Optimal sampling plan for an unreliable multistage production system subject to competing and propagating random shifts

Abstract

Sampling plans play an important role in monitoring production systems and reducing quality- and maintenance-related costs. Existing sampling plans usually focus on one assignable cause. However, multiple assignable causes may occur, especially for a multistage production system, and the resulting process shift may propagate downstream. This article addresses the problem of finding the optimal sampling plan for an unreliable multistage production system subject to competing and propagating random quality shifts. In particular, a serial production system with two unreliable machines that produce a product at a fixed production rate is studied. It is assumed that both machines are subject to random quality shifts with increased nonconforming rates and can suddenly fail with increasing failure rates. A sampling plan is implemented at the end of the production line to determine whether the system has shifted or not. If a process shift is detected, a necessary maintenance action will be initiated. The optimal sample size, sampling interval, and acceptance threshold are determined by minimizing the long-run cost rate subject to the constraints on average time to signal a true alarm, effective production rate, and system availability. A numerical example on an automatic shot blasting and painting system is provided to illustrate the application of the proposed sampling plan and the effects of key parameters and system constraints on the optimal sampling plan. Moreover, the proposed model shows better performance for various cases than an alternative model that ignores shift propagation.

Keywords:

• Sampling plan
• multistage production systems
• competing and propagating random shifts

Acknowledgments

The authors would like to thank the Department Editor, Associate Editor and two reviewers for their insightful comments and suggestions that greatly improved the quality of this paper.

Additional information

Funding

This research was partly supported by the U.S. National Science Foundation (Grant #CMMI 1635379).

Notes on contributors

Sinan Obaidat

Dr. Sinan Obaidat received his BS and MS degrees in industrial engineering from Jordan University of Science & Technology and PhD degree in industrial engineering from the University of Arkansas – Fayetteville, USA. He is currently an assistant professor of the Department of Industrial Engineering at Yarmouk University, Jordan. His research interest is in the area of decision modeling of maintenance, quality, and reliability with applications in production systems.

Haitao Liao

Dr. Haitao Liao is a Professor and John and Mar Lib White Endowed Systems Integration Chair in the Department of Industrial Engineering at the University of Arkansas – Fayetteville. He received a PhD degree in industrial and systems engineering from Rutgers University in 2004. He also earned MS degrees in industrial engineering and statistics from Rutgers University, and a BS degree in electrical engineering from Beijing Institute of Technology. His research interests include: (i) reliability models, (ii) maintenance and service logistics, (iii) prognostics, (iv) probabilistic risk assessment, and (v) analytics of sensor data. His research has been sponsored by the National Science Foundation, Department of Energy, Nuclear Regulatory Commission, Oak Ridge National Laboratory, and industry. The findings of his group have been published in IISE Transactions, European Journal of Operational Research, Naval Research Logistics, IEEE Transactions on Reliability, IEEE Transactions on Cybernetics, The Engineering Economist, Reliability Engineering & System Safety, etc. He received a National Science Foundation CAREER Award in 2010, IISE William A. J. Golomski Award in 2011, 2014 and 2018, SRE Stan Ofsthun Best Paper Award in 2015 and 2019, and 2017 Alan O. Plait Award for Tutorial Excellence. He is a Fellow of IISE, a member of INFORMS, and a lifetime member of SRE.