A CUSUM Chart for Monitoring a Proportion with Autocorrelated Binary Observations

• Autores: Shabnam Mousavi, Marion R. Reynolds Jr.
• Localización: Journal of quality technology: A quarterly journal of methods applications and related topics, ISSN 0022-4065, Vol. 41, Nº. 4, 2009, págs. 401-414
• Idioma: inglés
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• Resumen

  • When monitoring a proportion ρ with conventional control charts, it is assumed that the binary observations are independent. However, the observations from many processes are autocorrelated, and this can have an adverse effect on the performance of the charts. The problem of monitoring ρ is investigated when there is a continuous stream of binary observations that follow a two-state Markov chain model with first order dependence. A Markov binary CUSUM chart is constructed based on a log-likelihood-ratio statistic. Results show this chart can detect most increases in ρ faster than competing charts. The effect of the size of the Phase I data set used in constructing the proposed chart is also discussed.