Optimal Maintenance Policy for a Technical System Subject to Hidden Faults and Randomly Occurring Hazards

Abstract

The paper presents a method of finding the optimal time between inspections for a system subject to degradation-related faults which make the system vulnerable to randomly occurring external hazards that may cause its damage. Since faults are assumed to be hidden, periodic inspections and repairs have to be performed in order to detect and remove them. Otherwise, leaving the faulty system unmaintained would eventually lead to a very costly damage. It is also assumed that the time to occurrence of a fault is exponentially distributed and hazardous events constitute a Poisson process. The fault rate, the intensity of the Poisson process and the probability with which a hazardous event results in the system damage are the known parameters. The author presents two main results achieved by analyzing this maintenance model. First, the criteria to be fulfilled by the system parameters in order that preventive maintenance be cost-effective are given in the form of simple inequalities. These criteria must be met so that operating the system with preventive maintenance in place be less costly than operating it until a damage occurs and replacing it thereafter. Second, fairly simple equations are obtained from which the optimal time between inspections can be found numerically by the Newton-Raphson method. The analytical derivation of both the criteria and the equations is presented in detail and is the author’s original work. To the best of his knowledge the obtained results are new in the area of maintenance modeling and analysis. For better understanding, theoretical considerations are illustrated by an example of a generic explosion prevention system.