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Original Articles

Comparisons of frequentist and Bayesian inferences for interval estimation on process yield

ORCID Icon, ORCID Icon, & ORCID Icon
Pages 2694-2705 | Received 14 Feb 2020, Accepted 22 Nov 2021, Published online: 27 Dec 2021

References

  • Agresti, A., & Min, Y. (2005). Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 x 2 contingency tables. Biometrics, 61(2), 515–523. https://doi.org/10.1111/j.1541-0420.2005.031228.x
  • Ahmad, S., Alatefi, M., Alkahtani, M., Anwar, S., Sharaf, M., & Abdollahian, M. (2019). Bibliometric analysis for process capability research. Quality Technology & Quantitative Management, 16(4), 459–477. https://doi.org/10.1080/16843703.2018.1464426
  • Alfaro, M. E., Zoller, S., & Lutzoni, F. (2003). Bayes or bootstrap? A simulation study comparing the performance of Bayesian Markov chain Monte Carlo sampling and bootstrapping in assessing phylogenetic confidence. Molecular Biology and Evolution, 20(2), 255–266. https://doi.org/10.1093/molbev/msg028
  • Barnett, V. (1999). Comparative statistical inference (3rd ed.). Wiley.
  • Bernardo, J. (2005). Reference analysis. In Handbook of Statistics (Vol. 25, pp. 17–90). Elsevier. https://doi.org/10.1016/S0169-7161(05)25002-2
  • Boyles, R. A. (1994). Process capability with asymmetric tolerances. Communications in Statistics - Simulation and Computation, 23(3), 615–635. https://doi.org/10.1080/03610919408813190
  • Casella, G., & George, E. I. (1992). Explaining the Gibbs sampler. The American Statistician, 46(3), 167–174. https://doi.org/10.2307/2685208
  • Chen, J. P. (2005). Comparing four lower confidence limits for process yield index Spk. The International Journal of Advanced Manufacturing Technology, 26(5-6), 609–614. https://doi.org/10.1007/s00170-004-2351-9
  • Cowles, M. K., & Carlin, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: A comparative review. Journal of the American Statistical Association, 91(434), 883–904. https://doi.org/10.1080/01621459.1996.10476956
  • Davies, R. B. (1987). Hypothesis testing when a nuisance parameter is present only under the alternatives. Biometrika, 74(1), 33–43. https://doi.org/10.2307/2336019
  • Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721–741. https://doi.org/10.1109/tpami.1984.4767596
  • Geramian, A., Shahin, A., Minaei, B., & Antony, J. (2020). Enhanced FMEA: An integrative approach of fuzzy logic-based FMEA and collective process capability analysis. Journal of the Operational Research Society, 71(5), 800–812. https://doi.org/10.1080/01605682.2019.1606986
  • Gilks, W. R. (2005). Markov chain Monte Carlo. In Encyclopedia of biostatistics. John Wiley & Sons.
  • Gilks, W. R., Best, N., & Tan, K. (1995). Adaptive rejection Metropolis sampling within Gibbs sampling. Applied Statistics, 44(4), 455–472. https://doi.org/10.2307/2986138
  • Gilks, W. R., & Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41(2), 337–348. https://doi.org/10.2307/2347565
  • Gonnissen, Y., Gonçalves, S. I. V., De Geest, B. G., Remon, J. P., & Vervaet, C. (2008). Process design applied to optimise a directly compressible powder produced via a continuous manufacturing process. European Journal of Pharmaceutics and Biopharmaceutics : official Journal of Arbeitsgemeinschaft Fur Pharmazeutische Verfahrenstechnik e.V, 68(3), 760–770. https://doi.org/10.1016/j.ejpb.2007.09.007
  • Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109. https://doi.org/10.1093/biomet/57.1.97
  • Hsu, B. M., Wu, C. W., & Shu, M. H. (2008). Generalized confidence intervals for the process capability index Cpm. Metrika, 68(1), 65–82. https://doi.org/10.1007/s00184-007-0143-6
  • Jeffreys, H. (1961). Theory of probability (3rd ed.). In Oxford Classic Texts in the Physical Sciences. Oxford Univ. Press, Oxford.
  • Kane, E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41–52. https://doi.org/10.1080/00224065.1986.11978984
  • Khakifirooz, M., Chien, C. F., & Chen, Y. J. (2018). Bayesian inference for mining semiconductor manufacturing big data for yield enhancement and smart production to empower industry 4.0. Applied Soft Computing, 68, 990–999. https://doi.org/10.1016/j.asoc.2017.11.034
  • King, M. L. (1996). Hypothesis testing in the presence of nuisance parameters. Journal of Statistical Planning and Inference, 50(1), 103–120. https://doi.org/10.1016/0378-3758(95)00048-8
  • Lee, J. C., Hung, H. N., Pearn, W. L., & Kueng, T. L. (2002). On the distribution of the estimated process yield index Spk. Quality and Reliability Engineering International, 18(2), 111–116. https://doi.org/10.1002/qre.450
  • Mathew, T., Sebastian, G., & Kurian, K. M. (2007). Generalized confidence intervals for process capability indices. Quality and Reliability Engineering International, 23(4), 471–481. https://doi.org/10.1002/qre.828
  • Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092. https://doi.org/10.1063/1.1699114
  • Nicolaou, A. (1993). Bayesian intervals with good frequentist behaviour in the presence of nuisance parameters. Journal of the Royal Statistical Society: Series B (Methodological), 55(2), 377–390. https://doi.org/10.1111/j.2517-6161.1993.tb01908.x
  • Pearn, W. L., Hung, H. N., Cheng, Y. C., & Lin, G. H. (2010). Procedure of the convolution method for estimating production yield with sample size information. International Journal of Production Research, 48(5), 1245–1265. https://doi.org/10.1080/00207540802552667
  • Ravenzwaaij, D., Cassey, P., & Brown, S. D. (2018). A simple introduction to Markov Chain Monte–Carlo sampling. Psychonomic Bulletin & Review, 25(1), 143–154. https://doi.org/10.3758/s13423-016-1015-8
  • Ripley, B. (1987). Stochastic simulation. John Wiley & Sons.
  • Robert, C. P., Chopin, N., & Rousseau, J. (2009). Harold Jeffreys’s theory of probability revisited. Statistical Science, 24(2), 141–172. https://doi.org/10.1214/09-STS284
  • Samaniego, F. J. (2010). A comparison of Bayesian and frequentist approach to estimations. Springer.
  • VanderPlas, J. (2014). Freqentism and Bayesianism: A Python-driven primer [Paper presentation]. Proceedings of the 13th Python in Science Conference, SCIPY, 1–9.
  • Wang, F. K. (2016). Process yield analysis for multivariate linear profiles. Quality Technology & Quantitative Management, 13(2), 124–138. https://doi.org/10.1080/16843703.2016.1169676
  • Weerahandi, S. (1993). Generalized confidence intervals. Journal of the American Statistical Association, 88(423), 899–905. https://doi.org/10.1080/01621459.1993.10476355
  • Wu, C. W., & Chen, J. T. (2021). A modified sampling plan by variables with an adjustable mechanism for lot sentencing. Journal of the Operational Research Society, 72(3), 678–687. https://doi.org/10.1080/01605682.2019.1657366
  • Wu, C. W., Liao, M. Y., & Chen, J. C. (2012). An improved approach for constructing lower confidence bound on process yield. European J. of Industrial Engineering, 6(3), 369–390. https://doi.org/10.1504/EJIE.2012.046667
  • Wu, C. W., & Liu, S. W. (2014). Developing a sampling plan by variables inspection for controlling lot fraction of defectives. Applied Mathematical Modelling, 38(9-10), 2303–2310. https://doi.org/10.1016/j.apm.2013.10.043
  • Wu, C. W., Pearn, W. L., & Kotz, S. (2009). An overview of theory and practice on process capability indices for quality assurance. International Journal of Production Economics, 117(2), 338–359. https://doi.org/10.1016/j.ijpe.2008.11.008
  • Yum, B. J., & Kim, K. W. (2011). A bibliography of the literature on process capability indices: 2000-2009. Quality and Reliability Engineering International, 27(3), 251–268. https://doi.org/10.1002/qre.1115

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