Scheduling Preventive Maintenance as a Function of an Imperfect Inspection Interval

Abstract

This paper considers a system with periodic inspections and periodic preventive maintenance (PM) to detect and correct hidden failures that generate a penalty cost per unit time undetected. Imperfect periodic inspections (IPIs) occur at a chosen interval , and detect hidden failures with probability . Both reactive maintenance (RM), performed when a hidden failure is detected by an IPI, and PM, performed at a chosen time , renew the system. The objective is to determine the optimal frequency and quantity of imperfect inspections between PM such that the expected cost (which includes the costs of undetected failures, IPIs, PM, and RM) per unit time is minimized over an infinite horizon. We analytically establish conditions for the existence of a finite optimal for a given value of , and discuss the asymptotic behavior of the objective function for large and . These results are further exploited to describe convergence properties of a proposed approach for finding a globally optimal solution. Also, for the special case of a Weibull time-to-failure distribution, we derive conditions that guarantee the uniqueness of a locally optimal solution for a given value of . Index Terms-Imperfect inspections, maintenance optimization, preventive maintenance (PM). ACRONYMS AND ABBREVIATIONSPM preventive maintenance IPI imperfect periodic inspection RM reactive maintenance cdf cumulative distribution function pdf probability density function TTF time to failure NOTATION probability that an IPI detects an underlying failure cost per PM or RM cost per IPI instantaneous cost of a hidden failure cost rate of a hidden failure when the length of the undetected time period is ,

Availability and maintenance modelling for systems subject to multiple failure modes

“…It would be of interest to investigate various reliability indices and the optimal maintenance policy for multiple failure modes system with imperfect inspections (Hsu and Hsu, 2013;He et al, 2015).…”

“…For systems suffering from hidden failures, to improve the system availability, an inspection policy is usually adopted to detect whether a failure has occurred or not (see, e.g., Cui et al, 2010;He, 2015; Berrade et al, 2013). Based on the intervals between successive inspections, two types of inspections have been considered in literature, namely: periodic inspection and non-periodic inspection.…”

A novel data-driven approach to optimizing replacement policy

“…In preference to previous works (e.g. see [8,9,11,13,17,23,[25][26][27][28][29][31][32][33]), both the cost structure and the inspection model explored here respond to the variation of the system state. Examples of papers that use particular cost structures can be found in [11,23,26,33].…”

“…Using the net cost consisting of deterministic components, Tsai et al [27] study a trivariate replacement policy for a deteriorating system whose failures can only be detected through inspection. He et al [13], given a more flexible cost structure, consider a system with periodic inspection and preventive maintenance with the aim of minimizing the expected cost with respect to some maintenance system parameters. Aperiodic inspection policies proposed in literature (e.g.…”

“…From the above literature review, we can conclude: Although some maintenance models consider joint inspection and preventive maintenance policies (e.g. see [13,19,27,30]) for systems subject to hidden failures, a unified maintenance model which accounts for all these factors does not exist. To fill up this knowledge gap, this paper assumes that the failure of a component in a parallel system can only be detected through an inspection and then proposes two-step method.…”