Resilience improvement of a critical infrastructure via optimal replacement and reordering of critical components

ABSTRACT

One of the most important obstacles in improving the resilience of critical infrastructures is the timely replacement of critical components. However, the shortage of spare parts often keeps practitioners from achieving this goal. Moreover, it is common that spare parts may deteriorate on the shelf. In this paper, we focus on a one-component deteriorating system carrying one deteriorating spare part. Both failure-switching and preventive-switching strategies are considered for component replacement during each operating cycle to minimize the long-run cost rates. A case study on gearbox replacements for an offshore wind farm is provided to illustrate the proposed joint component replacement and reordering policies in improving the resilience of critical infrastructures. Although the chance of failure of such a system may be reduced by the preventive-switching strategy, the failure-switching strategy may still result in better economic performance due to the on-shelf deterioration and salvage of spare parts.

Abbreviations: CDF: cumulativedistributionfunction; PDF: probabilitydensityfunction; PR: preventivereplacement; CE: cumulativeexposure

KEYWORDS:

• Resilience
• deteriorating spare part
• maintenance
• part reordering
• optimization

Acknowledgments

The authors would like to thank the Associate Editor and three reviewers for their insightful comments and suggestions that greatly improved the quality of this paper. This research was sponsored by the U.S. National Science Foundation under grant CMMI-1745353.

Disclosure statement

No potential conflict of interest was reported by the authors.

Nomenclature

$F_j(t)$ CDF of the lifetime of a unit under operation (j = 1) or storage condition (j = 2)

$f_j(t)$ PDF of the lifetime of a unit under operation (j = 1) or storage condition (j = 2)

$R_j(t)$reliability function of a unit under operation (j = 1) or storage condition (j = 2)

$F_s(t)$CDF of the lifetime of the system

$f_s(t)$PDF of the lifetime of the system

$R_s(t)$system reliability function

$\omega (t)$effective age of the spare part when switching ti end of the ith cycle

$t_p$length of a regular reorder cycle, i.e., mandatory PR interval

$t_s$preventive-switching time

$\tau$order lead time

$c_h$holding cost for a spare part per unit time

$\pi$system downtime cost per unit time

$c_s$salvage value of an unused spare part

$c_{pr}$cost for mandatory PR or preventive switching

$c_f$failure replacement cost

$T_A$potential lifetime of primary unit A

$T_B$potential lifetime of spare unit B

$TT$uptime of the system

${ }^{X^{+}}$max(X; 0)

$G(t_p)$random system operation cost in one cycle given tp

$M(t_p)$random system maintenance cost in one cycle given tp

$L(t_p)$random system cycle length given tp

Additional information

Funding

This work was sponsored by the National Science Foundation Division of Civil, Mechanical and Manufacturing Innovation [1745353].

Notes on contributors

Hongwei Luo

Hongwei Luo received his B.S. degree (2011) in logistics engineering from Tianjin University, and M.S. degree (2013) and Ph.D. degree (2016) in systems and industrial engineering from the University of Arizona. His research is focused on reliability models, maintenance and spare parts inventory control, and operations research models.

Basem A. Alkhaleel

Basem A. Alkhaleel is a Ph.D. candidate in the Department of Industrial Engineering at the University of Arkansas. He received a B.S. degree in industrial engineering from King Saud University, Riyadh, Saudi Arabia, in 2012, and an M.S. degree in industrial engineering from Texas A&M University, College Station, TX, USA, in 2015. His main research interests are centered around systems reliability, networks optimization, and resilience of critical infrastructures.

Haitao Liao

Haitao Liao is a Professor, and John and Mary Lib White Endowed Systems Integration Chair in the Department of Industrial Engineering at the University of Arkansas. He received a Ph.D. degree in industrial and systems engineering from Rutgers University in 2004. He also earned M.S. degrees in industrial engineering and statistics from Rutgers University, and a B.S. degree in electrical engineering from Beijing Institute of Technology. His research has been sponsored by the U.S. National Science Foundation, Department of Energy, Nuclear Regulatory Commission, Oak Ridge National Laboratory, and industry. The research 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. In2014, he served as Chair of INFORMS Quality, Statistics and Reliability (QSR) Section, and President of IISE Quality Control and Reliability Engineering (QCRE) Division. He served as Associate Editor for Journal of Quality Technology and IEEE Transactions on Reliability, and currently serves as Associate Editor for IISE Transactions on Quality and Reliability Engineering. He received the U.S. National Science Foundation CAREER Award in 2010, the IISE QCRE William A.J. Golomski Award for three times, 2013 QCRE Track Best Paper Award, Stan Ofsthun Best Paper Award twice, and the prestigious 2017 Alan O. Plait Award for Tutorial Excellence. He is a Fellow of IISE, and a member of INFORMS and SRE.

Rodrigo Pascual

Rodrigo Pascual is currently an Associate Professor at the School of Engineering of the University of Chile. He graduated in Mechanical Engineering at the University of Concepción, Chile, and obtained his Ph.D. degree at the University of Liege, Belgium. He has worked in the academic world for more than 25 years in Belgium, Canada, and Chile. Since 2001 he has been researching Physical Asset Management, Reliability Modelling, and Engineering Education. He has an active level of involvement in several industrial and university-based projects.