Run length distribution for a modified EWMA scheme fitted with a stationary AR(p) model

Abstract

A modified exponentially weighted moving average (EWMA) scheme is a quality control chart which can quickly detect small shifts in autocorrelated data. In this article, an explicit formula is presented to calculate the average run length (ARL) for a modified EWMA chart with an autoregressive AR(p) model involving exponential white noise. Its performance is compared with a numerical integral equation method via a simulation study to determine whether the explicit formula can help decrease the processing time. Moreover, this scheme is tested against a classical EWMA control chart using the ARL and RMI results. Finally, the explicit formula for ARL is applied to a real numerical example from the health field to demonstrate the efficacy of our method.

Keywords:

• Autoregressive model
• Average run length
• Explicit formula
• Integral equation
• Modified EWMA

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62P30
• 65R20
• 45B05

Additional information

Funding

The research was funding by King Mongkut's University of Technology North Bangkok Contract no. KMUTNB-FF-65-45.