A teaching–learning based optimization approach for economic design of X-bar control chart

Abstract

Being simple to use X-bar control chart has been most widely used in industry for monitoring and controlling manufacturing processes. Measurements of a quality characteristic in terms of samples are taken from the production process at regular interval and the sample means are plotted on this chart. Design of a control chart involves the selection of three parameters, namely the sample size (n), the sampling interval (h) and the width of control limits (k). In case of economic design, these three control chart parameters are selected in such a manner that the total cost of controlling the process is the least. The effectiveness of this design depends on the accuracy of determination of these three parameters. In this paper, a new efficient and effective optimization technique named as teaching–learning based optimization (TLBO) has been used for the global minimization of a loss cost function expressed as a function of three variables n, h and k in an economic model of X-bar chart based on unified approach. In this work, the TLBO algorithm has been modified to simplify the tuning of teaching factor. A MATLAB computer program has been developed for this purpose. A numerical example has been solved and the results are found to be better than the earlier published results. Further, the sensitivity analysis using fractional factorial design and analysis of variance have been carried out to identify the critical process and cost parameters affecting the economic design.