Explicit analytical solutions for ARL of CUSUM chart for a long-memory SARFIMA model

ABSTRACT

This paper aims to derive explicit analytical solutions for Average Run Length (ARL) of CUSUM chart for the SARFIMA(P,D,Q)_S process with exponential white noise. Measurement of performance was done with the ARL in terms of percentage error and CPU time. The results obtained from the explicit formulas were compared focusing on the performance using the numerical integral equation (NIE) method. Both methods had similarly excellent agreement with the percentage error at less than 0.25%. Meanwhile, the explicit formulas consumed less CPU time than the NIE method. It is clear that the explicit formulas are a good alternative in real applications.

KEYWORDS:

• SARFIMA(P,D,Q)_S process
• Average Run Length (ARL)
• Numerical Integral Equation (NIE) method
• Exponential white noise

Conflict of interests

The authors declare that they have no conflict of interests.

Acknowledgements

The research was funding by King Mongkut's University of Technology North Bangkok Contract no. KMUTNB-60-ART-47.