On efficient CUSUM-type location control charts using auxiliary information

Abstract Statistical quality control deals with controlling and monitoring of production/manufacturing processes for improved quality of products. Control charts are the major tools that are widely applied in industry to keep the process variability under control. One of the most popular categories of control charts is CUSUM chart which is memory chart. It is based on utilizing the information on cumulative sum pattern. This article proposes a new structure for CUSUM charts based on the utilization of auxiliary information using different estimators. We have used a variety of performance measures including average run length, Extra Quadratic Loss, Ratio of Average Run Lengths and Performance Comparison Index. These performance measures of the proposed chart are evaluated in terms of varying shifts in study variable and are compared with some existing control structures meant for the same purposes. The comparisons revealed that the proposed charts perform very well relative to the other competing charts under discussion. A real life industrial example is also provided to demonstrate the application procedure of the proposals of this study.

[1]  Smiley W. Cheng,et al.  A New EWMA Control Chart for Monitoring Both Location and Dispersion , 2004 .

[2]  S. K. Srivastava.  An Estimator Using Auxiliary Information in Sample Serveys , 1967 .

[3]  Theodora Kourti,et al.  The Process Analytical Technology initiative and multivariate process analysis, monitoring and control , 2006, Analytical and bioanalytical chemistry.

[4]  Stephen V. Crowder,et al.  Design of Exponentially Weighted Moving Average Schemes , 1989 .

[5]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[6]  Amitava Mukherjee,et al.  Distribution‐free Phase II CUSUM Control Chart for Joint Monitoring of Location and Scale , 2015, Qual. Reliab. Eng. Int..

[7]  Muhammad Riaz,et al.  Monitoring process mean level using auxiliary information , 2008 .

[8]  Di Wen,et al.  A comparison study on effectiveness and robustness of control charts for monitoring process mean and variance , 2012, Qual. Reliab. Eng. Int..

[9]  J. Andel.  Sequential Analysis , 2022, The SAGE Encyclopedia of Research Design.

[10]  Deborah F. Cook,et al.  Excel-based application of data visualization techniques for process monitoring in the forest products industry. , 2004 .

[11]  K. W. Kemp,et al.  Sampling inspection of continuous processes with no autocorrelation between successive results , 1960 .

[12]  Corli Van Zyl,et al.  CUSUM procedures based on sequential ranks , 2015 .

[13]  F. B. Adebola,et al.  A Class of Regression Estimator with Cum-Dual Ratio Estimator as Intercept , 2015 .

[14]  Arthur B. Yeh,et al.  Unified CUSUM Charts for Monitoring Process Mean and Variability , 2004 .

[15]  Amitava Mukherjee,et al.  Design and implementation of CUSUM exceedance control charts for unknown location , 2014 .

[16]  James M. Lucas,et al.  Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start , 2000, Technometrics.

[17]  Lawrence G. Tatum.  Control charts for the detection of a periodic component , 1996 .

[18]  Ying Liu,et al.  An enhanced adaptive CUSUM control chart , 2009 .

[19]  Cheng-Der Fuh,et al.  SPRT and CUSUM in hidden Markov models , 2003 .

[20]  Walter Krämer,et al.  The CUSUM test for OLS residuals , 1992 .

[21]  James Tannock,et al.  Taguchi experimental design for manufacturing process optimisation using historical data and a neural network process model , 2005 .

[22]  Changliang Zou,et al.  A Directional Multivariate Sign EWMA Control Chart , 2013 .

[23]  William H. Woodall,et al.  The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables , 1983 .

[24]  Amitava Mukherjee,et al.  Distribution-Free Exceedance CUSUM Control Charts for Location , 2013, Commun. Stat. Simul. Comput..

[25]  Maria E. Calzada,et al.  The Synthetic t and Synthetic EWMA t Charts , 2013 .

[26]  Muhammad Riaz,et al.  A process variability control chart , 2009, Comput. Stat..

[27]  Muhammad Riaz,et al.  Monitoring process variability using auxiliary information , 2008, Comput. Stat..

[28]  W. A. Shewhart,et al.  Some applications of statistical methods to the analysis of physical and engineering data , 1924 .

[29]  Marion R. Reynolds,et al.  Cusum Charts for Monitoring an Autocorrelated Process , 2001 .

[30]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[31]  Roger M. Sauter,et al.  Introduction to Statistical Quality Control (2nd ed.) , 1992 .

[32]  S. W. Roberts,et al.  Control Chart Tests Based on Geometric Moving Averages , 2000, Technometrics.

[33]  Fah Fatt Gan,et al.  An optimal design of CUSUM quality control charts , 1991 .

[34]  Amitava Mukherjee,et al.  Design and Implementation of Two CUSUM Schemes for Simultaneously Monitoring the Process Mean and Variance with Unknown Parameters , 2016, Qual. Reliab. Eng. Int..

[35]  D. A. Evans,et al.  An approach to the probability distribution of cusum run length , 1972 .

[36]  Cem Kadilar,et al.  Ratio estimators in simple random sampling , 2004, Appl. Math. Comput..

[37]  Monika Eisenhower,et al.  Elements Of Survey Sampling , 2016 .

[38]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[39]  Amitava Mukherjee,et al.  A distribution-free phase-II CUSUM procedure for monitoring service quality , 2017 .