Economic and economic-statistical designs of the side sensitive group runs chart

A new optimization algorithm is proposed for the economic models of the SSGR chart.Optimal design parameters of the SSGR chart are computed based on ARL and EARL.Sensitivity analyses are conducted for various input parameters of the cost model.Effects of misspecification of the shift size on the performance of the SSGR chart are investigated.The performance of the SSGR chart is compared with that of the Shewhart X ? , synthetic, GR and EWMA charts. The idea of proposing the economic and economic-statistical designs of the side sensitive group runs (SSGR) chart is presented in this paper. In the economic design, a simplified algorithm is used to search for the optimal design parameters that minimize the expected hourly cost. Nevertheless, this design has a major weakness, where it overlooks the statistical performance of the control chart. Therefore, in order to improve the effectiveness of the control chart in detecting process shifts, the economic-statistical design takes into account the statistical properties while the cost is minimized by placing statistical constraints upon the cost model of the economic design. Besides formulating the economic and economic-statistical designs based on the average run length (ARL), the economic and economic-statistical designs of the SSGR chart are also formulated based on the expected average run length (EARL) since the process shift size is usually unknown in real situations. In this paper, the sensitivity analyses of the optimal cost and the optimal design parameters are implemented for various input parameters. The effects of misspecification of the shift size on the performance of the SSGR chart are also illustrated based on numerical examples for different input parameters. This paper will also look at whether the SSGR chart performs economically better than the Shewhart X ? , synthetic, group runs (GR) and EWMA charts in the economic-statistical design based on the EARL. From the results of comparison, it is shown that the economic performance of the SSGR chart is better than that of the other four control charts in most practical situations.

[1]  Seyed Taghi Akhavan Niaki,et al.  Economic Design of Variable Sampling Interval X-Bar Control Charts for Monitoring Correlated Non Normal Samples , 2013 .

[2]  R. N. Rattihalli,et al.  A Side Sensitive Group Runs Control Chart for Detecting Shifts in the Process Mean , 2007, Stat. Methods Appl..

[3]  Philippe Castagliola,et al.  Synthetic double sampling np control chart for attributes , 2014, Comput. Ind. Eng..

[4]  A. Amiri,et al.  Economic‐Statistical Design of Acceptance Control Chart , 2013, Qual. Reliab. Eng. Int..

[5]  R. N. Rattihalli,et al.  A Group Runs Control Chart for Detecting Shifts in the Process Mean , 2004 .

[6]  Zhi-Fang Guo,et al.  Economic Design of the Variable Parameters X¯ Control Chart with a Corrected A&L Switching Rule , 2014, Qual. Reliab. Eng. Int..

[7]  Michael B. C. Khoo,et al.  Side-sensitive group runs double sampling (SSGRDS) chart for detecting mean shifts , 2015 .

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

[9]  Philippe Castagliola,et al.  Economic‐Statistical Design of the Synthetic X¯ Chart with Estimated Process Parameters , 2015, Qual. Reliab. Eng. Int..

[10]  Marion R. Reynolds,et al.  Control Charts and the Efficient Allocation of Sampling Resources , 2004, Technometrics.

[11]  Trevor A Spedding,et al.  A Synthetic Control Chart for Detecting Small Shifts in the Process Mean , 2000 .

[12]  Philippe Castagliola,et al.  Economically Optimum Design of a Synthetic X¯ Chart , 2012, Qual. Reliab. Eng. Int..

[13]  Seyed Taghi Akhavan Niaki,et al.  Economic and Economic‐Statistical Designs of Phase II Profile Monitoring , 2014, Qual. Reliab. Eng. Int..

[14]  Chi Zhang,et al.  A general framework for monitoring complex processes with both in-control and out-of-control information , 2015, Comput. Ind. Eng..

[15]  Zhang Wu,et al.  Optimization design of control charts based on Taguchi's loss function and random process shifts , 2004 .

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

[17]  Rukmini V. Kasarapu,et al.  Economic design of x¯ control charts considering process shift distributions , 2014 .

[18]  Tongdan Jin,et al.  An improved self-starting cumulative count of conforming chart for monitoring high-quality processes under group inspection , 2012 .

[19]  Wen-Chih Chiu,et al.  Economic-statistical Design of Maximum Exponentially Weighted Moving Average Control Charts , 2013, Qual. Reliab. Eng. Int..

[20]  Marion R. Reynolds,et al.  Should Observations Be Grouped for Effective Process Monitoring? , 2004 .

[21]  H. Saunders,et al.  Probabilistic Engineering Design—Principles and Applications , 1987 .

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

[23]  Divya Pandey,et al.  A methodology for joint optimization for maintenance planning, process quality and production scheduling , 2011, Comput. Ind. Eng..

[24]  Dogan A. Serel,et al.  Economic design of EWMA control charts based on loss function , 2009, Math. Comput. Model..

[25]  Sebnem Yilmaz,et al.  An Economic Approach to the Management of High-Quality Processes , 2013, Qual. Reliab. Eng. Int..

[26]  Thong Ngee Goh,et al.  Economic design of time-between-events control chart system , 2011, Comput. Ind. Eng..

[27]  Miaomiao Yu,et al.  Economic and economic-statistical designs of an control chart for two-unit series systems with condition-based maintenance , 2013, Eur. J. Oper. Res..

[28]  Philippe Castagliola,et al.  A new memory-type monitoring technique for count data , 2015, Comput. Ind. Eng..

[29]  Philippe Castagliola,et al.  Optimal design of the double sampling X chart with estimated parameters based on median run length , 2014, Comput. Ind. Eng..

[30]  Chi-Hyuck Jun,et al.  An exponentially weighted moving average chart controlling false discovery rate , 2014 .

[31]  Seyyed M. T. Fatemi Ghomi,et al.  Economic Design of Exponentially Weighted Moving Average Control Chart Based on Measurement Error Using Genetic Algorithm , 2014, Qual. Reliab. Eng. Int..

[32]  Antonio F. B. Costa,et al.  Some Comments Regarding the Synthetic Chart , 2014 .

[33]  Toni Lupo.  Comparing the Economic Effectiveness of Various Adaptive Schemes for the c Chart , 2014, Qual. Reliab. Eng. Int..

[34]  Sotiris Bersimis,et al.  A compound control chart for monitoring and controlling high quality processes , 2014, Eur. J. Oper. Res..

[35]  Kun-Jen Chung,et al.  A simplified procedure for the economic design of X¯ -charts , 1990 .

[36]  Thong Ngee Goh,et al.  Economic design of cumulative count of conforming charts under inspection by samples , 2008 .

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

[38]  Antonio Fernando Branco Costa,et al.  The steady‐state behavior of the synthetic and side‐sensitive synthetic double sampling X¯ charts , 2015, Qual. Reliab. Eng. Int..

[39]  S. Raissi,et al.  Economic design of Hotelling’s T2 control chart on the presence of fixed sampling rate and exponentially assignable causes , 2014 .

[40]  Michael B. C. Khoo,et al.  Economic and economic statistical designs of the synthetic chart using loss functions , 2013, Eur. J. Oper. Res..

[41]  Giovanni Celano,et al.  Economic design of inspection strategies to monitor dispersion in short production runs , 2010, Comput. Ind. Eng..

[42]  Seyed Taghi Akhavan Niaki,et al.  A parameter-tuned genetic algorithm to optimize two-echelon continuous review inventory systems , 2011, Expert Syst. Appl..

[43]  Ross Sparks,et al.  CUSUM Charts for Signalling Varying Location Shifts , 2000 .

[44]  Giovanni Celano.  On the economic-statistical design of control charts constrained by the inspection workstation configuration , 2010 .

[45]  Philippe Castagliola,et al.  Development of a multiattribute synthetic-np chart , 2014 .

[46]  Amirhossein Amiri,et al.  Robust economic and economic-statistical design of EWMA control chart , 2015 .

[47]  Jennifer Brown,et al.  Improved Exponentially Weighted Moving Average Control Charts for Monitoring Process Mean and Dispersion , 2015, Qual. Reliab. Eng. Int..

[48]  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..

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

[50]  Shing I. Chang,et al.  Economic design of two-stage non-central chi-square charts for dependent variables , 2011, Comput. Ind. Eng..

[51]  Wen-Chih Chiu.  Economic-Statistical Design of EWMA Control Charts Based on Taguchi's Loss Function , 2015, Commun. Stat. Simul. Comput..

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

[53]  Tiantian Wang,et al.  An economically designed Sequential Probability Ratio Test control chart for short-run production , 2014, Comput. Ind. Eng..

[54]  Kun-Jen Chung.  A simplified procedure for the economic design of control charts : a unified approach , 1991 .

[55]  Thong Ngee Goh,et al.  On economic design of cumulative count of conforming chart , 2001 .

[56]  Michael B. C. Khoo,et al.  Economically Optimal Design of a Multivariate Synthetic T 2 Chart , 2014, Commun. Stat. Simul. Comput..

[57]  Alireza Faraz,et al.  Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to X¯ bar and S2 Charts , 2013, Qual. Reliab. Eng. Int..

[58]  Seoung Bum Kim,et al.  Gower distance-based multivariate control charts for a mixture of continuous and categorical variables , 2014, Expert Syst. Appl..