A neuro-fuzzy multi-objective design of shewhart control charts

Abstract

Control charts are widely used to establish statistical process control (SPC) and maintain manufacturing processes in desired operating conditions. Effective use of a control chart requires finding the best parameters for the optimal operation of the chart, which is called design of control chart. The design of control chart involves the selection of three parameters namely, the sample size, the sampling interval, and the control limits coefficients. Conventional approaches to design control charts include complex mathematical models and associated optimization schemes. Also, Conventional approaches usually use point estimators of the input parameters which are not able to represent the true parameters sufficiently. The input parameters are suffered from ambiguity uncertainty, which can be effectively modeled by using fuzzy set theory. In this paper a fuzzy multi-objective model for economic-statistical design of X-bar control chart, in which the input parameters are expressed by fuzzy membership functions, is proposed. Moreover, an ANFIS approach is used to transform the complex fuzzy multi-objective model into a fuzzy rule-base. Next, a genetic algorithm (GA) has been developed to find the best design (input) parameters of control charts. Finally, the proposed approach is tested and validated by using a numerical example. © 2007 Springer-Verlag Berlin Heidelberg.