Economic design of exponential charts for time between events monitoring

Abstract

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.

Keywords:

• Control chart
• Economic design
• Exponential distribution
• Homogeneous Poisson process
• Time between events

Acknowledgements

The authors are very grateful to the anonymous referees for valuable comments and suggestions that have greatly improved the paper.