Comparison between two methods of the economic-statistical design of profile monitoring under the double sampling scheme

Abstract

In many applications, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. This functional relationship is referred to as a profile. We extend two existing methods for monitoring the shift of slope of linear profiles. We consider the single sampling (SS) and the double sampling (DS) scheme for the economic-statistical design (ESD) model of profile monitoring in Phase II. The results of a numerical example indicate the DS ${\hat{\beta }}_1$ control chart has better performance than the DS $T^2$ control chart when ${\rho }_{{\hat{\beta }}_0,{\hat{\beta }}_1}$ is low. Comparison of the ESD of DS $\widehat{{\beta }_1}$ and the SD of DS $\widehat{{\beta }_1}$ control charts show that an ESD has an improvement over the pure SD. Also, we compare the ESD of the DS $\widehat{{\beta }_1}$ with the ESD of the SS $\widehat{{\beta }_1}$ control chart. The results show that the DS $\widehat{{\beta }_1}$ control charts are more efficient in terms of minimizing the $E(L)$.

Keywords:

• Double sampling
• profile monitoring
• $T^2$ Hotelling
• Panagos's cost model
• economic-statistical design
• statistical design

2010 Mathematics Subject Classifications:

• 62P30
• 62D99

Acknowledgments

The authors would like to thank the AE and the reviewers for their comments and suggestions to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.