A hierarchy of adaptive (X)over-bar control charts

Abstract

The purpose of this article is to present a statistical design of a hierarchy of two-states adaptive parameters (X) over bar charts. We assume that the shift in the process mean does not occur at the beginning of the production process but at some random time in the future. The occurrence time of the shift is assumed to be an exponentially distributed random variable. This assumption allows the application of the Markov chain approach for developing performance measures. Seven adaptive (X) over bar charts result from the combinations of the design parameters, that is, the sample size, the sampling interval, and the factor used to define the control limits, when one, two, or all of them are allowed to vary. arranged in a hierarchy. When comparing the performance between different two-state charts one sometimes can use a chart with fewer parameters varying and yet achieve good performance, however this depends on the size of process shift. One can change the probability of the control system to be in a state of loose control: considering that, its effect on the adjusted average time to signal and on the design parameters was analyzed numerically. (C) 2009 Elsevier B.V. All rights reserved.