which allow a user to select the appropriate value of the upper control limit given these three conditions.

Keywords:

• Multivariate quality control
• Secant method
• Radau quadrature