On the constrained economic design of control charts: a literature review

Sobre planejamento de gráficos de controle com restrição: uma revisão da literatura

Celano, Giovanni

Downloads: 0
Views: 232


The economic design is an appealing approach to settle the design parameters of a control chart. Unfortunately, the economic models to design control charts have been scarcely implemented by quality practitioners due to the simplifying assumptions when representing the multifaceted complexity and constraints present within manufacturing and transactional environments. Although there has been an increasing scepticism about the economic models usefulness in practice, some recent studies proposed in literature face the problem of the control charts economic design from a new point of view: the objective is to achieve a well balanced trade-off between the operational and the statistical aspects. Under this perspective, the economic design problem can be intended in a broader sense as the constrained design of a SPC inspection procedure. This paper presents a discussion of some recent trends in the economic design stream of research and outlines the importance of considering the constraints related to SPC resources availability and modelling the occurrence of random shifts.


Control chart. Economic design. Resource availability. Random shift


O planejamento econômico é uma abordagem interessante para estabelecer os parâmetros de um gráfico de controle. Infelizmente, os modelos econômicos para planejar gráficos de controle têm sido pouco aplicados por profissionais de qualidade, devido às suposições simplificadoras utilizadas para representar complexos e multifacetados (com restrições presentes) processos de produção e ambientes transacionais. Embora tenha havido um crescente ceticismo sobre a utilidade de modelos econômicos, na prática, alguns estudos recentes na literatura tratam o problema de planejameto econômico dos gráficos de controle sob um novo ponto de vista: o objetivo é conseguir um bom trade‑off e ligação entre aspectos operacionais e estatísticos. Sob essa perspectiva, o problema de planejamento econômico pode ser visto, em um sentido mais amplo, como um planejamento com restrição em um procedimento de inspeção no controle estatístico de processo. Este trabalho apresenta uma discussão de algumas das novas tendências no que se refere às pesquisas em planejamento econômico e descreve a importância de considerar as restrições relacionadas com a disponibilidade de recursos em um controle estatístico de processo e modelagem da ocorrência de mudanças aleatórias.


Gráfico de controle. Planejamento econômico. Disponibilidade de recursos. Mudança aleatória.


ALT, F. B. Multivariate quality control. In: JOHNSON, N. L.; KOTZ, S. (Ed.). Encyclopedia of Statistical Science. New York: Wiley, 1985.

BASSEVILLE, M.; NIKIFOROV, I. Detection of abrupt changes - Theory and application. Englewood Cliffs: Prentice Hall, 1993.

BENJAMINI, Y.; HOCHBERG, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society B, v. 57, p. 289-300, 1995.

BOCK, D. Aspects on the control of false alarms in statistical surveillance and the impact on the return of financial decision systems. Journal of Applied Statistics, v. 35, p. 213-227, 2008.

BODNAR, O.; SCHMID, W. Year. CUSUM control schemes for multivariate time series. In: FRONTIERS in statistical quality control. Intelligent statistical quality control. Warsaw, 2004.

CHAN, L. K.; ZHANG, J. Cumulative sum control charts for the covariance matrix. Statistica Sinica, v. 11, p. 767-790, 2001.

CROSIER, R. B. Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, v. 30, p. 291-303, 1988.

FRICKER, R. D. Directionally sensitive multivariate statistical process control procedures with application to syndromic surveillance. Advances in Disease Surveillance, v. 3, p. 1-17, 2007.

FRISÉN, M. Evaluations of methods for statistical surveillance. Statistics in Medicine, v. 11, p. 1489-1502, 1992.

FRISÉN, M. Statistical surveillance. Optimality and methods. International Statistical Review, v. 71, p. 403-434, 2003.

FRISÉN, M.; ANDERSSON, E.; SCHIÖLER, L. Evaluation of multivariate surveillance. Journal of Applied Statistics, 2010a.

FRISÉN, M.; ANDERSSON, E.; SCHIÖLER, L. Sufficient reduction in multivariate surveillance. Communications in Statistics - Theory and Methods, 2010b.

FRISÉN, M.; DE MARÉ, J. Optimal surveillance. Biometrika, v. 78, p. 271-80, 1991.

FUCHS, C.; BENJAMINI, Y. Multivariate profile charts for statistical process control. Technometrics, v. 36, p. 182-195, 1994.

GOLOSNOY, V.; SCHMID, W.; OKHRIN, I. Sequential monitoring of optimal portfolioweights. In: FRISÉN, M. (Ed.). Financial surveillance. Chichester: Wiley, 2007.

HAUCK, D. J.; RUNGER, G. C.; MONTGOMERY, D. C. Multivariate statistical process monitoring and diagnosis with grouped regression-adjusted variables. Communications in Statistics. Simulation and Computation, v. 28, p. 309-328, 1999.

HAWKINS, D. M. Multivariate quality control based on regression-adjusted variables. Technometrics, v. 33, p. 61-75, 1991.

HEALY, J. D. A note on multivariate CUSUM procedures. Technometrics, v. 29, p. 409-412, 1987.

HOCHBERG, Y.; TAMHANE, A. C. Multiple comparison procedures. New York: Wiley, 1987.

HOTELLING, H. Multivariate quality control. In: EISENHART, C.; HASTAY, M. W.; WALLIS, W. A. (Ed.). Techniques of statistical analysis. New York: McGraw-Hill, 1947.

JACKSON, J. E. Multivariate quality control. Communications in statistics. Theory and methods, v. 14, p. 2657-2688, 1985.

KNOTH, S.; SCHMID, W. Monitoring the mean and the variance of a stationary process. Statistica Neerlandica, v. 56, p. 77-100, 2002.

KOURTI, T.; MACGREGOR, J. F. Multivariate SPC methods for process and product monitoring. Journal of Quality Technology, v. 28, p. 409-428, 1996.

LIU, R. Y. Control charts for multivariate processes. Journal of the American Statistical Association, v. 90, p. 1380-1387, 1995.

LOWRY, C. A. et al. A multivariate exponentially weighted moving average control chart. Technometrics, v. 34, p. 46-53, 1992.

LOWRY, C. A.; MONTGOMERY, D. C. A review of multivariate control charts. IIE Transactions, v. 27, p. 800-810, 1995.

LU, X. S. et al. Control chart for multivariate attribute processes. International Journal of Production Research, v. 36, p. 3477-3489, 1998.

MARAVELAKIS, P. E. et al. Identifying the out of control variable in a multivariate control chart. Communications in Statistics. Theory and Methods, v. 31, p. 2391-2408, 2002.

MARSHALL, C. et al. Statistical issues in the prospective monitoring of health outcomes across multiple units. Journal of the Royal Statistical Society A, v. 167, p. 541-559, 2004.

MASON, R. L.; TRACY, N. D.; YOUNG, J. C. Decomposition of T2 for multivariate control chart interpretation. Journal of Quality Technology, v. 27, p. 99-108, 1995.

MASTRANGELO, C. M.; RUNGER, G. C.; MONTGOMERY, D. C. Statistical process monitoring with principal components. Quality and Reliability Engineering International, v. 12, p. 203-210, 1996.

MOHEBBI, C.; HAVRE, L. Multivariate control charts: A loss function approach. Sequential Analysis, v. 8, p. 253-268, 1989.

MOSTASHARI, F.; HARTMAN, J. Syndromic surveillance: a local perspective. Journal of Urban Health, v. 80, p. 11-I7, 2003.

NGAI, H. M.; ZHANG, J. Multivariate cumulative sum control charts based on projection pursuit. Statistica Sinica, v. 11, p. 747-766, 2001.

OKHRIN, Y.; SCHMID, W. Surveillance of univariate and multivariate nonlinear time series. In: FRISÉN, M. (Ed.). Financial surveillance. Chichester: Wiley, 2007.

PIGNATIELLO, J. J.; RUNGER, G. C. Comparisons of multivariate CUSUM charts. Journal of Quality Technology, v. 22, p. 173-186, 1990.

ROGERSON, P. A. Surveillance systems for monitoring the development of spatial patterns. Statistics in Medicine, v. 16, p. 2081-2093, 1997.

ROLKA, H. et al. Issues in applied statistics for public health bioterrorism surveillance using multiple data streams: research needs. Statistics in Medicine, v. 26, p. 1834-1856, 2007.

ROSOLOWSKI, M.; SCHMID, W. EWMA charts for monitoring the mean and the autocovariances of stationary Gaussian processes. Sequential Analysis, v. 22, p. 257-285, 2003.

RUNGER, G. C. et al. Optimal monitoring of multivariate data for fault detection. Journal of Quality Technology, v. 39, p. 159-172, 2007.

RUNGER, G. C. Projections and the U2 chart for multivariate statistical process control. Journal of Quality Technology, v. 28, p. 313-319, 1996.

RYAN, T. P. Statistical methods for quality improvement. New York: Wiley, 2000.

SAHNI, N. S.; AASTVEIT, A. H.; NAES, T. In-Line process and product control using spectroscopy and multivariate calibration. Journal of Quality Technology, v. 37, p. 1-20. 2005.

SHEWHART, W. A. Economic control of quality of manufactured product. London: MacMillan and Co., 1931.

SHIRYAEV, A. N. On optimum methods in quickest detection problems. Theory of Probability and its Applications, v. 8, p. 22-46, 1963.

SKINNER, K. R.; MONTGOMERY, D. C.; RUNGER, G. C. Process monitoring for multiple count data using generalized linear model-based control charts. International Journal of Production Research, v. 41, p. 1167-1180, 2003.

SONESSON, C.; FRISÉN, M. Multivariate surveillance. In: LAWSON, A.; KLEINMAN, K. (Ed.). Spatial surveillance for public health. New York: Wiley, 2005.

STEINER, S. H.; COOK, R. J.; FAREWELL, V. T. Monitoring paired binary surgical outcomes using cumulative sum charts. Statistics in Medicine, v. 18, p. 69-86, 1999.

SULLIVAN, J. H.; JONES, L. A. A self-starting control chart for multivariate individual observations. Technometrics, v. 44, p. 24-33, 2002.

TIMM, N. H. Multivariate quality control using finite intersection tests. Journal of Quality Technology, v. 28, p. 233-243, 1996.

TSUI, K. L.; WOODALL, W. H. Multivariate control charts based on loss functions. Sequential Analysis, v. 12, p. 79-92, 1993.

TSUNG, F.; LI, Y.; JIN, M. Statistical process control for multistage manufacturing and service operations: a review and some extensions International Journal of Services Operations and Informatics, v. 3, p. 191-204, 2008.

WÄRMEFJORD, K. Multivariate quality control and diagnosis of sources of variation in assembled products. Thesis (Licentiat)-Göteborg University, 2004.

WESSMAN, P. Some Principles for surveillance adopted for multivariate processes with a common change point. Communications in Statistics. Theory and Methods, v. 27, p. 1143-1161, 1998.

WOODALL, W. H. Current research on profile monitoring. Produção, v. 17, p. 420-425, 2007.

WOODALL, W. H.; AMIRIPARIAN, S. On the economic design of multivariate control charts. Communications in Statistics - Theory and Methods, v. 31, p. 1665-1673, 2002.

WOODALL, W. H.; NCUBE, M. M. Multivariate cusum quality control procedures. Technometrics, v. 27, p. 285-292, 1985.

YASHCHIN, E. Monitoring variance components. Technometrics, v. 36, p. 379-393, 1994.

YEH, A. B. et al. A multivariate exponentially weighted moving average control chart for monitoring process variability. Journal of Applied Statistics, v. 30, p. 507-536, 2003.

5883a3c27f8c9da00c8b4621 1574685864 Articles
Links & Downloads


Share this page
Page Sections