Economic design of exponential charts for time between events monitoring

The occurrence of defects or non-conformities in manufacturing processes can usually be modeled by a homogeneous Poisson process. However, the process parameter may change over time and it can be monitored with statistical process control techniques. Control charts based on an exponential distribution, called exponential charts in this paper, can be developed to monitor the occurrence rate of such events. For manufacturers, the economic objective of production is very important and has to be optimized. An economic approach is developed in this paper for the design of exponential charts. We compare and contrast the performances of statistical design, economic design and economic–statistical design. The usefulness of the proposed economic design approach is justified. The relationships among these designs are illustrated through numerical examples. In particular, the economic–statistical design approach is interpreted from a multi-objective optimization viewpoint. The limitations of the approach as well as future research are also discussed.

[1]  E. Saniga.  Economic Statistical Control-Chart Designs with an Application to X̄ and R Charts@@@Economic Statistical Control-Chart Designs with an Application to X and R Charts , 1989 .

[2]  Thong Ngee Goh,et al.  A study of economic design of control charts for cumulative count of conforming items , 1997 .

[3]  Douglas C. Montgomery,et al.  Research Issues and Ideas in Statistical Process Control , 1999 .

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

[5]  Thong Ngee Goh,et al.  Cumulative quantity control charts for monitoring production processes , 2000 .

[6]  A. Duncan.  The Economic Design of -Charts When There is a Multiplicity of Assignable Causes , 1971 .

[7]  Abdur Rahim,et al.  An economic model for \font\twelveit=cmti10 scaled 1600$\overline{\kern‐0.85ex\hbox{\twelveit X}}$\nopagenumbers\end and R charts with time‐varying parameters , 2002 .

[8]  Thong Ngee Goh,et al.  Some effective control chart procedures for reliability monitoring , 2002, Reliab. Eng. Syst. Saf..

[9]  Chung-Ho Chen,et al.  Economic-Statistical Design of Multivariate Control Charts Using Quality Loss Function , 2002 .

[10]  Erwin M. Saniga,et al.  Economic-Statistical Design of X̄ and R or X̄ and S Charts , 2001 .

[11]  Eugenio K. Epprecht,et al.  Constrained optimization model for the design of an adaptive X chart , 2002 .

[12]  W. Woodall,et al.  ON THE ECONOMIC DESIGN OF MULTIVARIATE CONTROL CHARTS , 2002 .

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

[14]  Connie M. Borror,et al.  Robustness of the time between events CUSUM , 2003 .

[15]  Changsoon Park,et al.  Economic design of a variable sampling rate EWMA chart , 2004 .

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

[17]  Eli A. Glushkovsky.  ‘On-line’ G-control chart for attribute data , 1994 .

[18]  Antonio Fernando Branco Costa,et al.  Economic design of X charts with variable parameters: The Markov chain approach , 2001 .

[19]  Sheldon M. Ross,et al.  Introduction to probability models , 1975 .

[20]  Douglas C. Montgomery,et al.  Statistically constrained economic design of the multivariate exponentially weighted moving average control chart , 2001 .

[21]  Chao-Yu Chou,et al.  Economic-statistical design of X ¥ charts for non-normal data by considering quality loss , 2000 .

[22]  Chung-Ho Chen,et al.  Economic design of X charts for non-normally correlated data , 2001 .

[23]  James M. Lucas,et al.  Counted Data CUSUM's , 1985 .

[24]  Charles W. Champ,et al.  Phase I control charts for times between events , 2002 .