Construction of Six Sigma-based control chart for interval-valued data

Abstract

Construction of control charts is straightforward if the data are real-valued. However, there are situations where data are essentially interval-valued in which each observation is represented by minimum and maximum values. While there are only few attempts to develop control charts for interval-valued data, there have been no simple-to-use approaches developed to deal with such type of data. In this article, we propose to make use of the popular Taguchi orthogonal array experiment to first redefine the data for experimental setup and then use Six Sigma control limits to determine overall control limits for interval-valued data. The resulting multiple control limits have inner and outer control limits for simultaneously monitoring minimum and maximum values of the averages of interval-valued data. The proposed control chart is then illustrated using a data set, and conclusions are drawn based on the results. It is observed that the proposed Six Sigma-based control chart for interval-valued data is, in fact, easy-to-use, and it performs better in detecting the out-of-control situations. We have established this using average run length comparisons as well with the traditional charts.