ARL Numerics for MEWMA Charts

Abstract

The FORTRAN code in Bodden and Rigdon (1999) for the in-control average run length (ARL) of multivariate exponentially weighted moving average charts (MEWMA) became quite popular and is widely used in statistical software systems such as MINITAB and STATISTICA. We find that the algorithms' accuracy is poor for low-dimensional processes. The Markov chain approximation described in Runger and Prabhu (1996) is not able to resolve the issue. The same holds for the calculation of the out-of-control ARL as proposed in Ridgon (1995b). We present two concepts that achieve higher accuracy for all dimensions. The competing numerical procedures are implemented in the R package spc.

• Collocation
• Fredholm Integral Equation of the Second Kind
• Markov Chain Approximation
• Multivariate Statistical Process Control
• Nyström Method
• Software implementation

Additional information

Notes on contributors

Sven Knoth

Dr. Knoth is a Professor in the Department of Mathematics and Statistics within the School of Economic and Social Sciences. His email is [email protected].