The Improved EWMA Chart for Heteroscedasticity Process

Annals of Data Science - Tập 5 - Trang 21-27 - 2017
Dan Zhou1, Liu Liu1, Xin Lai2
1School of Mathematics and VC & VR Province Key Laboratory, Sichuan Normal University, Chengdu, China
2School of Management, Xi’an Jiaotong University, Xi’an, China

Tóm tắt

It is doubtful of the validity of the EWMA chart that the observations from heteroscedasticity processes violate the assumption of identical distribution. In this paper, we discuss the effect of heteroscedasticity on the performance of the conventional EWMA chart. Then we analyze the principle of the improved EWMA chart for monitoring heteroscedasticity processes. Then we compare the detection performance of the improved EWMA chart with the conventional EWMA chart by using a criteria based on average run length (ARL). Finally, an instance is given to indicate the effectiveness of the proposed method and analyze the best trading time of the stock.

Tài liệu tham khảo

Gani W, Taleb H, L M (2011) An assessment of the kernel-distance-based multivariate control chart through an industrial application. Qual Reliab Eng Int 27(4):391–401 Harris L N. Quality control and industrial statistics (fifth edition). Acheson J. Duncan, Irwin, 1986. number of pages: 1123. Quality and Reliability Engineering International, 1989, 5(3): 250–251 Chiang LH, Colegrove LF (2007) Industrial implementation of on-line multivariate quality control. Chemom Intell Lab Syst 88(2):143–153 Liu Liu, Jian Zhang (2013) A sequential rank-based combined nonparametric EWMA control chart. J Appl Stat Manag 32(6):1049–1059 Liu Liu, Xuemin Zi, Jian Zhang, Zhaojun Wang (2013) A sequential rank-based nonparametric adaptive EWMA control chart. Commun Stat Simul Comput 42:841–859 Liu Liu, Jian Zhang, Xuemin Zi (2014) Dual Nonparametric CUSUM Control Chart Based on Rank. Commun Stat Simul Comput 44(3):756–772 Liu Liu, Tsung F, Jian Zhang (2014) Adaptive nonparametric CUSUM scheme for detecting unknown shifts in location. Int J Prod Res 52(6):1592–1606 Liu Liu, Xuemin Zi, Jian Zhang (2015) Nonparametric adaptive CUSUM procedures with markovian mean estimation. J Appl Stat Manag 34(3):463–475 Liu Liu, Zepei Deng, Jian Zhang et al (2016) Dynamic nonparametric control charts with variable sampling interval based on sequential ranks. J Syst Sci Math Sci 36(10):1804–1814 Qin Cheng, Jian Zhang, Liu Liu (2017) A study on the CUSUM control chart in steering lamp of motorcycle parts. Modern Manuf Eng 1:114–116 Van Brackle LN, Reynolds MR (1997) EWMA and CUSUM control charts in the presence of correlation. Commun Stat Simul Conput 26(3):979–1008 Alwan LC, Roberts HV (1988) Time-series modeling for statistical process control. J Bus Econ Stat 6(1):87–95 Wei J, Tsui KL, Woodall W (2000) A new SPC monitoring method: the ARMA chart [J]. Technometrics 42(4):399–470 Zhilei Zhang (2008) The improved EWMA chart for autocorrelated processes. J Appl Stat Manag 27(3):466–472 Zhilei Zhang (2011) The residual control chart for autocorrelated processes. J Appl Stat Manag 30(5):888–895 Bickel PJ (1978) Using residuals robustly I: tests for heteroscedasticity, nonlinearity. Ann Stat 6(2):266–291 Lei Zhang, Mei Changlin (2008) Testing heteroscedasticity in nonparametric regression models based on residual analysis. Appl Math A J Chin Univ Ser B 23(3):265–272