The capability index when some assumptions are not satisfiedanalysis and empirical comparisons

  1. JUAN FRANCISCO MUÑOZ ROSAS 1
  2. ENCARNACIÓN ÁLVAREZ VERDEJO 1
  3. Pablo José Moya Fernández
  1. 1 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

Revista:
Estudios de economía aplicada

ISSN: 1133-3197,  1697-5731

Año de publicación: 2016

Título del ejemplar: Datos, información y conocimiento en Economía

Volumen: 34

Número: 3

Páginas: 649-674

Tipo: Artículo

DOI: 10.25115/EAE.V34I3.3064 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Estudios de economía aplicada

Resumen

El índice de capacidad (PCI) evalúa la habilidad de un proceso para producir artículos con determinados requerimientos de calidad. El PCI depende de la desviación típica del proceso, la cual suele ser desconocida y estimada a partir de la desviación típica muestral. La construcción de intervalos de confianza para el PCI también es un tema relevante. El estimador estándar del PCI y su correspondiente intervalo de confianza están basados en varias hipótesis de partida, tal como normalidad, el hecho de que el proceso se encuentra bajo control, o muestras seleccionadas de poblaciones infinitas. El principal objetivo de este trabajo es investigar las propiedades empíricas de dos estimadores del PCI, y analizar numéricamente el efecto en los intervalos de confianza cuando no se cumplen tales hipótesis, puesto que estas situaciones pueden presentarse en la práctica.

Referencias bibliográficas

  • ÁLVAREZ, E.; MOYA-FÉRNANDEZ, P.J.; BLANCO-ENCOMIENDA, F.J. and MUÑOZ, J.F. (2015). “Methodological insights for industrial quality control management: The impact of various estimators of the standard deviation on the process capability index”. Journal of King Saud University-Science, 27, pp. 271-277.
  • ASLAM, M.; AZAM, M.; WU, C. and JUN, C. (2015). “Mixed acceptance sampling plans for product inspection using process capability index”. Quality Control and Applied Statistics, 60, pp. 455-486.
  • BESTERFIELD, D (2014).: Quality improvement (9th edn). Harlow: Pearson Education.
  • BREYFOGLE, F.W. (2003). Implementing six sigma - smarter solutions using statistical methods. 2nd Edition. New Jersey: John Wiley & Sons, Inc.
  • SCRUCCA, L. (2004). “qcc: an R package for quality control charting and statistical process control”. R News 4 (1). pp. 11-17.
  • CHAKRABORTI, S.; HUMAN, S.W. and GRAHAN, M.A. (2008). “Phase I Statistical Process Control Charts: An overview and some results”. Quality Engineering, 21, pp. 52-62.
  • CHEN, G. (1997). “The mean and standard deviation of the run length distribution of X-bar charts when control limits are estimated”. Statistica Sinica, 7, pp. 789-798.
  • CHOU, Y.M. and OWEN, D.B. (1989). “On the distribution of the estimated process capability indices”. Communications in Statistics - Theory and Methods, 18, pp. 4549-4560.
  • CHOU, Y.M.; OWEN, D.B. and BORREGO, A.S.A. (1990). “Lower confidence limits on process capability indices”. Journal of Quality Technology, 22, pp. 223-229.
  • DOVICH, R. A. (1992). Quality engineering statistics, Milwaukee,Wisconsin: ASQ Quality Press.
  • DUNCAN, A.J. (1986). Quality control and industrial statistics, 5th ed. Homewood, IL: Richard D. Irwin.
  • EVANS, J. R. and LINDSAY, W. M. (1999). The management and control of quality. 8th ed. South Western College.
  • FRANKLIN, L.A. and WASSERMAN, G.S. (1992) “A note on the conservative nature of the tables of lower confidence limits for Cpk with a suggested correction”. Statistics-Simulation and Computation, 21(4), pp. 1165-1169.
  • GUIRGUIS, G. H. and RODRIGUEZ, R.N. (1992). “Computation of Owen's Q function applied to process capability analysis”. Journal of Quality Technology, 24(4), pp. 236-246.
  • HARMS, T. and DUCHESNE, P. (2006). “On calibration estimation for quantiles”. Survey Methodology, 32, pp.37-52.
  • HEAVLIN, W. D. (1988). “Statistical properties of capability indices”. Technical report, 320, Tech. Library, Advanced Micro Devices, Inc., Sunnyvale, California.
  • JENSEN, W. A.; JONES-FARMER, L. A.; CHAMP, C. W. and Woodall, W. H. (2006). “Effects of parameter estimation on control chart properties: a literature review”. Journal of Quality Technology, 38(4), pp. 349-364.
  • JONES, L.A.; CHAMP, C.W. and RIGDON, S.E. (2001). “The performance of exponentially weighted moving average charts with estimated parameters”. Technometrics, 43(2), pp. 156-167.
  • KANE, V.E. (1986). “Process capability indices”. Journal of Quality Technology, 18(1), pp. 41-52.
  • KOTZ, S. and JHONSON, N.L. (1993). Process capability indices. New York: CRC Press.
  • KOTZ, S. and JHONSON, N.L. (2002). “Process capability indices: a review 1992–2000. Discussions”. Journal of Quality Technology, 34(1), pp. 2-19.
  • KOTZ, S. and LOVELACE, C.R. (1998). Process capability indices in theory and practice. London: Arnold.
  • KUSHLER, R.H. and HURLEY, P. (1992). “Confidence bounds for capability indices”. Journal of Quality Technology, 24(4), pp. 188-195.
  • LI, H.; OWEN, D.B. and BORREGO, A.S.A. (1990). “Lower confidence limits on process capability indices based on the range”. Communications in Statistics - Simulation and Computation, 19, pp. 1-24.
  • LUKO, S.N. (1996). “Concerning the estimators 𝑅𝑅􀴤𝑑𝑑2⁄ and 𝑅𝑅􀴤𝑑𝑑2∗⁄ in estimating variability in a Normal Universe”. Quality Engineering, 8 (3), pp. 481-487.
  • MITRA, A. (2008). Fundamentals of quality control and improvement. New York: Wiley.
  • MONTGOMERY, D.C. (1985). Introduction to statistical quality control. New York: Wiley.
  • MONTGOMERY, D.C. (2009). Statistical quality control. A modern introduction (6th edn). New York: Wiley.
  • MUÑOZ, J.F.; ÁLVAREZ-VERDEJO, E.; PÉREZ-ARÓSTEGUI, M.N. and GUTIÉRREZ-GUTIÉRREZ, L. (2016). “Empirical comparisons of X-bar charts when control limits are estimated”. Quality and Reliability Engineering International, 32, pp. 453-464.
  • NAGATA, Y. and NAGAHATA, H. (1994). “Approximation formulas for the lower confidence limits of process capability indices”. Okayama Economic Review, 25(4), pp. 301-314.
  • NEZHAD, M. and NIAKI, S. (2013). “A new acceptance sampling policy based on number of successive conforming items”. Communications in Statistics - Theory and Methods, 42, pp. 1542-1552.
  • OTT, E.R. (1975). Process quality control. New York: McGraw-Hill.
  • RAO, J. N. K.; KOVAR, J. G. and MANTEL, H. J. (1990). “On estimating distribution functions and quantiles from survey data using auxiliary information”. Biometrika, 77, pp. 365-375.
  • RAO, G.S.; ROSAIAH, K.; BABU, M. and SIVAKUMAR, C. (2016). “New acceptance sampling plans based on percentiles for exponentiated Fréchet distribution”. Economic Quality Control, DOI: 10.1515/eqc-2015-0011.
  • SILVA, P. N. and SKINNER, C. J. (1995). “Estimating distribution functions with auxiliary information using poststratification”. Journal of Official Statistics, 11(5), pp. 277-294.
  • SPIRING, F.; LEUNG, B.; CHENG, S. and YEUNG, A. (2003). “A bibliography of process capability papers”. Quality and Reliability Engineering International, 19(5), pp. 445-460.
  • VARDEMAN, S.B. (1999). “A brief tutorial on the estimation of the process standard deviation”. IIE Transact, 31, pp. 503-507.
  • WHEELER, D.J. (1995). Advanced topics in statistical process control. Knoxville, TN: SPC press.
  • WOLTER, K.M. (2007). Introduction to variance estimation. 2nd ed. New York: Springer.
  • WOODALL, W.H. and MONTGOMERY, D.C (2000) “Using ranges to estimate variability”. IIE Quality Engineering, 13(2), pp. 211-217.
Fuente de los datos: Dialnet