A distribution-free Shewhart-type Mann–Whitney control chart for monitoring finite horizon productions

Abstract

Distribution-free control charts have been proposed in recent years to monitor processes with insufficient information about the distribution of observations. A promising field of application of these charts is the small production of finite batches of products, where the number of scheduled inspections is limited to a few tens. Following the machine reconfiguration after a process set-up, the quality practitioner cannot rely on past production runs to get knowledge about the distribution of the observations: this scenario can be referred to as the Case U (Unknown) condition in statistical process monitoring. Here, we investigate the issues related to the implementation of Mann–Whitney (MW) type control charts for monitoring the location in a finite horizon production (FHP) process. The practitioner-to-practitioner variability is considered while designing the control limits. The in-control and out-of-control chart performances are investigated over a wide set of scenarios and some graphical tools are proposed to help practitioners during the decision-making process. A comparison with the Shewhart Sign control chart for FHP processes is also presented. An illustrative example is provided to demonstrate the implementation of the proposed chart on a real industrial dataset.

Keywords:

• Quality control
• distribution-free
• case u
• location
• inspection
• conditional performance
• finite horizon production

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Università di Catania Award-id: Piano della Ricerca Dip. 2016-2018 del DICAR.

Notes on contributors

Giovanni Celano

Giovanni Celano is an associate professor at the University of Catania (Italy). He holds a PhD in production engineering from the University of Palermo (Italy). His current research is focused on developing and implementing statistical process monitoring techniques for online quality control with a particular focus on small production runs. He has authored/coauthored about 130 papers in international journals and in proceedings of national and international conferences. He is a member of the ENBIS (European Network of Business and Industrial Statistics). He is an Advisory Editor of the Engineering Reports journal and an Associate Editor of the Quality Technology and Quantitative Management journal

Subhabrata Chakraborti

Subhabrata Chakraborti is Professor of Statistics and Morrow Faculty Fellow at the University of Alabama, Tuscaloosa, AL, USA. He is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute. Professor Chakraborti has authored and co-authored over 100 publications. His current research interests include applications of statistical methods, including nonparametric methods, to various problems in industrial statistics and allied areas. He is the co-author of Nonparametric Statistical Process Control (2019), published by John Wiley and Nonparametric Statistical Inference, fifth edition (2010), published by Taylor and Francis. Professor Chakraborti has been a Fulbright Scholar and a visiting professor in several countries including South Africa, Turkey, Holland, India and Brazil. He has been recognized for his mentoring and collaborative work with students and scholars from around the world. Professor Chakraborti is serving his 25-year term as an Associate Editor of Communications in Statistics and he is a member of the Quality Engineering editorial review board.