The variable sampling interval control chart for finite-horizon processes

Abstract

The requirement to be globally competitive requires companies to have a high level of flexibility to allow for the production of a large variety of products. To limit work-in-process, decision makers periodically schedule according to a make-to-order management strategy i.e. the production of finite batches of the same product code. Scheduling calls for frequent set up activities, which require the reconfiguration of a manufacturing process, and allows manufacturers to switch between different codes. This can limit the production horizon of one product code to a few hours or shifts. In this context, efficient online quality control monitoring using control charts is strategic to eliminate scrap or rework and to meet the demand at the time specified by the production plan. The design of control charts for a process with a limited production horizon is a challenge for statistical process control practitioners. Under this framework, this article investigates the issues related to the implementation of the Variable Sampling Interval (VSI) Shewhart control chart in a process with finite production horizon. When the production horizon is finite, the statistical properties of a control chart are known to be a function of the number of scheduled inspections. In the case of a VSI control chart, the quality practitioner cannot fix the number of inspections a priori due to the stochastic nature of the sampling interval selection. Therefore, the aim of this article is to propose a new Markov chain approach for the exact computation of the statistical performance of the VSI control chart in processes with an unknown and finite number of inspections. The proposed approach is general and does not depend on the monitored sample statistic. With reference to the process mean monitoring, an extensive numerical analysis compares the performance of the VSI chart to the Variable Sample Size and Fixed Sampling Rate z charts. Numerical results show that the VSI chart outperforms other charts for moderate to large shift sizes. An illustrative example shows the implementation of the VSI chart in a short run producing a finite batch of mechanical parts.

Keywords::

• Control chart
• quality control
• short production run
• statistical performance
• variable sampling interval

Additional information

Notes on contributors

George Nenes

George Nenes is an Assistant Professor at the Department of Mechanical Engineering at the University of Western Macedonia, Greece. He is also a research associate at the Department of Mechanical Engineering at Aristotle University of Thessaloniki. He has obtained a Diploma (5-year degree) in Mechanical Engineering, an M.Sc. in Management of Production Systems, and a Ph.D. in Statistical Quality Control from the Aristotle University of Thessaloniki. He has worked as a Post Doc researcher at the Erasmus University of Rotterdam and as a visiting lecturer in various engineering departments in Greece. His work has been published in a variety of journals, including European Journal of Operational Research, IIE Transactions, and International Journal of Production Economics. His main research interests are in the area of statistical quality control and supply chain management.

Philippe Castagliola

Philippe Castagliola graduated (Ph.D. 1991) from the Université de Technologie de Compiègne, France. He is currently a Professor at the Université de Nantes, Institut Universitaire de Technologie de Nantes, France, and he is also a member of the Institut de Recherche en Communications et Cybernétique de Nantes, UMR CNRS 6597. His research activity includes the development of new SPC techniques.

Giovanni Celano

Giovanni Celano has a master's degree in Mechanical Engineering and holds a Ph.D. in Manufacturing Engineering from the University of Palermo (Italy). Currently, he is an Assistant Professor at the University of Catania (Italy), where he teaches quality management. His research is mainly focused on statistical quality control. He has authored/co-authored more than 100 papers in many international journals, including Journal of Quality Technology, International Journal of Production Economics, and Computers and Industrial Engineering, and in proceedings of national and international conferences. He is currently Associate Editor of the Quality Technology and Quantitative Management journal and the Journal of Industrial Engineering. He is member of the Associazione Italiana di Tecnologia Meccanica and the European Network of Business and Industrial Statistics.

Sofia Panagiotidou

Sofia Panagiotidou is a Mechanical Engineer and holds an M.Sc. in the Management of Production Systems and a Ph.D. in Maintenance and Statistical Quality Control, both awarded by Aristotle University of Thessaloniki. She is currently a Lecturer at the Department of Mechanical Engineering at the University of Western Macedonia, Greece, a Visiting Lecturer at the Hellenic Open University, and a Research Associate at the Department of Mechanical Engineering at Aristotle University of Thessaloniki. She has also worked as a Post Doc researcher at the Erasmus University of Rotterdam. Her work has been published in a variety of journals, including Production and Operations Management, European Journal of Operational Research, International Journal of Production Economics, and others. Her main research interests are in the area of statistical quality control, maintenance, and supply chain management.