Prognostics-Based Two-Operator Competition in Proactive Replacement and Service Parts Procurement

Abstract

Effective prognostics and timely maintenance of degrading components can improve the availability and economic efficiency of an engineering system. However, possible shortage of required service parts usually makes near-zero downtime difficult to achieve. To coordinate service parts availability with scheduled maintenance, it is necessary for the operator to decide when to order the service parts and how to compete with other operators in parts procurement. In this article, we consider a situation where two operators are to make prognostics-based replacement decisions and strategically procure the needed service parts. When a competition occurs, each of the operators has a bounded continuum of strategies. A one-shot sequential game (Stackelberg game) is formulated and a sequential, constrained maximin experimental design approach is proposed to facilitate searching for the equilibrium solution. This approach is quite useful in handling cases where the follower's best response to the leader's strategy, both chosen from continuums of strategy sets, is difficult to obtain analytically. Numerical studies on wind turbine operation are provided to demonstrate the use of the sequential decision-making method in solving such complex, yet realistic maintenance and service parts logistics problems.

Nomenclature

C(i)	=	price paid by operator i to acquire a service part
Co	=	regular ordering cost for a part from the primary supplier
C'o	=	emergency ordering cost for a part from the secondary supplier
Cp(i)	=	total preventive replacement cost of operator i
Cu(i)	=	total corrective replacement cost of operator i
Cf(i)	=	unit downtime cost of operator i due to a failure
Ch(i)	=	unit holding cost of operator i
Cp(i)	=	unit downtime cost of operator i due to preventive replacement
fRUL(i)(u)	=	pdf of RUL(i) with scale parameter ηi and shape parameter βi
M	=	extra charge for bidding on a part from the primary supplier
NE	=	Nash equilibrium
pdf	=	probability density function
RUL	=	remaining useful life
RUL(i)	=	random RUL of the unit being used by operator i
RRULω(u)	=	reliability function of RUL(i)
Ti	=	time to perform preventive replacement of operator i
To(i)	=	time to order a service part of operator i
TTI	=	inspection interval
Tw(i)	=	actual waiting time of operator i for receiving a part
i	=	a specific strategy [C(i),To(i),Ti] of operator i
Πi( · )	=	objective function of operator i
τ1	=	primary supplier's replenishment lead time
τ′1	=	secondary supplier's replenishment lead time
τ2	=	time needed to perform preventive replacement
τ3	=	time needed to perform corrective replacement
Ωi	=	the strategy set of operator i

Additional information

Notes on contributors

Faranak Fathi Aghdam

Faranak Fathi Aghdam, M.S., is a Ph.D. student in the Systems and Industrial Engineering Department at The University of Arizona. She received her B.S. degree in industrial engineering from Iran University of Science and Technology, and her M.S. degree in industrial engineering from the University of Tennessee–Knoxville. Her research focuses on modeling of device reliability and nanowire growth process.

Haitao Liao

Haitao Liao, Ph.D., is an associate professor in the Systems and Industrial Engineering Department at The University of Arizona (UofA), Tucson, Arizona. He is also the Director of Reliability & Intelligent Systems Engineering (RISE) Laboratory at UofA. He received his Ph.D. in industrial and systems engineering from Rutgers University, New Jersey. He also received his M.S. degrees in industrial engineering and statistics from Rutgers University and B.S. in electrical engineering from the Beijing Institute of Technology. His research interests include modeling of accelerated testing, maintenance models and optimization, service parts logistics, prognostics, and probabilistic risk assessment. He is a recipient of the National Science Foundation CAREER Award in 2010, the winner of 2010 and 2013 William A. J. Golomski Award, and 2013 IIE QCRE Track Best Paper Award. He is a member of IIE, INFORMS, IEEE, and SRE.