Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Geometric charts with bootstrap-based control limits using the Bayes estimator

  • Kim, Minji (Department of Applied Statistics, Chung-Ang University) ;
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
  • Received : 2019.07.27
  • Accepted : 2019.11.09
  • Published : 2020.01.31
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Abstract

Geometric charts are effective in monitoring the fraction nonconforming in high-quality processes. The in-control fraction nonconforming is unknown in most actual processes; therefore, it should be estimated using the Phase I sample. However, if the Phase I sample size is small the practitioner may not achieve the desired in-control performance because estimation errors can occur when the parameters are estimated. Therefore, in this paper, we adjust the control limits of geometric charts with the bootstrap algorithm to improve the in-control performance of charts with smaller sample sizes. The simulation results show that the adjustment with the bootstrap algorithm improves the in-control performance of geometric charts by controlling the probability that the in-control average run length has a value greater than the desired one. The out-of-control performance of geometric charts with adjusted limits is also discussed.

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References

  1. Apley DW (2012). Posterior distribution charts: A Bayesian approach for graphically exploring a Process Mean, Technometrics, 54, 279-293. https://doi.org/10.1080/00401706.2012.694722
  2. Faraz A, Heuchenne C, and Saniga E (2017). The np chart with guaranteed in-control average run lengths, Quality and Reliability Engineering International, 33, 1057-1066. https://doi.org/10.1002/qre.2091
  3. Faraz A, Woodall WH, and Heuchenne C (2015). Guaranteed conditional performance of the S 2 control chart with estimated parameters, International Journal of Production Research, 53, 4405-4413. https://doi.org/10.1080/00207543.2015.1008112
  4. Gandy A and Kvaloy JT (2013). Guaranteed conditional performance of control charts via bootstrap methods, Scandinavian Journal of Statistics, 40, 647-668. https://doi.org/10.1002/sjos.12006
  5. Han SW, Lee J, and Park J (2018). A Bernoulli GLR chart based on Bayes estimator, Journal of the Korean Data & Information Science Society, 29, 37-47. https://doi.org/10.7465/jkdi.2018.29.1.37
  6. Hong H and Lee J (2015). Comparisons of the performance with Bayes estimator and MLE for control charts based on geometric distribution, The Korean Journal of Applied Statistics, 28, 907-920. https://doi.org/10.5351/KJAS.2015.28.5.907
  7. Jensen WA, Jones-Farmer LA, Champ CW, and Woodall WH (2006). Effects of parameter estimation on control chart properties: a literature review, Journal of Quality Technology, 38, 349-364. https://doi.org/10.1080/00224065.2006.11918623
  8. Jones MA and Steiner SH (2012). Assessing the effect of estimation error on the risk-adjusted CUSUM chart performance, International Journal for Quality in Health Care, 24, 176-181. https://doi.org/10.1093/intqhc/mzr082
  9. N and Chakraborti S (2017). Bayesian monitoring of times between events: The Shewhart $t_r$-chart, Journal of Quality Technology, 49, 136-154. https://doi.org/10.1080/00224065.2017.11917985
  10. Lee J, Wang N, Xu L, Schuh A, and Woodall WH (2013). The effect of parameter estimation on upper-sided Bernoulli cumulative sum charts, Quality and Reliability Engineering International, 29, 639-651. https://doi.org/10.1002/qre.1413
  11. Pan R and Rigdon SE (2012). A Bayesian approach to change point estimation in multivariate SPC, Journal of Quality Technology, 44, 231-248. https://doi.org/10.1080/00224065.2012.11917897
  12. Psarakis S, Vyniou AK, and Castagliola P (2014). Some recent developments on the effects of param-eter estimation on control charts, Quality and Reliability Engineering International, 30, 1113-1129. https://doi.org/10.1002/qre.1556
  13. Saleh NA, Mahmoud MA, Jones-Farmer LA, Zwetsloot IM, and Woodall WH (2015). Another look at the EWMA control chart with estimated parameters, Journal of Quality Technology, 47, 363-382. https://doi.org/10.1080/00224065.2015.11918140
  14. Szarka JL III and Woodall WH (2011). A review and perspective on surveillance of high quality Bernoulli processes, Quality and Reliability Engineering International, 27, 735-752. https://doi.org/10.1002/qre.1256
  15. Tan MHY and Shi J (2012). A Bayesian approach for interpreting mean shifts in multivariate quality control, Technometrics, 54, 294-307. https://doi.org/10.1080/00401706.2012.694789
  16. Tang LC and Cheong WT (2004). Cumulative conformance count chart with sequentially updated parameters, IIE Transactions, 36, 841-853. https://doi.org/10.1080/07408170490473024
  17. Yang Z, Xie M, Kuralmani V, and Tsui K-L (2002). On the performance of geometric charts with estimated control limits, Journal of Quality Technology, 34, 448-458. https://doi.org/10.1080/00224065.2002.11980176
  18. Zhang M, Hou X, He Z, and Xu Y (2017). Performance comparison for the CRL control charts with estimated parameters for high-quality processes, Quality Technology & Quantitative Management, 14, 31-43. https://doi.org/10.1080/16843703.2016.1191143
  19. Zhang M, Megahed FM, and Woodall WH (2014). Exponential CUSUM charts with estimated control limits, Quality and Reliability Engineering International, 30, 275-286. https://doi.org/10.1002/qre.1495
  20. Zhang M, Peng Y, Schuh A, Megahed FM, and Woodall WH (2013). Geometric charts with estimated control limits, Quality and Reliability Engineering International, 29, 209-223. https://doi.org/10.1002/qre.1304
  21. Zhao MJ and Driscoll AR (2016). The c-chart with bootstrap adjusted control limits to improve conditional performance, Quality and Reliability Engineering International, 32, 2871-2881. https://doi.org/10.1002/qre.1971