System reliability optimization with two-sided power distributed component failure times

Abstract

Many systems connected in series are subject to failure earlier in their design life. The failure rate of such systems has been described by a two-sided power distribution, which enables modeling the entirety of the bathtub curve failure modes with a single distribution. We propose a time-dependent reliability optimization model for improving a system’s reliability through the optimal allocation of redundant components whose failure distribution follows a two-sided power distribution. To solve the multi-criteria optimization model, we propose an algorithm that (i) identifies the scale tolerance at which a selected component will have a higher mean residual life, (ii) identifies the level of redundancy for enhancing system reliability, and (iii) identifies other optimal system characteristics, including minimized cost and minimized volume.

Highlights

• Two sided power (TSP) distribution with four parameters (a, b, c, η) models time-to-failure.

• We consider an n-stage series system and assign redundancy within the stages.

• We propose a multi-objective optimization problem to assign redundancy, accounting for reliability, cost, and system volume.

• An illustrative example is solved using the NSGA-II algorithm.

Keywords:

• two-sided power distribution
• system reliability
• redundancy allocation
• time-dependent reliability
• mean residual life

Acknowledgement

We are grateful to Editors, and anonymous referees for their valuable comments and helpful suggestions, which have helped us to improve this work significantly.

Additional information

Notes on contributors

B. Maneckshaw

Maneckshaw Balakrishnan is a research scholar in the Department of Mathematics at National Institute of Technology, Puducherry in India. He is also working as Lecturer in Mathematics and attached to institutions run by Pondicherry Institute of Post Matric Technical Education (PIPMATE), as well as at Indira Gandhi Polytechnic College, Mahe. He completed his M.S. at St. Joseph's College (Autonomous) in Thiruchirapalli, India and an M.Phil. in Graph Theory at Pondicherry Central University. He is presently pursuing research in reliability engineering.

Kash Barker

Dr. Kash Barker is the John A. Myers Professor and a David L. Boren Professor in the School of Industrial and Systems Engineering at the University of Oklahoma. He earned B.S. and M.S. degrees in industrial engineering from the University of Oklahoma and a Ph.D. in systems engineering from the University of Virginia. His primary research interests lie in the reliability, resilience, and economic impacts of infrastructure and community networks.

G. S. Mahapatra

Dr. G.S. Mahapatra holds M.Sc. and Ph.D. degrees in Applied Mathematics from Indian Institute of Engineering Science and Technology, Shibpur, India. He is an Associate Professor in the Department of Mathematics in National Institute of Technology, Puducherry, India. He has been involved in teaching and research for more than 17 years. He has published more than hundred research papers in topics spanning inventory management, reliability, optimization, fuzzy set theory, mathematical biology, and soft computing.