Joint statistical design of double sampling X and s charts

Abstract In statistical quality control, usually the mean and variance of a manufacturing process are monitored jointly by two statistical control charts, e.g., a X ¯ chart and a R chart. Because of the efficiency of double sampling (DS) X ¯ charts in detecting shifts in process mean and DS s charts in process standard deviation it seems reasonable to investigate the joint DS X ¯ and s charts for statistical quality control. In this paper, a joint DS X ¯ and s chart scheme is proposed. The statistical design of the joint DS X ¯ and s charts is defined and formulated as an optimization problem and solved using a genetic algorithm. The performance of the joint DS X ¯ and s charts is also investigated. The results of the investigation indicate that the joint DS X ¯ and s charts offer a better statistical efficiency in terms of average run length (ARL) than combined EWMA and CUSUM schemes, omnibus EWMA scheme over certain shift ranges when all schemes are optimized to detect certain shifts. In comparison with the joint standard, two-stage samplings and variable sampling size X ¯ and R charts, the joint DS charts offer a better statistical efficiency for all ranges of the shifts.

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

[2]  Nielen Stander,et al.  The genetic algorithm applied to stiffness maximization of laminated plates: review and comparison , 1998 .

[3]  Douglas C. Montgomery,et al.  The Economic Design of Control Charts: A Review and Literature Survey , 1980 .

[4]  Charles W. Champ,et al.  A multivariate exponentially weighted moving average control chart , 1992 .

[5]  Kenneth E. Case,et al.  Economic Design of a Joint X- and R -Control Chart , 1981 .

[6]  Rickie J. Domangue,et al.  Some omnibus exponentially weighted moving average statistical process monitoring schemes , 1991 .

[7]  F. Gan.  Joint monitoring of process mean and variance using exponentially weighted moving average control charts , 1995 .

[8]  Aristides T. Hatjimihait,et al.  Genetic algorithms-based design and optimization of statistical quality-control procedures. , 1993, Clinical chemistry.

[9]  David He,et al.  An improved double sampling s chart , 2003 .

[10]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

[11]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[12]  Lucila Ohno-Machado,et al.  A genetic algorithm approach to multi-disorder diagnosis , 2000, Artif. Intell. Medicine.

[13]  Emmanuel Yashchin,et al.  Some aspects of the theory of statistical control schemes , 1987 .

[14]  William H. Woodall,et al.  Weaknesses of The Economic Design of Control Charts , 1986 .

[15]  Antonio Fernando Branco Costa,et al.  Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals , 1999 .

[16]  D. Hawkins.  A Cusum for a Scale Parameter , 1981 .

[17]  E. Saniga.  Economic Statistical Control-Chart Designs with an Application to X̄ and R Charts@@@Economic Statistical Control-Chart Designs with an Application to X and R Charts , 1989 .

[18]  Antonio Fernando Branco Costa.  Joint X̄ and R charts with variable parameters , 1998 .

[19]  Smiley W. Cheng,et al.  Monitoring Process Mean and Variability with One EWMA Chart , 2001 .

[20]  Lonnie C. Vance,et al.  The Economic Design of Control Charts: A Unified Approach , 1986 .

[21]  Antonio Fernando Branco Costa,et al.  Joint ―X and R Charts with Two‐stage Samplings , 2004 .

[22]  Duc Truong Pham,et al.  Artificial intelligence in engineering , 1999 .

[23]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[24]  S. Crowder.  A simple method for studying run-length distribution of exponentially weighted moving average charts , 1987 .

[25]  Antonio Fernando Branco Costa,et al.  JOINT ECONOMIC DESIGN OF X¯ AND R CONTROL CHARTS FOR PROCESSES SUBJECT TO TWO INDEPENDENT ASSIGNABLE CAUSES , 1993 .

[26]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[27]  David He,et al.  Construction of double sampling s‐control charts for agile manufacturing , 2002 .

[28]  Erwin M. Saniga,et al.  Joint Statistical Design of X̄ and R Control Charts , 1991 .

[29]  Curtis F. Gerald.  Applied numerical analysis , 1970 .

[30]  S. Crowder.  Average Run Lengths of Exponentially Weighted Moving Average Control Charts , 1987 .

[31]  David He,et al.  Design of double- and triple-sampling X-bar control charts using genetic algorithms , 2002 .

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

[33]  M. A. Rahim.  Determination of Optimal Design Parameters of Joint X̄ and R Charts , 1989 .

[34]  Charles W. Champ,et al.  A generalized quality control procedure , 1991 .

[35]  Francisco Aparisi,et al.  Optimization of univariate and multivariate exponentially weighted moving-average control charts using genetic algorithms , 2004, Comput. Oper. Res..

[36]  Antonio Fernando Branco Costa,et al.  Economic design of ?? andR charts under Weibull shock models , 2000 .

[37]  Jean-Jacques Daudin,et al.  Double sampling X charts , 1992 .

[38]  J. Healy.  A note on multivariate CUSUM procedures , 1987 .

[39]  M. A. Raim,et al.  JOINT ECONOMIC DESIGN OF MEAN AND VARIANCE CONTROL CHARTS , 1988 .