Distribution-free Phase-I scheme for location, scale and skewness shifts with an application in monitoring customers' waiting time

References

• S.A. Abbasi, M. Riaz, A. Miller, and S. Ahmad, On the performance of Phase-I dispersion control charts for process monitoring, Qual. Reliab. Eng. Int. 31 (2015), pp. 1705–1716.
   Web of Science ®Google Scholar
• W. Albers and W.C.M. Kallenberg, Empirical non-parametric control charts: Estimation effects and corrections, J. Appl. Stat. 31 (2004), pp. 345–360.
   Web of Science ®Google Scholar
• R.C. Bell, L.A. Jones-Farmer, and N. Billor, A distribution-free multivariate Phase-I location control chart for subgrouped data from elliptical distributions, Technometrics 56 (2014), pp. 528–538.
   Web of Science ®Google Scholar
• D.D. Boos, Comparing K populations with linear rank statistics, J. Am. Stat. Assoc. 81 (1986), pp. 1018–1025.
   Web of Science ®Google Scholar
• G. Capizzi and G. Masarotto, Phase-I distribution-free analysis of univariate data, J. Qual. Technol. 45 (2013), pp. 273–284.
   Web of Science ®Google Scholar
• G. Capizzi and G. Masarotto, Phase-I distribution-free analysis of multivariate data, Technometrics 59 (2017), pp. 484–495.
   Web of Science ®Google Scholar
• C.-R. Cheng and J.-J.H. Shiau, A distribution-free multivariate control chart for Phase-I applications, Qual. Reliab. Eng. Int. 31 (2015), pp. 97–111.
   Web of Science ®Google Scholar
• O. Cucconi, Un nuovo test non parametrico per il confronto tra due gruppi campionari, Giorn. Econ. Ann. Econ. 27 (1968), pp. 225–248.
   Google Scholar
• M.A. Fligner and T.J. Killeen, Distribution-free two-sample tests for scale, J. Am. Stat. Assoc. 71 (1976), pp. 210–213.
   Web of Science ®Google Scholar
• J.D. Gibbons and S. Chakraborti, Nonparametric Statistical Inference, 5th ed., CRC Press, Boca Raton, FL, 2010.
   Google Scholar
• M.A. Graham, S.W. Human, and S. Chakraborti, A Phase-I nonparametric shewhart-type control chart based on the median, J. Appl. Stat. 37 (2010), pp. 1795–1813.
   Web of Science ®Google Scholar
• L.A. Jones-Farmer and C.W. Champ, A distribution-free Phase-I control chart for subgroup scale, J. Qual. Technol. 42 (2010), pp. 373–387.
   Web of Science ®Google Scholar
• L.A. Jones-Farmer, V. Jordan, and C.W. Champ, Distribution-free Phase-I control charts for subgroup location, J. Qual. Technol. 41 (2009), pp. 304–316.
   Web of Science ®Google Scholar
• L.A. Jones-Farmer, W.H. Woodall, S.H. Steiner, and C.W. Champ, An overview of Phase-I analysis for process improvement and monitoring, J. Qual. Technol. 46 (2014), pp. 265–280.
   Web of Science ®Google Scholar
• M. Keshavarz, S. Asadzadeh, and S.T.A. Niaki, Risk-adjusted frailty-based CUSUM control chart for Phase-I monitoring of patients' lifetime, J. Stat. Comput. Simul. 91 (2021), pp. 334–352.
   Web of Science ®Google Scholar
• W.H. Kruskal and W.A. Wallis, Use of ranks in one-criterion variance analysis, J. Am. Stat. Assoc. 47 (1952), pp. 583–621.
   Web of Science ®Google Scholar
• Y. Lepage, A combination of Wilcoxon's and Ansari-Bradley's statistics, Biometrika 58 (1971), pp. 213–217.
   Web of Science ®Google Scholar
• C. Li, A. Mukherjee, and M. Marozzi, A new distribution-free Phase-I procedure for bi-aspect monitoring based on the multi-sample Cucconi statistic, Comput. Ind. Eng. 149 (2020), Article ID 106760.
   PubMed Web of Science ®Google Scholar
• C. Li, A. Mukherjee, and Q. Su, A distribution-free Phase-I monitoring scheme for subgroup location and scale based on the multi-sample Lepage statistic, Comput. Ind. Eng. 129 (2019), pp. 259–273.
   Web of Science ®Google Scholar
• Z. Li, Y. Dai, and Z. Wang, Multivariate change point control chart based on data depth for Phase-I analysis, Comm. Statist. Simulation Comput. 43 (2013), pp. 1490–1507.
   Web of Science ®Google Scholar
• M. Marozzi, The multisample Cucconi test, Stat. Methods Appl. 23 (2014), pp. 209–227.
   Web of Science ®Google Scholar
• D.C. Montgomery, Statistical Quality Control, 7th ed., John Willey & Sons, Hoboken, NJ, 2012.
   Google Scholar
• T. Nishino and H. Murakami, The null and non-null limiting distributions of the modified multisample Cucconi test, Statistics 52 (2018), pp. 1344–1358.
   Web of Science ®Google Scholar
• T. Nishino and H. Murakami, The generalized Cucconi test statistic for the two-sample problem, J. Korean Stat. Soc. 48 (2019), pp. 593–612.
   Web of Science ®Google Scholar
• A.N. Pettitt, A two-sample Anderson-Darling rank statistic, Biometrika 63 (1976), pp. 161–168.
   Web of Science ®Google Scholar
• P. Qiu, Introduction to Statistical Process Control, CRC Press, Boca Raton, FL, 2014.
   Google Scholar
• F. Rublik, The multisample version of the lepage test, Kybernetika 41 (2005), pp. 713–733.
   Web of Science ®Google Scholar
• F. Sogandi, M. Aminnayeri, A. Mohammadpour, and A. Amiri, Phase-I risk-adjusted Bernoulli chart in multistage healthcare processes based on the state-space model, J. Stat. Comput. Simul. 91 (2021), pp. 522–542.
   Web of Science ®Google Scholar
• M.C. Testik, C.H. Weiß, Y. Koca, and O.M. Testik, Effectiveness of Phase-I applications for identifying randomly scattered out-of-control observations and estimating control chart parameters, Qual. Reliab. Eng. Int. 34 (2018), pp. 78–92.
   Web of Science ®Google Scholar
• W.S. Tsai, B.S. Duran, and T.O. Lewis, Tsai, small-sample behavior of some multisample nonparametric tests for scale, J. Am. Stat. Assoc. 70 (1975), pp. 791–796.
   Web of Science ®Google Scholar
• W.H. Woodall, Bridging the gap between theory and practice in basic statistical process monitoring, Qual. Eng. 29 (2017), pp. 2–15.
   Web of Science ®Google Scholar