The Economic Design of Cusum Charts for Controlling Normal Means

Abstract

Summary This paper proposes a production model for quality surveillance, which is based on a cusum chart using the decision interval criterion. An algorithm for determining the economically optimum control parameters is presented. Some criticisms of the conventional ad hoc design of a cusum chart are made, and it is suggested that the average run lengths (ARL) at the rejectable quality level should be less than 2 when this model is applicable. A simplified version of the algorithm is also devised which gives control plans which are close to optimum. This scheme is suitable for application at the factory level. Also included is a table of ARL for some neglected, but useful, values of the decision interval and the process deviate.

Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts

“…We designed four experiments-three are essentially the same as in Saniga et al (2006b) after example problems in the literature provided by Chiu (1974) and Lorenzen and Vance (1986). These are defined in Saniga et al (2012), but we provide some definition here as well because there is a slight difference.…”

“…The four experiments are as follows: Experiment A: Here we find designs for 7,680 configurations of cost and system parameters derived from Chiu's (1974) In each of the experiments we also allow an alternative process control strategy to be employed if it is economically better than either the CUSUM or N X chart. This policy is a regular search policy.…”

Performance Measures for ―X Charts with Asymmetric Control Limits

“…The essential features of Duncan's 3 production process model are slightly generalized 1,[9][10][11][12] . The model is also extended to allow actions targeted toward specific types of assignable causes 13 .…”

The Detection of flow Meter Drift by Using Statistical Process Control

“…The purpose of doing this was to enable these parameters to be chosen optimally under the average cost criterion. Chiu [27] had some criticisms on Taylor's method. Chiu presented a study of the economic design of cusum charts, which, according to Chiu, overcame the aforementioned criticisms.…”