Guaranteed conditional performance of the S² control chart with estimated parameters

Abstract

We evaluate the in-control performance of the S² control chart with estimated parameters conditional on the Phase I sample. Simulation results indicate no realistic amount of Phase I data is enough to have confidence that the in-control average run length (ARL) obtained will be near the desired value. To overcome this problem, we adjust the S² chart’s control limits such that the in-control ARL is guaranteed to be above a specified value with a certain specified probability. The required adjustment does not have too much of an adverse effect on the out-of-control performance of the chart.

Keywords:

• average of ARL (AARL)
• average run length (ARL)
• bootstrap
• effect of estimation error
• standard deviation of ARL (SDARL)

Acknowledgements

The authors of this manuscript are grateful to the reviewers and the Associate Editor for their valuable comments which allowed us to improve the quality of the manuscript.

Additional information

Funding

Alireza Faraz acknowledges financial support from F.R.S.-FNRS (postdoctoral researcher grant from ‘Fonds de la Recherche Scientifique-FNRS’, Belgium) and from IAP research network P7/06 of the Belgian Government (Belgian Science Policy). The work of Woodall was supported by the U.S. National Science Foundation under Grant CMMI-1436365. Heuchenne acknowledges financial support from IAP research network P7/06 of the Belgian Government (Belgian Science Policy) and from the contract ‘Projet d’Actions de Recherche Concertees’ (ARC) 11/16-039 of the ‘Communaute Francaise de Belgique’, granted by the ‘Academie Universitaire Louvain’.