Saowanit Sukparungsee

DOI: 10.14456/sjst-psu.2018.168

pp. 1368 - 1377

Abstract

The objective of this research is to propose an approximation average run length (ARL) using the Markov chain
approach (MCA) of a generally weighted moving average chart (GWMA) when observations are based on an underlying
binomial distribution. The numerical results obtained from the MCA were compared with the results obtained from a Monte
Carlo (MC) simulation method and the efficiency of the ARL was measured by CPU time. The performances of the GWMA and
exponentially weighted moving average (EWMA) charts were compared in terms of monitoring the change in the process mean
as defined by an out-of-control average run length (ARL1). The numerical results showed that the results of the ARL obtained
from MCA were in good agreement with the results obtained from MC; however, the MCA took less CPU time than the MC
simulation method. Furthermore, the performance of the GWMA chart was superior to the EWMA chart when the magnitudes of
change were small (δ≤0.05), otherwise the EWMA performed better than the GWMA chart.

Keywords

• closed-form formulae
• time-varying chart
• time consuming
• binomial distribution and stopping times