An approximation of average run length using the Markov chain approach of a generally weighted moving average chart to monitor the number of defects

摘要

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