Interval-valued process data monitoring and controlling

Statistical process control, a recognized technique for improving quality and productivity, has been widely employed throughout various industries. The conventional Shewhart control charts are applicable only when the collected sample data are real-valued data. For the purpose of controlling uncertain information when interval-valued data inevitably appear in the manufacturing or service processes, in this paper an interval-data analysis methodology is first applied. We construct Shewhart control charts whose control limits, consequently as interval numbers, are obtained by using the united extension principle, which is an effective method for dealing with closed interval data. Then, to identify the special causes of variation and alarm the requirement for corrective actions, we propose new rules for classifying current conditions of the manufacturing process based on an acceptability function of two interval numbers constructed from interval-valued sample data. Finally, the proposed methodologies are illustrated by practical examples to show their potential applications.