AVERAGE RUN LENGTH COMPUTATION OF ARMA CHARTS FOR STATIONARY PROCESSES

Abstract

The ARMA chart is a unified family of statistical process control techniques proposed in [1] for monitoring the mean level of stationary processes. Based on simulation studies, the ARMA chart has been shown to be comparable to the optimal EWMA chart for monitoring IID processes and outperform other conventional charts proposed for monitoring autocorrelated processes. In this paper, a Markov chain model is developed for evaluating the run length performance of the ARMA chart applied to an ARMA(p, q) process. The algorithm is implemented using Sparse Matrix operations in MATLAB and the approximation results are consistent with the simulation results.

Keywords:

• Average run length
• Markov chain
• Sparse matrix
• Statistical process control

ACKNOWLEDGMENT

I would like to thank the editor and the associate editor for their many helpful suggestions that significantly improved the content and quality of this paper.