A generalized approach to economic design of control charts: A discussion on implementing

Abstract

ABSTRACTDue to the importance of choosing between uniform and non uniform sampling schemes in quality control inspections, two generalized models for the economic design of control charts under both schemes are presented separately in this paper. Under uniform sampling plan, two leading models of Lorenzen and Vance (1986) and McWilliams (1989) can be obtained by applying, respectively, Exponential and Weibull in-control time distributions in the uniform generalized model. Furthermore, the generalized model of Rahim and Banerjee (1993) is achieved by using an alternative approach under arbitrary sampling interval plan. These outcomes lead us to present a comprehensive discussion on implementing the economic and economic statistical design of control charts. By imposing a new proposed restriction on the economic model, we can guarantee to have control charts whose power to report the true alarm at the end of each sampling interval is more than shift conditional probability over that interval given no shift till its start. The new restricted economic model, which we call “high-powered economic design of control charts”, can be considered as a special case of economic statistical design. The advantages of our proposed model are highlighted by some numerical examples.