Monitoring processes with multiple dependent production lines using time between events control charts

Abstract

This article develops Time Between Events (TBE) control charts to monitor processes with multiple dependent production lines. To this end, a Shewhart-type and an EWMA-type TBE chart have been proposed. The copula approach is used to describe the dependence between production lines and the homogeneous Poisson process is considered to model the number of defectives. Performance of the proposed methods is evaluated using average time to signal metric. The numerical study showed that the EWMA-TBE chart uniformly performs better than the Shewhart-type chart. Eventually, the EWMA-TBE chart is applied to monitor two real-world processes with two and four production lines.

Keywords:

• Time between events control chart
• EWMA approach
• average time to signal
• exponential distribution
• homogeneous poisson process

Additional information

Notes on contributors

Hussam Ahmad

Hussam Ahmad received his MSc in Mathematical Statistics at the Ferdowsi University of Mashhad, Iran. He is now a PhD student at the Ferdowsi University of Mashhad (Iran). His research interests include Statistical Quality Control and Copula Theory.

Adel Ahmadi Nadi

Adel Ahmadi Nadi is currently do research in the Department of Statistics and Actuarial Science at the University of Waterloo in Canada as a PostDoc Fellowship. Adel received his PhD in Statistics from the Ferdowsi University of Mashhad, Iran. His research focuses on Statistical Quality Control, Measurement Systems Analysis, and Reliability Engineering.

Mohammad Amini

Mohammad Amini is a professor of Statistics at the Ferdowsi University of Mashhad, Iran. He received his PhD in Statistics at the Ferdowsi University of Mashhad. His research interests include Copula Theory and dependence modelling, Law of Large numbers, and Distribution Theory.

Bahram Sadeghpour Gildeh

Bahram Sadeghpour Gildeh is a professor of Statistics at the Ferdowsi University of Mashhad, Iran. He received his MSc in Mathematical Statistics at the Ferdowsi University of Mashhad (Iran) and PhD in Informatics at the Blaise Pascal University (France). His research interests include Statistical Quality Control, Process Capability Analysis, and Fuzzy Statistics.