A new auxiliary information based cumulative sum median control chart for location monitoring

Shahid HUSSAIN; Li-xin SONG; Shabbir AHMAD; Muhammad RIAZ

doi:10.1631/FITEE.1700428

Your Location：

Home >

Browse articles >

A new auxiliary information based cumulative sum median control chart for location monitoring

Regular Papers | Updated：2022-05-19

- A new auxiliary information based cumulative sum median control chart for location monitoring
- 一种基于辅助信息的新型位置监测累积和中值控制图
- Frontiers of Information Technology & Electronic Engineering Vol. 20, Issue 4, Pages: 554-570(2019)
- Affiliations：
  
  School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
  Department of Mathematics, COMSATS Institute of Information Technology, Attock 43600, Pakistan
  Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt 47040, Pakistan
  Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
- Author bio：
  
  Shahid HUSSAIN, E-mail: shahid_libra82@hotmail.com
- Funds：
- DOI：10.1631/FITEE.1700428
  CLC： O213.1
- Received：28 June 2017，
  
  Revised：2019-;4-11，
  
  Published：2019-04
- Accepted：
Scan QR Code
Shahid HUSSAIN, Li-xin SONG, Shabbir AHMAD, et al. A new auxiliary information based cumulative sum median control chart for location monitoring[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(4): 554-570.
DOI：

Shahid HUSSAIN, Li-xin SONG, Shabbir AHMAD, et al. A new auxiliary information based cumulative sum median control chart for location monitoring[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(4): 554-570. DOI： 10.1631/FITEE.1700428.

摘要

控制图能检测过程参数变化，是统计过程控制常用工具。休哈特控制图能有效监测大位移，而累积和（CUSUM）控制图能有效监测中、小位移。控制图在使用时通常假定数据无异常值，并且参数已知或已正确估计。实际应用中，某些过程偶尔出现异常值，所以这些假设通常不成立。位置参数监测通常基于均值控制图，严重受不成立假设影响。本文提出几种基于辅助变量的累积和中值控制图，并与其相对应均值控制图进行比较。为监测位置参数，分别检测包含与不含异常值时均值和中值控制图性能。研究对称与非对称过程，并利用累积和控制图监测位置参数，进一步研究所提控制图性能。基于不同运行链长，研究受控和非受控累积和控制图性能。结果表明，存在异常值时，所提控制图比传统控制图性能更优。最后，提供了一个基于混凝土抗压强度与生产质量关系的应用实例。

Abstract

Control charts are commonly used tools in statistical process control for the detection of shifts in process parameters. Shewhart-type charts are efficient for large shift values

whereas cumulative sum (CUSUM) charts are effective in detecting medium and small shifts. Control chart use commonly assumes that data are free of outliers and parameters are known or correctly estimated based on an in-control process. In practice

these assumptions are not often true because some processes occasionally have outliers. Monitoring the location parameter is usually based on mean charts

which are seriously affected by violations of these assumptions. In this paper we propose several CUSUM median control charts based on auxiliary variables

and offer comparisons with their corresponding mean control charts. To monitor the location parameter

we examined the performance of mean and median control charts in the presence and absence of outliers. Both symmetric and non-symmetric processes were studied to examine the properties of the proposed control charts to monitor the location parameter using CUSUM control charts. We used different run length measures to study in-control and out-of-control performances of CUSUM charts. Results revealed that our proposed control charts perform much better than the traditional charts in the presence of outliers. A real application of our study was provided using data on concrete compressive strength as it relates to the quality of cement manufacturing.

关键词

Keywords

references

N Abbas , , , M Riaz , , , RJMM Does . . An EWMA-type control chart for monitoring the process mean using auxiliary information . . Commun Stat Theory Methods , , 2014 . . 43 ( ( 16 ): ): 3485 - - 3498 . . DOI: 10.1080/03610926.2012.700368 http://doi.org/10.1080/03610926.2012.700368 . .

SA Abbasi , , , M Riaz . . On enhanced control charting for process monitoring . . Int J Phys Sci , , 2013 . . 8 ( ( 17 ): ): 759 - - 775 . . DOI: 10.5897/IJPS12.252 http://doi.org/10.5897/IJPS12.252 . .

MR Abujiya , , , MH Lee , , , M Riaz . . Increasing the sensitivity of cumulative sum charts for location . . Qual Reliab Eng Int , , 2015a . . 31 ( ( 6 ): ): 1035 - - 1051 . . DOI: 10.1002/qre.1661 http://doi.org/10.1002/qre.1661 . .

MR Abujiya , , , M Riaz , , , MH Lee . . Enhanced cumulative sum charts for monitoring process dispersion . . PLOS ONE , , 2015b . . 10 ( ( 4 ): ): e0124520 DOI: 10.1371/journal.pone.0124520 http://doi.org/10.1371/journal.pone.0124520 . .

FB Adebola , , , NA Adegoke , , , RA Sanusi . . A class of regression estimator with cum-dual ratio estimator as intercept . . Int J Prob Stat , , 2015 . . 4 ( ( 2 ): ): 42 - - 50 . . DOI: 10.5923/j.ijps.20150402.02 http://doi.org/10.5923/j.ijps.20150402.02 . .

S Ahmad , , , ZY Lin , , , SA Abbasi , , , 等 . . On efficient monitoring of process dispersion using interquartile range . . Open J Appl Sci , , 2013 . . 2 ( ( 4B ): ): 39 - - 43 . . DOI: 10.4236/ojapps.2012.24B010 http://doi.org/10.4236/ojapps.2012.24B010 . .

S Ahmad , , , M Riaz , , , SA Abbasi , , , 等 . . On efficient median control charting . . J Chin Inst Eng , , 2014a . . 37 ( ( 3 ): ): 358 - - 375 . . DOI: 10.1080/02533839.2013.781794 http://doi.org/10.1080/02533839.2013.781794 . .

S Ahmad , , , M Riaz , , , SA Abbasi , , , 等 . . On median control charting under double sampling scheme . . Eur J Ind Eng , , 2014b . . 8 ( ( 4 ): ): 478 - - 512 . . DOI: 10.1504/EJIE.2014.064755 http://doi.org/10.1504/EJIE.2014.064755 . .

D Brook , , , DA Evans . . An approach to probability distribution of CUSUM run length . . Biometrika , , 1972 . . 59 ( ( 3 ): ): 539 - - 549 . . DOI: 10.1093/biomet/59.3.539 http://doi.org/10.1093/biomet/59.3.539 . .

P Castagliola . . An EWMA control chart for monitoring the process sample median . . Int J Reliab Qual Saf Eng , , 2001 . . 8 ( ( 2 ): ): 123 - - 135 . . DOI: 10.1142/S0218539301000414 http://doi.org/10.1142/S0218539301000414 . .

P Castagliola , , , PE Maravelakis , , , FO Figueiredo . . The EWMA median chart with estimated parameters . . IIE Trans , , 2015 . . 48 ( ( 1 ): ): 66 - - 74 . . DOI: 10.1080/0740817X.2015.1056861 http://doi.org/10.1080/0740817X.2015.1056861 . .

YK Chen , , , KC Chiou . . An evaluation of median Rankit control charts . . IEEE Int Conf on Systems, Man and Cybernetics , , 2008 . . p.3601 - - 3605 . . DOI: 10.1109/ICSMC.2008.4811857 http://doi.org/10.1109/ICSMC.2008.4811857 . .

S Gupta , , , J Shabbir . . On the use of transformed auxiliary variables in estimating population mean by using two auxiliary variables . . J Stat Plan Infer , , 2007 . . 137 ( ( 5 ): ): 1606 - - 1611 . . DOI: 10.1016/j.jspi.2006.09.008 http://doi.org/10.1016/j.jspi.2006.09.008 . .

AMA Haridy , , , AZ Elshabrawy . . The economic design of cumulative sum charts used to maintain current control of non-normal process means . . Comput Ind Eng , , 1996 . . 31 ( ( 3-4 ): ): 783 - - 790 . . DOI: 10.1016/s0360-8352(96)00242-2 http://doi.org/10.1016/s0360-8352(96)00242-2 . .

DM Hawkins . . A CUSUM for a scale parameter . . J Qual Technol , , 1981 . . 13 ( ( 4 ): ): 228 - - 231 . . DOI: 10.1080/00224065.1981.11978762 http://doi.org/10.1080/00224065.1981.11978762 . .

DM Hawkins . . Regression adjustment for variables in multivariate quality control . . J Qual Technol , , 1993 . . 25 ( ( 3 ): ): 170 - - 182 . . DOI: 10.1080/00224065.1993.11979451 http://doi.org/10.1080/00224065.1993.11979451 . .

DM Hawkins , , , DH Olwell . . Cumulative Sum Charts and Charting for Quality Improvement . . Springer Science & Business Media, Jensen , , 2012 . . .

DM Hawkins , , , QF Wu . . The CUSUM and the EWMA head-to-head . . Qual Eng , , 2014 . . 26 ( ( 2 ): ): 215 - - 222 . . DOI: 10.1080/08982112.2013.817014 http://doi.org/10.1080/08982112.2013.817014 . .

WP Huang , , , LJ Shu , , , WH Woodall , , , 等 . . CUSUM procedures with probability control limits for monitoring processes with variable sample sizes . . IIE Trans , , 2016 . . 48 ( ( 8 ): ): 759 - - 771 . . DOI: 10.1080/0740817X.2016.1146422 http://doi.org/10.1080/0740817X.2016.1146422 . .

C Kadilar , , , H Cingi . . Ratio estimators in stratified random sampling . . Biometr J , , 2003 . . 45 ( ( 2 ): ): 218 - - 225 . . DOI: 10.1002/bimj.200390007 http://doi.org/10.1002/bimj.200390007 . .

C Kadilar , , , H Cingi . . A new estimator using two auxiliary variables . . Appl Math Comput , , 2005a . . 162 ( ( 2 ): ): 901 - - 908 . . DOI: 10.1016/j.amc.2003.12.130 http://doi.org/10.1016/j.amc.2003.12.130 . .

C Kadilar , , , H Cingi . . A new ratio estimator in stratified random sampling . . Commun Stat Theory Methods , , 2005b . . 34 ( ( 3 ): ): 597 - - 602 . . DOI: 10.1081/STA-200052156 http://doi.org/10.1081/STA-200052156 . .

GK Kanji , , , OH Arif . . Median Rankit control chart by the quantile approach . . J Appl Stat , , 2000 . . 27 ( ( 6 ): ): 757 - - 770 . . DOI: 10.1080/02664760050081933 http://doi.org/10.1080/02664760050081933 . .

GK Kanji , , , OH Arif . . Median Rankit control chart for Weibull distribution . . Total Qual Manag , , 2001 . . 12 ( ( 5 ): ): 629 - - 642 . . DOI: 10.1080/09544120120060114 http://doi.org/10.1080/09544120120060114 . .

MBC Khoo . . A control chart based on sample median for the detection of a permanent shift in the process mean . . Qual Eng , , 2005 . . 17 ( ( 2 ): ): 243 - - 257 . . DOI: 10.1081/QEN-200057329 http://doi.org/10.1081/QEN-200057329 . .

R Mehmood , , , M Riaz , , , RJMM Does . . Control charts for location based on different sampling schemes . . J Appl Stat , , 2013 . . 40 ( ( 3 ): ): 483 - - 494 . . DOI: 10.1080/02664763.2012.740624 http://doi.org/10.1080/02664763.2012.740624 . .

DC Montgomery . . Introduction to Statistical Quality Control (6 th Ed.) . . John Wiley & Sons, Hoboken, NJ. , , 2007 . . .

A Mukherjee , , , MA Graham , , , S Chakraborti . . Distribution-free exceedance CUSUM control charts for location . . Commun Stat Simul Comput , , 2013 . . 42 ( ( 5 ): ): 1153 - - 1187 . . DOI: 10.1080/03610918.2012.661638 http://doi.org/10.1080/03610918.2012.661638 . .

DJ Mundform , , , J Schaffer , , , MJ Kim , , , 等 . . Number of replications required in Monte Carlo simulation studies: a synthesis of four studies . . J Mod Appl Stat Methods , , 2011 . . 10 ( ( 1 ): ): Article 4 . .

HZ Nazir , , , M Riaz , , , RJ Does , , , 等 . . Robust CUSUM control charting . . Qual Eng , , 2013 . . 25 ( ( 3 ): ): 211 - - 224 . . . .

HZ Nazir , , , M Riaz , , , RJ Does . . Robust CUSUM control charting for process dispersion . . Qual Reliab Eng Int , , 2015 . . 31 ( ( 3 ): ): 369 - - 379 . . DOI: 10.22237/jmasm/1304222580 http://doi.org/10.22237/jmasm/1304222580 . .

JS Oakland . . Statistical Process Control (6 th Ed.) . . Routledge, London , , 2007 . . .

YJ Ou , , , D Wen , , , Z Wu , , , 等 . . A comparison study on effectiveness and robustness of control charts for monitoring process mean and variance . . Qual Reliab Eng Int , , 2012a . . 28 ( ( 1 ): ): 3 - - 17 . . DOI: 10.1002/qre.1208 http://doi.org/10.1002/qre.1208 . .

YJ Ou , , , Z Wu , , , F Tsung . . A comparison study of effectiveness and robustness of control charts for monitoring process mean . . Int J Prod Econ , , 2012b . . 135 ( ( 1 ): ): 479 - - 490 . . DOI: 10.1016/j.ijpe.2011.08.026 http://doi.org/10.1016/j.ijpe.2011.08.026 . .

ES Page . . Continuous inspection schemes . . Biometrika , , 1954 . . 41 ( ( 1-2 ): ): 100 - - 115 . . . .

PH Qiu , , , D Hawkins . . A rank-based multivariate CUSUM procedure . . Technometrics , , 2011 . . 43 ( ( 2 ): ): 120 - - 132 . . DOI: 10.1198/004017001750386242 http://doi.org/10.1198/004017001750386242 . .

AC Rakitzis , , , P Castagliola , , , PE Maravelakis . . Cumulative sum control charts for monitoring geometrically inflated Poisson processes: an application to infectious disease counts data . . Stat Methods Med Res , , 2018 . . 27 ( ( 2 ): ): 622 - - 641 . . DOI: 10.1177/0962280216641985 http://doi.org/10.1177/0962280216641985 . .

GS Rao . . One-sided cumulative sum (CUSUM) control charts for the Erlang-truncated exponential distribution . . Comput Methods Sci Technol , , 2013 . . 19 ( ( 4 ): ): 229 - - 234 . . . .

M Riaz . . Monitoring process mean level using auxiliary information . . Stat Neerl , , 2008a . . 62 ( ( 4 ): ): 458 - - 481 . . DOI: 10.1111/j.1467-9574.2008.00390.x http://doi.org/10.1111/j.1467-9574.2008.00390.x . .

M Riaz . . Monitoring process variability using auxiliary information . . Comput Stat , , 2008b . . 23 ( ( 2 ): ): 253 - - 276 . . DOI: 10.1007/s00180-007-0084-6 http://doi.org/10.1007/s00180-007-0084-6 . .

M Riaz . . Control charting and survey sampling techniques in process monitoring . . J Chin Inst Eng , , 2015 . . 38 ( ( 3 ): ): 342 - - 354 . . DOI: 10.1080/02533839.2014.970355 http://doi.org/10.1080/02533839.2014.970355 . .

M Riaz , , , RJMM Does . . A process variability control chart . . Comput Stat , , 2009 . . 24 ( ( 2 ): ): 345 - - 368 . . DOI: 10.1007/s00180-008-0122-z http://doi.org/10.1007/s00180-008-0122-z . .

M Riaz , , , N Abbas , , , RJMM Does . . Improving the performance of CUSUM charts . . Qual Reliab Eng Int , , 2011 . . 27 ( ( 4 ): ): 415 - - 424 . . DOI: 10.1002/qre.1124 http://doi.org/10.1002/qre.1124 . .

M Riaz , , , R Mehmood , , , S Ahmad , , , 等 . . On the performance of auxiliary-based control charting under normality and nonnormality with estimation effects . . Qual Reliab Eng Int , , 2013 . . 29 ( ( 8 ): ): 1165 - - 1179 . . DOI: 10.1002/qre.1467 http://doi.org/10.1002/qre.1467 . .

SW Roberts . . Control chart tests based on geometric moving averages . . Technometrics , , 1959 . . 1 ( ( 3 ): ): 239 - - 250 . . DOI: 10.1080/00401706.1959.10489860 http://doi.org/10.1080/00401706.1959.10489860 . .

JH Ryu , , , HG Wan , , , S Kim . . Optimal design of a CUSUM chart for a mean shift of unknown size . . J Qual Technol , , 2010 . . 42 ( ( 3 ): ): 311 - - 326 . . DOI: 10.1080/00224065.2010.11917826 http://doi.org/10.1080/00224065.2010.11917826 . .

RA Sanusi , , , MR Abujiya , , , M Riaz . . Combined Shewhart CUSUM charts using auxiliary variable . . Comput Ind Eng , , 2017 . . 105 329 - - 337 . . DOI: 10.1016/j.cie.2017.01.018 http://doi.org/10.1016/j.cie.2017.01.018 . .

RA Sanusi , , , N Abbas , , , M Riaz . . On efficient CUSUM-type location control charts using auxiliary information . . Qual Technol Quant Manag , , 2018 . . 15 ( ( 1 ): ): 87 - - 105 . . DOI: 10.1080/16843703.2017.1304039 http://doi.org/10.1080/16843703.2017.1304039 . .

JR Schaffer , , , MJ Kim . . Number of replications required in control chart Monte Carlo simulation studies . . Commun Stat Simul Comput , , 2007 . . 36 ( ( 5 ): ): 1075 - - 1087 . . DOI: 10.1080/03610910701539963 http://doi.org/10.1080/03610910701539963 . .

A Seplveda , , , JA Nachlas . . A simulation approach to multivariate quality control . . Comput Ind Eng , , 1997 . . 33 ( ( 1-2 ): ): 113 - - 116 . . DOI: 10.1016/s0360-8352(97)00053-3 http://doi.org/10.1016/s0360-8352(97)00053-3 . .

MS Shafae , , , RM Dickinson , , , WH Woodall , , , 等 . . Cumulative sum control charts for monitoring Weibull-distributed time between events . . Qual Reliab Eng Int , , 2015 . . 31 ( ( 5 ): ): 839 - - 849 . . DOI: 10.1002/qre.1643 http://doi.org/10.1002/qre.1643 . .

SH Sheu , , , L Yang . . The generally weighted moving average control chart for monitoring the process median . . Qual Eng , , 2006a . . 18 ( ( 3 ): ): 333 - - 344 . . DOI: 10.1080/08982110600719431 http://doi.org/10.1080/08982110600719431 . .

SH Sheu , , , L Yang . . The generally weighted moving average median control chart . . Qual Technol Quant Manag , , 2006b . . 3 ( ( 4 ): ): 455 - - 471 . . DOI: 10.1080/16843703.2006.11673126 http://doi.org/10.1080/16843703.2006.11673126 . .

SH Sheu , , , SH Tai , , , YT Hsieh , , , 等 . . Monitoring process mean and variability with generally weighted moving average control charts . . Comput Ind Eng , , 2009 . . 57 ( ( 1 ): ): 401 - - 407 . . DOI: 10.1016/j.cie.2008.12.010 http://doi.org/10.1016/j.cie.2008.12.010 . .

WA Shewhart . . Some applications of statistical methods to the analysis of physical and engineering data . . Bell Syst Techn J , , 1924 . . 3 ( ( 1 ): ): 43 - - 87 . . DOI: 10.1002/j.1538-7305.1924.tb01347.x http://doi.org/10.1002/j.1538-7305.1924.tb01347.x . .

LJ Shu , , , F Tsung , , , KL Tsui . . Effects of estimation errors on cause-selecting charts . . IIE Trans , , 2005 . . 37 ( ( 6 ): ): 559 - - 567 . . DOI: 10.1080/07408170590929027 http://doi.org/10.1080/07408170590929027 . .

HP Singh , , , RS Solanki . . An efficient class of estimators for the population mean using auxiliary information in systematic sampling . . J Stat Theory Pract , , 2012 . . 6 ( ( 2 ): ): 274 - - 285 . . DOI: 10.1080/15598608.2012.673881 http://doi.org/10.1080/15598608.2012.673881 . .

HP Singh , , , LN Upadhyaya , , , P Chandra . . A general family of estimators for estimating population mean using two auxiliary variables in two-phase sampling . . Stat Trans , , 2004 . . 6 ( ( 7 ): ): 1055 - - 1077 . . . .

HP Singh , , , R Tailor , , , S Singh , , , 等 . . A modified estimator of population mean using power transformation . . Stat Pap , , 2008 . . 49 ( ( 1 ): ): 37 - - 58 . . DOI: 10.1007/s00362-006-0371-2 http://doi.org/10.1007/s00362-006-0371-2 . .

R Singh , , , M Kumar . . A note on transformations on auxiliary variable in survey sampling . . Model Assisted Stat Appl , , 2011 . . 6 ( ( 1 ): ): 17 - - 19 . . DOI: 10.3233/MAS-2011-0154 http://doi.org/10.3233/MAS-2011-0154 . .

R Singh , , , P Chauhan , , , N Sawan , , , 等 . . Auxiliary information and a priori values in construction of improved estimators . . 2007 . . https://arxiv.org/abs/0712.0096 https://arxiv.org/abs/0712.0096 , , . .

R Singh , , , P Chauhan , , , N Sawan , , , 等 . . Ratio estimators in simple random sampling using information on auxiliary attribute . . 2009 . . https://arxiv.org/abs/0907.4182 https://arxiv.org/abs/0907.4182 , , . .

RS Solanki , , , HP Singh , , , A Rathour . . An alternative estimator for estimating the finite population mean using auxiliary information in sample surveys . . ISRN Prob Stat , , 2012 . . 2012 65682 DOI: 10.5402/2012/657682 http://doi.org/10.5402/2012/657682 . .

R Tailor , , , B Sharma . . A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis . . Stat Trans , , 2009 . . 10 ( ( 1 ): ): 15 - - 24 . . . .

R Tailor , , , S Chouhan , , , R Tailor , , , 等 . . A ratio-cum-product estimator of population mean in stratified random sampling using two auxiliary variables . . Statistica , , 2012 . . 72 ( ( 3 ): ): 287 - - 297 . . . .

RC Team . . R: a Language and Environment for Statistical Computing . . R Foundation for Statistical Computing, Vienna, Austria , , 2015 . . .

EJ Umble . . Cumulative sum charts and charting for quality improvement . . Technometrics , , 2001 . . 43 ( ( 1 ): ): 107 DOI: 10.1198/tech.2001.s561 http://doi.org/10.1198/tech.2001.s561 . .

WH Woodall , , , DC Montgomery . . Research issues and ideas in statistical process control . . J Qual Technol , , 1999 . . 31 ( ( 4 ): ): 376 - - 386 . . DOI: 10.1080/00224065.1999.11979944 http://doi.org/10.1080/00224065.1999.11979944 . .

Z Wu , , , J Jiao , , , M Yang , , , 等 . . An enhanced adaptive CUSUM control chart . . IIE Trans , , 2009 . . 141 ( ( 7 ): ): 642 - - 653 . . DOI: 10.1080/07408170802712582 http://doi.org/10.1080/07408170802712582 . .

L Yang , , , S Pai , , , YR Wang . . A novel CUSUM median control chart . . Proc Int Multiconf of Engineers and Computer Scientists , , 2010 . . p.1707 - - 1710 . . . .

IC Yeh . . Modeling of strength of high-performance concrete using artificial neural networks . . Cem Concr Res , , 1998 . . 28 ( ( 12 ): ): 1797 - - 1808 . . DOI: 10.1016/S0008-8846(98)00165-3 http://doi.org/10.1016/S0008-8846(98)00165-3 . .

IC Yeh . . Prediction of strength of fly ash and slag concrete by the use of artificial neural networks . . J Chin Inst Civil Hydraul Eng , , 2003 . . 15 ( ( 4 ): ): 659 - - 663 . . . .

IC Yeh . . Analysis of strength of concrete using design of experiments and neural networks . . J Mater Civ Eng , , 2006 . . 18 ( ( 4 ): ): 597 - - 604 . . DOI: 10.1061/(ASCE)0899-1561(2006)18:4(597) http://doi.org/10.1061/(ASCE)0899-1561(2006)18:4(597) . .

S Zhang , , , Z Wu . . Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals . . IIE Trans , , 2006 . . 38 ( ( 4 ): ): 377 - - 387 . . DOI: 10.1080/07408170500232578 http://doi.org/10.1080/07408170500232578 . .

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

Chat

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰