Flexible Control Limits for Interval-Valued Data Using Mixture Probability Distributions

Abstract

Availability of data in different forms is a boon or bane as it may require different approaches to deal with. In fact, while the construction of control charts is straightforward if the data are real-valued, in many practical situations data are essentially interval-valued with observations often represented by minimum and maximum values. While there are only fewer attempts to develop control charts for interval-valued data, no simple-to-use approaches have been proposed to deal with such type of data. In this paper, considering the idea of the development of control limits for multi-stream processes, we propose to make use of the mixture probability distributions approach to determine control limits for the interval-valued data. The resulting control limits are flexible in nature as they are linked to the control limits of the overall distribution that is based on the average of the means of two upper and lower populations along with their respective standard deviations. We have studied and numerically evaluated the average run length (ARL) properties of the proposed control chart to demonstrate the ways of determining the control chart coefficients. The proposed control chart is then illustrated using a dataset and conclusions are drawn based on the results.