Economical-Statistical design of one- sided CCC-r control chart based on analytical hierarchy process

Document Type : Research Paper


Yazd University


The cumulative count of a conforming (CCC) control chart is used for high quality processes.The CCC − r chart is an improvement of the CCC chart that is based on the cumulative number of items inspected until observing r non-conforming ones. This paper aims to propose a new approach for manufacturer’s decision making according to the criteria among the available options. The objective function of the proposed model is to minimize three criteria simultaneously, including expected cost per hour(C), modified producer risk (PR) and modified consumer risk (CR).the solution method for the proposed model is designed by using AHP technique and a case study is analyzed described in numerical illustration section. In addition, sensitivity analysis is performed to illustrate efficacy of the input parameters on the optimal solutions of the proposed model.


Main Subjects

Zhang, C.W., M. Xie, and T. Jin, An improved self-starting cumulative count of conforming chart for monitoring high-quality processes under group inspection. International Journal of Production Research, 2012. 50(23): p. 7026-7043.
Zhang, C., M. Xie, and T. Goh, On cumulative conforming type of control charts for high quality processes under sampling inspection. Economic Quality Control, 2005. 20(2): p. 205-222.
Calvin, T.W., Quality Control Techniques for" Zero Defects". Components, Hybrids, and Manufacturing Technology, IEEE Transactions on, 1983. 6(3): p. 323-328.
Goh, T., A control chart for very high yield processes. Quality Assurance, 1987. 13(1): p. 18-22.
 Xie, M., T. Goh, and X. Lu, A comparative study of CCC and CUSUM charts. Quality and Reliability Engineering International, 1998. 14(5): p. 339-345.
Tang, L.C. and W.T. Cheong, Cumulative conformance count chart with sequentially updated parameters. IIE Transactions, 2004. 36(9): p. 841-853.
Liu, J., et al., Cumulative count of conforming chart with variable sampling intervals. International Journal of Production Economics, 2006. 101(2): p. 286-297.
Zhang, C.W., M. Xie, and T.N. Goh, Economic design of cumulative count of conforming charts under inspection by samples. International Journal of Production Economics, 2008. 111(1): p. 93-104.
Chan, L.-Y. and S. Wu, Optimal design for inspection and maintenance policy based on the CCC chart. Computers & Industrial Engineering, 2009. 57(3): p. 667-676.
Chen, J.T., A new approach to setting control limits of cumulative count of conforming charts for high‐yield processes. Quality and Reliability Engineering International, 2009. 25(8): p. 973-986.
Chen, Y.K., C.Y. Chen, and K.C. Chiou, Cumulative conformance count chart with variable sampling intervals and control limits. Applied Stochastic Models in Business and Industry, 2011. 27(4): p. 410-420.
Acosta-Mejia, C.A., Two-sided charts for monitoring nonconforming parts per million. Quality Engineering, 2012. 25(1): p. 34-45.
Moghaddam, A.S., A. Amiri, and M. Bashiri, MULTI-OBJECTIVE ECONOMIC-STATISTICAL DESIGN OF CUMULATIVE COUNT OF CONFORMING CONTROL CHART. International Journal of Engineering-Transactions A: Basics, 2014. 27(10): p. 1591.
Ohta, H., E. Kusukawa, and A. Rahim, A CCC-r chart for high-yield processes. Quality and Reliability Engineering International, 2001. 17(6): p. 439-446.
Wu, Z., X. Zhang, and S.H. Yeo, Design of the sum-of-conforming-run-length control charts. European Journal of Operational Research, 2001. 132(1): p. 187-196.
Kuralmani, V., et al., A conditional decision procedure for high yield processes. IIE Transactions, 2002. 34(12): p. 1021-1030.
Chan, L., et al., A two-stage decision procedure for monitoring processes with low fraction nonconforming. European Journal of Operational Research, 2003. 150(2): p. 420-436.
Schwertman, N.C., Designing accurate control charts based on the geometric and negative binomial distributions. Quality and Reliability Engineering International, 2005. 21(8): p. 743-756.
Albers, W., The optimal choice of negative binomial charts for monitoring high-quality processes. Journal of Statistical Planning and Inference, 2010. 140(1): p. 214-225.
Tang, X., M. Xie, and T. Goh, A note on economic-statistical design of cumulative count of conforming control chart. Economic Quality Control, 2000. 15: p. 3-14.
Lorenzen, T.J. and L.C. Vance, The economic design of control charts: a unified approach. Technometrics, 1986. 28(1): p. 3-10.
Xie, M., X. Tang, and T. Goh, On economic design of cumulative count of conforming chart. International Journal of Production Economics, 2001. 72(1): p. 89-97.
Duncan, A.J., The economic design of X charts used to maintain current control of a process. Journal of the American Statistical Association, 1956. 51(274): p. 228-242.
Zhang, H., et al., Economic design of time-between-events control chart system. Computers & Industrial Engineering, 2011. 60(4): p. 485-492.
Yılmaz, Ş. and N. Burnak, An Economic Approach to the Management of High‐Quality Processes. Quality and Reliability Engineering International, 2013. 29(5): p. 681-690.
Fallahnezhad, M. and V. Golbafian, "Economic design of CCC-r control charts based on Average Number of Inspected items". Scientia Iranica (In Press) 2016.
Fallahnezhad, M.S. and A.A. Yazdi, A New Optimization Model for Designing Acceptance Sampling Plan Based on Run Length of Conforming Items. Journal of Industrial and Systems Engineering, 2016. 9(2): p. 0-0.
Colson, G. and C. De Bruyn, Models and methods in multiple objectives decision making. Mathematical and Computer Modelling, 1989. 12(10): p. 1201-1211.
Aksakal, E. and M. Dağdeviren, Analyzing Reward Management Framework with Multi Criteria Decision Making Methods. Procedia-Social and Behavioral Sciences, 2014. 147: p. 147-152.
Volume 9, Issue 3
July 2016
Pages 127-145
  • Receive Date: 12 April 2016
  • Revise Date: 11 June 2016
  • Accept Date: 25 July 2016
  • First Publish Date: 25 July 2016