Multi-level maintenance strategy of deteriorating systems subject to two-stage inspection

Highlights

• A novel reliability and maintenance model is developed based on two-stage competing failure processes.

• The impacts of both the operational age and system state on the magnitude of external shock damage are investigated.

• A multi-level maintenance strategy incorporating age-based maintenance and regular inspection is developed.

• A two-stage inspection plan is schemed to manipulate maintenance frequencies based on the system state.

Abstract

Preventive maintenance, including time-based and condition-based maintenance, plays an important role in reducing system economic losses caused by unexpected failures. This paper studies a multi-level preventive maintenance strategy for a three-state industrial system subject to two competing failure processes. The first is a continuous degradation process characterized by the general path model, and the second is a shock process arriving according to a non-homogenous Poisson process. The degradation/hazard rate of the system undergoes an abrupt increase upon the initialization of the defective state, and the magnitude of the damage caused by a shock load is correlated to two factors: (a) operational age; (b) degradation speed. The system is preventively replaced at a pre-determined operational age, before which a finite number of inspections are executed according to a two-stage interval partition. The objective of this paper is to minimize the expected cost per unit time via the optimization of the replacement age, the control limit and two inspection intervals. A case study on a peristaltic pump is provided to illustrate the application of the maintenance model.

Introduction

Most industrial systems in real-world are exposed to various environmental stresses such as high temperature, voltage, vibration and extreme weather conditions, and may undergo various unexpected failures during their lifecycle. Such failures will not only cause tremendous economic losses, but also induce potential hazards to personnel and property safety. Preventive maintenance (PM) is an effective measure to reduce the risks of failures, and thus has received considerable attention in industrial department (Peng, Guo, Levitin, Mo, & Wang, 2013). According to the failure mechanism of target products, PM could be substantially classified into two main categories (Ahmad & Kamaruddin, 2012): (a) time-based maintenance (Li et al., 2016, Sheu et al., 2015); (b) condition-based maintenance (Liu et al., 2015, Zhang et al., 2014). With the development of industrial technologies, the scale and architectural complexities of modern devices/equipment are continuously increasing, resulting in more complicated failure behaviors (Qiu et al., 2018, Zheng et al., 2016). Consequently, single-scale maintenance actions could no longer satisfy both the availability and cost requirements of complex systems (Cui and Xie, 2005, Qiu et al., 2017, Qiu et al., 2017).

In practice, there are mainly two representative types of failures according to the failure consequences. The first type is soft failure, which is generally triggered by internal degradation, such as corrosion, fatigue and wear (Peng et al., 2017, Peng et al., 2017, Peng et al., 2017, Sun et al., 2017, Xu et al., 2018). Instead of stopping the system immediately, such failures only reduce the performance capacities or production output (Qiu et al., 2017, Qiu et al., 2017, Yang et al.,2018a, Yang et al., 2018b). The second type is hard failure, which is fatal and probably triggered by environmental impacts and improper maintenance actions (Yang et al.,2018a, Yang et al., 2018b). Reliability and maintenance models considering both types of failures are extensively reviewed in literature, among which the degradation-threshold-shock (DTS) model is addressed the most with a number of real-world applications. For instance, Shafiee, Finkelstein, and Bérenguer (2015) proposed an opportunistic maintenance policy for offshore wind turbine blades suffering corrosion cracking process and environmental shocks. Peng et al., 2010, Song et al., 2016, Rafiee et al., 2015 applied DTS models to micro-electro-mechanical systems (MEMS) subject to gradual wear and debris caused by shock loads. Ye et al., 2013, Ye et al., 2015 established reliability models under extreme shocks and natural graduation for automobile tires, laser devices and hard disks.

Most existing DTS models concentrated on stationary degradation/shock processes (Peng, Shen, et al., 2017), according to which the degradation/hazard rate is not affected by the discrete system state. Nevertheless, in industrial applications, maintainers can usually observe two or more discrete system states, corresponding to different performance capacities/deterioration speeds (Wang & Wang, 2015). Specially, industrial systems with a defective/potential failure state have received considerable attentions. Typical signals of defects include crack, dents, over-heating, over-vibration. A representative example is the crack propagation process of metallic materials (Scarf et al., 1996, Zhang et al., 2016), whose propagation speed increases abruptly when the crack length reaches a certain level. Analogously, onshore oil pipelines are much more susceptible to external damage when defects/dents occur at outer walls (Yang et al.,2018a, Yang et al., 2018b). This motivates us to investigate the DTS model within the framework of the delay time concept (Christer & Waller, 1984).

We also notice that the impacts of discrete system states on both degradation and shock processes have drawn little attention (Zhang et al., 2016). Indeed, a defective system is much more susceptible to both internal degradation and environmental shock load than a normal system. To address this, our DTS model defines two separate random coefficients and shock loads to characterize the impacts. Furthermore, this article investigates a novel extreme shock model, where the magnitude of a shock load is correlated to two main factors: (a) the operational age of the system; (b) the degradation speed (which varies with system start). This actually reflects the actual observations that a worn-out/defective device has less resistivity to shock damages.

Preventive maintenance of DTS models is extensively reviewed in literature, among which two classic strategies, age-based maintenance (Cha, Finkelstein, & Levitin, 2017) and regular inspection (Caballé et al., 2015, Chen et al., 2014, Do et al., 2015) are extensively reviewed. Although these two strategies are easy to execute, they may be sub-optimal from the perspective of cost reductions due to the following limitations: (a) age-based maintenance cannot ensure sufficient utilizations of system health information; (b) regular inspection is unable to reveal catastrophic failures. An elaborate incorporation of age-based maintenance and regular inspection, on the other hand, offers a promising solution to these problems. In this study, a novel multi-level maintenance policy is investigated, performing a finite number of inspections before replacement. To ensure a reasonable maintenance resource allocation, a two-stage inspection plan combing two different intervals, namely, normal interval and defective interval is also schemed. This is different from the constant interval setting in most delay-time based maintenance models.

The rest of this paper is structured as follows. Section 2 introduces the failure behavior and maintenance strategy of the system. On this basis, Section 3 formulates the reliability and maintenance model and develops an algorithm for the optimization of the maintenance cost. Section 4 provides a case study on a peristaltic pump to illustrate the model. Section 5 provides some final remarks.