Control charts: a cost‐optimization approach for processes with random shifts

Abstract

SUMMARYIn this paper we describe an approach for establishing control limits and sampling times which derives from economic performance criteria and a model for random shifts. The total cost related to both production and control is calculated, based on cost estimates for false alarms, for not identifying a true out of control situation, and for obtaining a data record through sampling. We describe the complete process for applying the method and compare with conventional procedures to real data from a Portuguese pulp and paper industrial plant. It turns out that substantial cost-reductions may be obtained.

Markov chain‐based cost‐optimal control charts for health care data

“…The methods and R implementation in this paper largely depend on the works of Zempléni et al The first part of this section gives a brief introduction to the methods used in their paper …”

“…The previous simple framework can be used for more general designs. Zempléni et al used this method to set up economically optimal control charts where shifts are assumed to have a random size and only the distribution of the shift size is known. This means that the shift size is no longer assumed to be fixed and known, which is important in modelling various processes not just in health care, but in industrial or engineering settings too.…”

“…The control chart design which is presented here for dealing with these problems is the Markov chain‐based framework. This framework was developed by Zempléni et al in 2004 and was successfully applied on data collected from a Portuguese pulp plant . Their article provided suitable basis for generalisations.…”

“…Cost‐efficient Markov chain‐based control charts build upon Duncan's cycle based model, as these also partition the time into different segments for cost calculation purposes. The previous paper from has already introduced the random shift size element. In this paper, we expand upon that idea and develop further generalisations to create cost‐efficient Markov chain‐based control charts for health care data.…”

Application of Markov Chains for Modeling and Managing Industrial Electronic Repair Processes

“…Third, Markov chains and processes are widely used for process improvement. For example, based on Markov processes, the optimal number of repairs was determined (Castro and Pérez-Ocón, 2006), an optimal production-maintenance policy was applied to minimize expected average cost of operation (Wang and Sheu, 2003), a Markov chain model was used to determine optimal replacement policies (Zhang and Love, 2000) and for finding the optimal values of control limits (Zempléni et al, 2004). Accordingly, modeling based on Markov chains not only agrees with the objective of modeling ERPs but fits to the object of the analysis as well.…”