Economic modelling for statistical process control subject to a general quality deterioration

Abstract

The applications of control chart have traditionally focused on the detection of step shifts in process mean. However, changes are usually gradual, not as perfect step shifts. The common consideration of a shift as a step function does not always adequately describe what actually happens in practice. Hence, there is a need for more realistic assumptions to be incorporated. This paper employs a Markov chain approach and provides a way to quantitatively measure the economic performance of control charts in the presence of a more general quality deterioration mechanism. The finite production run is considered in the model as it has become a very important production mode at present and the process failure mechanism is described by geometric distribution. The chart properties, particularly on the issues of the quality deterioration mechanism, are investigated. The findings provide critical insights on the use of step shift assumption when designing control charts.

Keywords:

• statistical process control
• economic design
• shift mechanism
• Markov chain
• finite production runs

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 70872091], [grant number 71371163]. This work was also funded by MOE (Ministry of Education in China) Project of Humanities and Social Sciences [grant number 13YJA630078].