0120-1751

S0120-17512006000200003

México

05 12 2006

29 2 163 180

Cartas de control Bayesianas para atributos y el tamaño de subgrupo grande en la carta p

Bayesian Control Charts for Attributes and the Large Subgroup Size in p Chart

HUMBERTO GUTIÉRREZ¹

¹Universidad de Guadalajara, Jalisco, México, Profesor, E-mail:humpulido@yahoo.com

Resumen

]]> Se analizan los problemas de las cartas de control para atributos. En particular, se ve que el procedimiento tradicional para obtener los límites de control tiene varias dificultades: no incorpora la incertidumbre sobre la estimación del parámetro del modelo, no contempla las variaciones en el parámetro del proceso y requiere un período base para obtener datos. Durante este período base no se tiene una carta de control para monitorear el proceso. Se ve que estos problemas son resueltos con métodos Bayesianos. Se ve cómo establecer los límites de control Bayesianos para las cartas de control p, np, c y u, en forma secuencial desde la primera observación. Esto elimina la necesidad del período base. Por último se analiza el problema de la carta p cuando esta se basa en un tamaño de subgrupo grande y se propone una solución Bayesiana para este problema.

Palabras clave: control de calidad, métodos Bayesianos, distribución betabinomial, distribución Poisson-gama.

Abstract

The problems of the control charts for attributes are analyzed. In particular, it is seen that the traditional procedure to obtain the control limits has several difficulties: it does not incorporate the uncertainty in the estimate of the parameter of the distribution, it does not include the variation of the process, and the procedure requires a base period to obtain the control limits. Along this period it does not have a control chart to analyze the process. It is seen that these problems are solved applying Bayesian methods. It is described a sequential procedure to obtain the Bayesian control limits for p, np, c and u charts, from the first observation. This eliminates the necessity of the base period. Lastly it is analyzed the problem of the p chart when it is based on a large subgroup size and it is proposed a Bayesian solution for this problem.

Key words: Quality control, Bayesian methods, Beta-binomial distribution, Poisson-gamma distribution.

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Referencias

1. Bayarri, M. & García-Donato, G. (2005), "Bayesian Sequential Look at u-control Charts", Technometrics 47(2), 142-151. [ Links ]

2. Bernardo, J. & Smith, A. (1994), Bayesian Theory, Wiley & Sons, New York. [ Links ]

3. Calvin, T. (1984), How and When to Perform Bayesian Acceptance Sampling, in "38th Annual Quality Congress", American Society for Quality, Milwaukee, EU, pp. 141-145. [ Links ]

4. Del Castillo, E., Grayson, J., Montgomery, D. & Runger, G. (1996), "A Review of Statistical Process Control Techniques for Short Run Manufacturing Systems", Communications in Statistics-Theory and Methods 25(11), 2723-2737. [ Links ]

5. Gutiérrez, H. & Aguirre, V. (2005), A Method of Moments Procedure for Eliciting Prior Distributions, Reporte técnico de-c05.8, Instituto Tecnológico Autónomo de México (ITAM), México. [ Links ]

6. Gutiérrez, H. & Camacho, O. (1996), Ineficiencia de la carta p para tamaños de subgrupo grandes: diagnóstico y alternativas., in "Memorias del X Foro Nacional de Estadística y del II Congreso Iberoamericano de Estadística", Asociación Mexicana de Estadística e Inegi, México. [ Links ]

7. Gutiérrez, H. & Camacho, O. (1998), "Modificación de las cartas de atributos (p, np, cyu) para mejorar su aproximación a la significancia bajo normalidad", Agrociencia 32(4), 385-394. [ Links ]

8.Gutiérrez, H. & De la Vara, R. (2004), Control estadístico de calidad y seis sigma, McGraw-Hill, México. [ Links ]

9. Hamada, M. (2002), "Bayesian Tolerance Interval Control Limits for Attributes", Quality and Reliability Engineering International 58(1), 45-52. [ Links ]

10.Heimann, P. (1996), "Atributes Control Charts with Large Sample Sizes", Journal of Quality Technology 28(4), 451-459. [ Links ]

11. Irony, T. & Pereira, C. (1994), "Motivation for the Use of Discrete Distribution in Quality Assurance", Test 3, 181-193. [ Links ]

12. Quarshie, B. & Shindo, H. (1996), "A Comparison of Operating Characteristics of the p - V and the p - Rp Charts", Quality Engineering 9(2), 221-228. [ Links ]

13. Sheaffer, R. &, Leavenworth, R. (1976), "The Negative Binomial Model for Counts in Units of Varying Size", Journal of Quality Technology 8, 158-163. [ Links ]

14. Tsiamyrtzis, P. & Hawkins, D. (2005), "A Bayesian Scheme to Detect Changes in the Mean of a Short-Run Process", Technometrics 47(4), 446-456. [ Links ] ]]> 1 2005 47 2 2 142-151 2 1994 3 1984 141-145 4 1996 25 11 11 2723-2737 5 2005 6 Asociación Mexicana de Estadística e Inegi 1996 7 1998 32 4 4 385-394 8 2004 9 2002 58 1 1 45-52 10 1996 28 4 4 451-459 11 1994 3 3 181-193 12 1996 9 2 2 221-228 13 1976 8 158-163 14 2005 47 4 4 446-456