Economic Design of X Control Charts for Monitoring a First Order Autoregressive Process

  • Antonio F. B. Costa UNESP
  • Fernando Antonio Elias Claro UNITAU
Keywords: Autocorrelation, First Order Autoregressive Model, Economic Design, Control Chart, Statistical Process Control


In this paper we deal with the economic design of an X control chart
used to monitor a quality characteristic whose observations fit to a first order
autoregressive model. The Duncan cost model is used to select the control
chart parameters, namely the sample size (n), the sampling interval (h) and
the control limit coefficient (k), that lead to the optimal monitoring cost. We
found that the autocorrelation has an adverse effect on the chart’s power, on
the false alarm risk and on the cost. It also increases n and h and decreases
k. To counteract this undesired effect we considered setting up the subgroups
using non-sequential observations. It is shown that this sampling strategy
significantly reduces the monitoring cost.


Author Biographies

Antonio F. B. Costa, UNESP

Antonio Fernando Branco Costa is an Associate Professor in the
Department of Production Engineering at UNESP – São Paulo State University,
Brazil. He was a postdoctoral fellow in the Center for Quality and Productivity
Improvement at University of Wisconsin, Madison, USA. His current interest
is in statistical quality control. He has published almost half hundred papers
in the Brazilian Journal of Operations & Production Management, Gestão e
Produção, Produção, Pesquisa Operacional, Journal of Quality Technology,
European Journal of Operational Research, IIE Transactions, Journal of Applied
Statistics, International Journal of Production Economics, International Journal
of Production Research, Journal of Quality Maintenance in Engineering,
Quality Technology and Quantitative Management, International Journal of
Advanced Manufacturing Technology, Quality and Reliability Engineering
International and Communications in Statistics. He is an active reviewer for
several journals and an ASQ Certified Quality Engineer. He was the recipient
of an IIE Transactions best paper award.


Fernando Antonio Elias Claro, UNITAU

Fernando Antonio Elias Claro is currently a visiting professor in the
post-graduation program of the Taubate University’s Mechanical Engineering
Dept. He is an ASQ certified quality engineer, certified reliability engineer and
certified Manager of Quality - Organizational Excellence. His current interest
is in statistical quality control and design of experiments.


How to Cite
Costa, A., & Claro, F. A. (1). Economic Design of X Control Charts for Monitoring a First Order Autoregressive Process. Brazilian Journal of Operations & Production Management, 6(2), 7-26. Retrieved from

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