Inspection and maintenance optimisation of multicomponent systems

Vladimir Oleg Babishin

doi:10.32920/ryerson.14648742

Abstract

The present research proposes methodology and mathematical models for optimisation of inspection and maintenance in complex multicomponent systems with finite planning horizon. Components are classified by failure types: hard-type and soft-type. The systems analysed are composed of either multiple identical hidden soft-type components in k-out-of-n redundant configuration, or a combination of hard-type and hidden soft-type components. Failures of hard-type components cause system failures. Failures of components in k-out-of-n systems and soft-type component failures are hidden and not discoverable until an inspection, but reduce the system’s reliability and performance. The systems are inspected either periodically, or non-periodically. They are also inspected opportunistically at the times of system failure (occurring at (k – n + 1)st component failures in k-out-of-n systems, or at hard failures in the systems composed of hard-type and soft-type components). Inspections have negligible duration. All components may undergo minimal repair, or corrective replacement, with hard-type components also having a possibility of preventive replacement under periodic inspections. We only consider minimal repair and corrective replacement under non-periodic inspections. We propose several models for joint optimisation of inspection and maintenance policies that result in the lowest total expected cost. Since soft failures are hidden, we generate expected values for the number of minimal repairs, number of replacements and downtime recursively. Due to multiple component interactions and system complexity, Monte Carlo simulation and genetic algorithms (GA) are used for optimisation. Using GA for optimisation allows to consider quasi-continuous inspection intervals due to improved computational efficiency compared to Monte Carlo simulation. Some of proposed models feature preventive component replacements and are applicable even for systems with hidden component failures. For k-out-of-n systems, we apply periodic model to series and parallel systems and compare the results. We provide expressions for expected number of system failures in terms of cost ratio and component failure intensity. We also provide a simplified expression for system reliability. In addition, we derive a formula for finding the planning horizon length based on expected number of system failures. It may be useful for planning the system’s operating horizon, at the system design stage and when analysing its performance.

Highlights

We propose several models for joint optimisation of inspection and maintenance policies that result in the lowest total expected cost
For the hardand-soft-type system, we find the optimal joint trivariate policy composed of the optimal replacement ages for the hard-type components, the optimal number of minimal repairs before replacement for the soft-type components and the optimal inspection scheme resulting in the minimal total expected cost
Techniques and approaches – both theoretical and practical – that have been proposed in the past, usually consider only simple systems consisting of very few components, or impose oversimplifying assumptions on the systems of interest, decreasing the practical value of such developments and hindering their real-world application and implementation

Summary

Introduction

Penalties (e.g. costs of downtime and lost work) are usually incurred whenever a system’s performance and/or reliability are adversely affected, e.g. a system stops operating completely (fails), or starts manifesting some sort of undesirable behaviour For this reason, it is usually desirable to keep the system reliability and availability as high as possible. Kassaei and Taghipour [10, 43] consider a k-out-of-n load-sharing system where each failure increases the hazard rates for the remaining operational components They develop a model for finding the optimal inspection interval minimising the total expected cost over a finite-time life cycle. Keeping the availability of such systems as high as possible reduces the risks of adverse consequences and excessive costs [110, 111, 112] For this reason, the problem of inspecting and maintaining multicomponent systems is very important. Series systems with mixed standby components are compared in terms of their cost/benefit ratio, time to failure and long-term availability by Wang and Kuo [13]

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Discussion

Conclusion