Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies

On-line monitoring of process variability is strategic to achieve high standards of quality and maintain at acceptable levels the number of nonconforming items. Shewhart control charts are the simplest Statistical Process Control (SPC) procedure to achieve this goal. An efficient implementation of a control chart requires the optimal selection of its design parameters. They can be selected according to an economic-statistical objective: an expected total cost per unit of time incurred during production is minimized subject to a statistical constraint limiting the number of false alarms issued by the control chart. This paper investigates the economic-statistical design of Shewhart control charts implementing skip sampling strategies for constructing subgroups and monitoring autocorrelated AR(1) processes. Implementing skip sampling strategies within a rational subgroup reduces the negative effects of autocorrelation on the statistical performance of the Shewhart control chart. A wide benchmark of examples has been generated as a screening experimental design to study the process and cost factors influencing the selection of the sampling strategy. Regression models have been fitted to the results to help practitioners in the selection of the most convenient sampling strategy. Finally, a sensitivity analysis has been performed to evaluate how the parameters misspecification biases the evaluation of the optimal cost per unit of time.

[1]  Using recurrent neural networks to detect changes in autocorrelated processes for quality monitoring , 2007, Comput. Ind. Eng..

[2]  Antonio Fernando Branco Costa,et al.  Double sampling $$\overline{X} $$ control chart for a first-order autoregressive moving average process model , 2008 .

[3]  Giovanni Celano.  Robust design of adaptive control charts for manual manufacturing/inspection workstations , 2009 .

[4]  Chao-Yu Chou,et al.  Minimum-loss design of x-bar charts for correlated data , 2002 .

[5]  Cinzia Mortarino,et al.  Duncan's model for X̄‐control charts: sensitivity analysis to input parameters , 2010, Qual. Reliab. Eng. Int..

[6]  Layth C. Alwan,et al.  TIME-SERIES INVESTIGATION OF SUBSAMPLE MEAN CHARTS , 1992 .

[7]  W. A. Shewhart,et al.  Quality control charts , 1926 .

[8]  Giovanni Celano,et al.  The economic performance of the Shewhart t chart , 2012, Qual. Reliab. Eng. Int..

[9]  Erwin M. Saniga,et al.  Economic, Statistical, and Economic-Statistical Design of Attribute Charts , 1995 .

[10]  Antonio Fernando Branco Costa,et al.  Variable parameter and double sampling charts in the presence of correlation: The Markov chain approach , 2011 .

[11]  Rassoul Noorossana,et al.  Simple linear profiles monitoring in the presence of within profile autocorrelation , 2009, Comput. Ind. Eng..

[12]  T. Harris,et al.  Statistical process control procedures for correlated observations , 1991 .

[13]  Acheson J. Duncan,et al.  The Economic Design of X Charts Used to Maintain Current Control of a Process , 1956 .

[14]  Stelios Psarakis,et al.  SPC Procedures for Monitoring Autocorrelated Processes , 2007 .

[15]  George Nenes,et al.  The economically designed CUSUM chart for monitoring short production runs , 2006 .

[16]  J. Bert Keats,et al.  Sensitivity study of the CUSUM control chart with an economic model , 1995 .

[17]  Richard A. Johnson,et al.  The Effect of Serial Correlation on the Performance of CUSUM Tests II , 1974 .

[18]  Erwin M. Saniga,et al.  Economic Statistical Control-Chart Designs With an Application to and R Charts , 1989 .

[19]  A. Vasilopoulos,et al.  Modification of Control Chart Limits in the Presence of Data Correlation , 1978 .

[20]  Philippe Castagliola,et al.  Effect of measurement error and autocorrelation on the X¯ chart , 2011 .

[21]  Giovanni Celano,et al.  The Economic Performance of a CUSUM t Control Chart for Monitoring Short Production Runs , 2012 .

[22]  Antonio Fernando Branco Costa,et al.  Economic-statistical design of the X chart used to control a wandering process mean using genetic algorithm , 2012, Expert Syst. Appl..

[23]  Douglas C. Montgomery,et al.  Statistical quality control : a modern introduction , 2009 .

[24]  D. Apley,et al.  The Autoregressive T2 Chart for Monitoring Univariate Autocorrelated Processes , 2002 .

[25]  Cheng-Chang Chang,et al.  Economic design of the VSSI control charts for correlated data , 2007 .

[26]  Ruey-Shiang Guh,et al.  Effective recognition of control chart patterns in autocorrelated data using a support vector machine based approach , 2011, Comput. Ind. Eng..

[27]  Giovanni Celano,et al.  A new sampling strategy to reduce the effect of autocorrelation on a control chart , 2014 .

[28]  John R. English,et al.  Detecting changes in autoregressive processes with X¯ and EWMA charts , 2000 .

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

[30]  Douglas C. Montgomery,et al.  Some Statistical Process Control Methods for Autocorrelated Data , 1991 .

[31]  Thaung Lwin.  Parameter estimation in first-order autoregressive model for statistical process monitoring in the p , 2011 .

[32]  Pei-Hsi Lee,et al.  An economic-statistical design of double sampling control chart , 2009 .

[33]  Kristof Mertens,et al.  An intelligent control chart for monitoring of autocorrelated egg production process data based on a synergistic control strategy , 2009 .

[34]  Rassoul Noorossana,et al.  Effect of Autocorrelation on Performance of the MCUSUM Control Chart , 2006, Qual. Reliab. Eng. Int..

[35]  Chao-Yu Chou,et al.  Economic Design of Averages Control Charts for Monitoring a Process with Correlated Samples , 2001 .

[36]  Giovanni Celano,et al.  A stochastic shift model for economically designed charts constrained by the process stage configuration , 2011 .

[37]  Shu-Ling Wang,et al.  Economic design of autoregressive moving average control chart using genetic algorithms , 2012, Expert Syst. Appl..