A direct procedure for monitoring the coefficient of variation using a variable sample size scheme

ABSTRACT A variable sample size (VSS) scheme directly monitoring the coefficient of variation (CV), instead of monitoring the transformed statistics, is proposed. Optimal chart parameters are computed based on two criteria: (i) minimizing the out-of-control ARL (ARL1) and (ii) minimizing the out-of-control ASS (ASS1). Then the performances are compared between these two criteria. The advantages of the proposed chart over the VSS chart based on the transformed statistics in the existing literature are: the former (i) provides an easier alternative as no transformation is involved and (ii) requires less number of observations to detect a shift when ASS1 is minimized.

[1]  Seyed Taghi Akhavan Niaki,et al.  A Parameter-Tuned Genetic Algorithm for Economic-Statistical Design of Variable Sampling Interval X-Bar Control Charts for Non-Normal Correlated Samples , 2014, Commun. Stat. Simul. Comput..

[2]  Philippe Castagliola,et al.  The Performance of Variable Sample Size X̄ Chart with Measurement Errors , 2016, Qual. Reliab. Eng. Int..

[3]  Giovanni Celano,et al.  Monitoring the Coefficient of Variation Using a Variable Sampling Interval Control Chart , 2013, Qual. Reliab. Eng. Int..

[4]  Antonio Fernando Branco Costa,et al.  X̄ charts with variable sample size , 1994 .

[5]  Shaomin Wu.  Optimal inspection policy for three-state systems monitored by variable sample size control charts , 2011 .

[6]  Wolfgang Reh,et al.  Significance tests and confidence intervals for coefficients of variation , 1996 .

[7]  Vaidyanathan Ramaswami,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 1999, ASA-SIAM Series on Statistics and Applied Mathematics.

[8]  Giovanni Celano,et al.  Monitoring the Coefficient of Variation Using EWMA Charts , 2011 .

[9]  Maria E. Calzada,et al.  A synthetic control chart for the coefficient of variation , 2013 .

[10]  Giovanni Celano,et al.  The variable sample size t control chart for monitoring short production runs , 2012 .

[11]  Bin Chen,et al.  A new exponentially weighted moving average control chart for monitoring the coefficient of variation , 2014, Comput. Ind. Eng..

[12]  Philippe Castagliola,et al.  A Control Chart for the Multivariate Coefficient of Variation , 2016, Qual. Reliab. Eng. Int..

[13]  Michael B. C. Khoo,et al.  Multivariate Synthetic |S| Control Chart with Variable Sampling Interval , 2015, Commun. Stat. Simul. Comput..

[14]  Amirhossein Amiri,et al.  A New Adaptive Variable Sample Size Approach in EWMA Control Chart , 2014, Commun. Stat. Simul. Comput..

[15]  Ying Zhang,et al.  The Variable Sample Size X¯ Chart with Estimated Parameters , 2012, Qual. Reliab. Eng. Int..

[16]  Marion R. Reynolds,et al.  The Design of the Variable Sampling Interval Generalized Likelihood Ratio Chart for Monitoring the Process Mean , 2015, Qual. Reliab. Eng. Int..

[17]  Raymond H. Myers,et al.  On the percentage points of the sample coefficient of variation , 1968 .

[18]  Giovanni Celano,et al.  Monitoring the coefficient of variation using a variable sample size control chart , 2015, The International Journal of Advanced Manufacturing Technology.

[19]  Tom Burr,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 2001, Technometrics.

[20]  George Tagaras.  A Survey of Recent Developments in the Design of Adaptive Control Charts , 1998 .

[21]  Douglas M. Hawkins,et al.  A Control Chart for the Coefficient of Variation , 2007 .

[22]  Giovanni Celano,et al.  Monitoring the Coefficient of Variation Using Control Charts with Run Rules , 2013 .

[23]  Yu-Ting Cheng,et al.  Optimal variable sample size and sampling interval MSE chart , 2011, ICSSSM11.

[24]  Eui-Pyo Hong,et al.  Development of CV Control Chart Using EWMA Technique , 2008 .

[25]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[26]  José Dias Curto,et al.  The coefficient of variation asymptotic distribution in the case of non-iid random variables , 2009 .

[27]  Giovanni Celano,et al.  The variable parameters T$$^{2}$$2 chart with run rules , 2014 .