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http://dx.doi.org/10.5351/KJAS.2020.33.4.451

Performance of CCC-r charts with bootstrap adjusted control limits  

Kim, Minji (Department of Applied Statistics, Chung-Ang University)
Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
Publication Information
The Korean Journal of Applied Statistics / v.33, no.4, 2020 , pp. 451-466 More about this Journal
Abstract
CCC-r chart is effective for high-quality processes with a very low fraction nonconforming. The values of process parameters should be estimated from the Phase I sample since they are often not known. However, if the Phase I sample size is not sufficiently large, an estimation error may occur when the parameter is estimated and the practitioner may not achieve the desired in-control performance. Therefore, we adjust the control limits of CCC-r charts using 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 CCC-r charts by controlling the probability that the in-control average number of observations to signal (ANOS) has a value greater than the desired one.
Keywords
average number of observations to signal; Bayes estimator; bootstrap algorithm; CCC-r chart; Phase I;
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Times Cited By KSCI : 6  (Citation Analysis)
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1 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.   DOI
2 Faraz, A.,Woodall, W. H., and Heuchenne, C. (2015). Guaranteed conditional performance of the S2 control chart with estimated parameters, International Journal of Production Research, 53, 4405-4413.   DOI
3 Gandy, A. and Kvaloy, J. T. (2013). Guaranteed conditional performance of control charts via bootstrap methods, Scandinavian Journal of Statistics, 40, 647-668.   DOI
4 Han, S. W., 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.   DOI
5 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.   DOI
6 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, 349-364.   DOI
7 Jones, M. A. and Steiner, S. H. (2012). Assessing the effect of estimation error on the risk-adjusted CUSUM chart performance, International Journal for Quality in Health Care, 24, 176-181.   DOI
8 Kim, J., Kim, M., and Lee, J. (2018). The in-control performance of the CCC-r chart with estimated parameters, The Korean Journal of Applied Statistics, 31, 485-495.   DOI
9 Kim, M. and Lee, J. (2020). Geometric chart with bootstrap-based control limits using the Bayes estimator, Communications for Statistical Applications and Methods, 27, 65-77.   DOI
10 Lee, J., Wang, N., Xu, L., Schuh, A., and Woodall, W. H. (2013). The effect of parameter estimation on upper-sided Bernoulli cumulative sum charts, Quality and Reliability Engineering International, 29, 639-651.   DOI
11 Page, E. S. (1954) Continuous inspection schemes. Boimetrica, 41, 100-115.   DOI
12 Psarakis, S., Vyniou, A. K., and Castagliola, P. (2014). Some recent developments on the effects of parameter estimation on control charts, Quality and Reliability Engineering International, 30, 1113-1129.   DOI
13 Wu, Z., Yeo, S. H., and Fan, H. (2000). A comparative study of the CRL-type control charts, Quality and Reliability Engineering International, 16, 269-279.   DOI
14 Roberts, S. W. (1959). Control chart tests based on geometric moving averages, Technometrics, 1, 239-250.   DOI
15 Saleh, N. A., Mahmoud, M. A., Jones-Farmer, L. A., Zwetsloot, I. M., and Woodall, W. H. (2015). Another look at the EWMA control chart with estimated parameters, Journal of Quality Technology, 47, 363-382.   DOI
16 Shewhart, W. A. (1931) Economic Control of Quality of Manufactured Product, Van Nostrand, New York, NY.
17 Xie, M., Lu, X. S., Goh, T. N., and Chan, L. Y. (1999). A quality monitoring and decision-making scheme for automated production processes, International Journal of Quality & Reliability Management, 16, 148-157.   DOI
18 Zhang, M., Hou, X., Chen, H., and He, S. (2019). CCC-r charts' performance with estimated parameter for high-quality process, Quality and Reliability Engineering International, 35, 946-958.   DOI
19 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.   DOI
20 Zhang, M., Megahed, F. M., and Woodall, W. H. (2014). Exponential CUSUM charts with estimated control limits, Quality and Reliability Engineering International, 30, 275-286.   DOI
21 Zhang, M., Peng, Y., Schuh, A., Megahed, F. M., and Woodall, W. H. (2013). Geometric charts with estimated control limits, Quality and Reliability Engineering International, 29, 209-223.   DOI
22 Zhao, M. J. and Driscoll, A. R. (2016). The c-chart with bootstrap adjusted control limits to improve conditional performance, Quality and Reliability Engineering International, 32, 2871-2881.   DOI