Statistical Design of Control Charts with Two Pairs of Control Limits

Abstract:

Aiming to the production processes which require two kinds of restoration procedures, this paper describes charts with two pairs of control limits. Different restoration procedures depend on where a sample mean is. We study the positions of these control limits and statistical properties of these charts. The conclusion is that these charts have the same average run length as the traditional Shewhart charts for in-control process or out-of-control process. However they can distinguish between the big shift sizes and the small shift sizes of the process mean effectively.

• Periodical: Advanced Materials Research (Volumes 538-541)
• Pages: 2882-2886
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.538-541.2882
• Online since: June 2012
• Authors: Bao Cai Guo
• Keywords: Control Chart, Control Limits, Statistical Design

References

[1] H.A. Kannpenberger and A.H.E. Grandage. "Minimum cost quality control tests," AIIE Transactions, vol. 1(1969), pp.24-32.

[2] A.J. Duncan. "The economic design of charts when there is a multiplicity of assignable causes," Journal of American Statistical Association, vol. 66(1971), pp.107-121.

DOI: 10.1080/01621459.1971.10482230

[3] C. Park..C and M.R. Reynolds. "Economic design of a variable sampling rate chart," Journal of Quality Technology, vol. 31(1999), pp.427-443.

DOI: 10.1080/00224065.1999.11979949

[4] F.J.Yu, J.L. Hou. "Optimization of design parameters for control charts with multiple assignable causes," Journal of Applied Statistics, vol. 33(2006), pp.279-290.

DOI: 10.1080/02664760500445541

[5] S Maysa, D Magalhaes., A.F.B. Costa and F.D.M. Neto. "Adaptive control charts: a Markovian approach for processes subject to independent disturbances," International Journal of Production Economics, vol. 99 (2006), pp.236-246.

DOI: 10.1016/j.ijpe.2004.12.013

[6] J.W. Schmidt, G.K. Benett and K.E. Case. "A three action cost model for acceptance sampling by variables," Journal of Quality Technology, vol. 12(1980), pp.10-18.

[7] G. Tagaras and H.L. Lee. "Economic design of control charts with different control limits for different assignable causes," Management Science, vol. 34 (1988), pp.1347-1366.

DOI: 10.1287/mnsc.34.11.1347

[8] Kun-jen Chung. "Economic design of control charts with two control limits" Computers &industrial Engineering, vol. 28 (1995), pp.437-455.

DOI: 10.1016/0360-8352(94)00202-x

[9] M Xie and Q Wang. "Economic design of control charts with different control limits for different assignable causes in 100% inspection," Application of Statistics and Management, vol. 20(2001), pp.17-23.

[10] W.H. Woodall. "Weakness of economic design of control charts,". Technometrics, vol. 28(1986), pp.408-409.