![Sample our Economics, Finance,Business & Industry journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5931/TOC-Subject-Sample-2021-Economics-Finance-Business-Industry.jpg"})
Abstract
The in-control performance of Shewhart and S2 control charts with estimated in-control parameters has been evaluated by a number of authors. Results indicate that an unrealistically large amount of Phase I data is needed to have the desired in-control average run length (ARL) value in Phase II. To overcome this problem, it has been recommended that the control limits be adjusted based on a bootstrap method to guarantee that the in-control ARL is at least a specified value with a certain specified probability. In this article we present simple formulas using the assumption of normality to compute the control limits and therefore, users do not have to use the bootstrap method. The advantage of our proposed method is in its simplicity for users; additionally, the control chart constants do not depend on the Phase I sample data.
Acknowledgements
The authors gratefully acknowledge the Editor-in-Chief, the Editor and the referees for their valuable comments and suggestions as well as W.H. Woodall, G. Celano and A. Seif for their supports and discussions on the various versions of this paper. Furthermore, Alireza Faraz acknowledges financial support from F.R.S.-FNRS (postdoctoral researcher grant from ‘Fonds de la Recherche Scientifique-FNRS’, Belgium). The work of C. 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’.