A compound control chart for monitoring and controlling high quality processes

In the present article, we propose a new control chart for monitoring high quality processes. More specifically, we suggest declaring the monitored process out of control, by exploiting a compound rule couching on the number of conforming units observed between the (i−1)th and the ith nonconforming item and the number of conforming items observed between the (i−2)th and the ith nonconforming item. Our numerical experimentation demonstrates that the proposed control chart, in most of the cases, exhibits a better (or at least equivalent) performance than its competitors.

[1]  Min Xie,et al.  Improvement Detection by Control Charts for High Yield Processes , 1993 .

[2]  Wee-Tat Cheong,et al.  A Control Scheme for High-Yield Correlated Production under Group Inspection , 2006 .

[3]  Małgorzata Roos,et al.  Runs and Scans With Applications , 2001 .

[4]  Arthur B. Yeh,et al.  EWMA control charts for monitoring high-yield processes based on non-transformed observations , 2008 .

[5]  A. J. Griffiths.  Monitoring, Targeting and the Use of Statistical Process Control within the Energy Profile of the Iron Founding Industry , 1988 .

[6]  James C. Benneyan,et al.  Statistical Control Charts Based on a Geometric Distribution , 1992 .

[7]  W. Y. Wendy Lou,et al.  Distribution Theory of Runs and Patterns and Its Applications: A Finite Markov Chain Imbedding Approach , 2003 .

[8]  Lloyd S. Nelson,et al.  A Control Chart for Parts-Per-Million Nonconforming Items , 1994 .

[9]  Babak Abbasi,et al.  On the monitoring of multi-attributes high-quality production processes , 2007 .

[10]  Roberto da Costa Quinino,et al.  Diagnostic errors and repetitive sequential classifications in on-line process control by attributes , 2010, Eur. J. Oper. Res..

[11]  Patrick D. Bourke,et al.  The RL2 chart versus the np chart for detecting upward shifts in fraction defective , 2006 .

[12]  Zhen He,et al.  Statistical computation and analyses for attribute events , 2009, Comput. Stat. Data Anal..

[13]  Patrick D. Bourke,et al.  Detecting a shift in fraction nonconforming using runlength control charts with 100% inspection , 1991 .

[14]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[15]  S. Bersimis,et al.  Run and Frequency Quota Rules in Process Monitoring and Acceptance Sampling , 2009 .

[16]  Philippe Castagliola,et al.  Computational Statistics and Data Analysis an Ewma Chart for Monitoring the Process Standard Deviation When Parameters Are Estimated , 2022 .

[17]  Willem Albers.  The optimal choice of negative binomial charts for monitoring high-quality processes , 2008 .

[18]  Kuo-Ching Chiou,et al.  Cumulative conformance count chart with variable sampling intervals and control limits , 2011 .

[19]  Abdur Rahim,et al.  A CCC‐r chart for high‐yield processes , 2001 .

[20]  William H. Woodall,et al.  On the Equivalence of the Bernoulli and Geometric CUSUM Charts , 2012 .

[21]  Thong Ngee Goh,et al.  A COMPARATIVE STUDY OF CCC AND CUSUM CHARTS , 1998 .

[22]  M. R. Reynolds,et al.  A general approach to modeling CUSUM charts for a proportion , 2000 .

[23]  William H. Woodall,et al.  Control Charts Based on Attribute Data: Bibliography and Review , 1997 .

[24]  Markos V. Koutras,et al.  Distribution Theory of Runs: A Markov Chain Approach , 1994 .

[25]  Zhang Wu,et al.  Optimal average sample number of the SPRT chart for monitoring fraction nonconforming , 2013, Eur. J. Oper. Res..

[26]  Willem Albers.  Empirical nonparametric control charts for high-quality processes , 2010 .

[27]  Stephen V. Crowder,et al.  An EWMA for Monitoring a Process Standard Deviation , 1992 .

[28]  T. Calvin,et al.  Quality Control Techniques for "Zero Defects" , 1983 .

[29]  Zhang Wu,et al.  Design of the sum-of-conforming-run-length control charts , 2001, Eur. J. Oper. Res..

[30]  Thong Ngee Goh,et al.  A two-stage decision procedure for monitoring processes with low fraction nonconforming , 2003, Eur. J. Oper. Res..

[31]  Charles P. Quesenberry,et al.  Geometric Q Charts for High Quality Processes , 1995 .

[32]  Thong Ngee Goh.  A Charting Technique for Control of Low‐Defective Production , 1987 .

[33]  Min Xie,et al.  Statistical Models and Control Charts for High-Quality Processes , 2002 .

[34]  D. Coleman.  Statistical Process Control—Theory and Practice , 1993 .

[35]  Maysa S. de Magalhães,et al.  Double-sampling control charts for attributes , 2011 .

[36]  Hsiuying Wang,et al.  Comparison of p control charts for low defective rate , 2009, Comput. Stat. Data Anal..

[37]  Thong Ngee Goh,et al.  Some procedures for decision making in controlling high yield processes , 1992 .

[38]  G. B. Wetherill,et al.  Quality Control and Industrial Statistics , 1975 .