Knowing the maintainability of a component or a system means that repair resource allocations, such as spare part procurement and maintenance training, can be planned and optimized more effectively. Repair data are often collected from multiple and distributed units in different operational conditions, which can introduce heterogeneity into the data. Part of such heterogeneity can be explained and isolated by the observable covariates, whose values and the way that they can affect the item's maintainability are known. However, some factors which may affect maintainability are typically unknown (unobserved covariates), leading to unobserved heterogeneity. Nevertheless, many researchers have ignored the effect of observed and un-observed covariates, and this may lead to erroneous model selection, as well as wrong conclusions and decisions. Moreover, many authors have simplified their analysis by considering a complex system as a single item. In these studies, the assumption is that all repair data represent an identical repair process for the item. In practice, mechanical systems are composed of multiple parts, with various failure mechanisms, which need different repair processes (repair modes) to return to the operational phase; classical distribution, such as lognormal, which is only a function of time, may not be able to model such complexity. The paper utilizes the Mixture Frailty Model (MFM) in the presence of some specific observed or unobserved covariates to predict maintainability more precisely. Mixture Frailty Models can model the effect of observed and unobserved covariates, as well as identifying different repair processes in the repair dataset. The application of the proposed model is demonstrated by a case study.

Risk management is a fundamental approach to improving critical infrastructure systems’ safety against disruptive events. This approach focuses on designing robust critical infrastructure systems (CISs) that could resist disruptive events by minimizing the possible events’ probability and consequences using preventive and protective programs. However, recent disasters like COVID-19 have shown that most CISs cannot stand against all potential disruptions. Recently there is a transition from robust design to resilience design of CISs, increasing the focus on preparedness, response, and recovery. Resilient CISs withstand most of the internal and external shocks, and if they fail, they can bounce back to the operational phase as soon as possible using minimum resources. Moreover, in resilient CISs, early warning enables managers to get timely information about the proximity and development of distributions. An understanding of the concept of resilience, its influential factors, and available evaluation and analyzing tools are required to have effective resilience management. Moreover, it is important to highlight the current gaps. Technological resilience is a new concept associated with some ambiguity around its definition, its terms, and its applications. Hence, using the concept of resilience without understanding these variations may lead to ineffective pre- and post-disruption planning. A well-established systematic literature review can provide a deep understanding regarding the concept of resilience, its limitation, and applications. The aim of this paper is to conduct a systematic literature review to study the current research around technological CISs’ resilience. In the review, 192 primary studies published between 2003 and 2020 are reviewed. Based on the results, the concept of resilience has gradually found its place among researchers since 2003, and the number of related studies has grown significantly. It emerges from the review that a CIS can be considered as resilient if it has (i) the ability to imagine what to expect, (ii) the ability to protect and resist a disruption, (iii) the ability to absorb the adverse effects of disruption, (iv) the ability to adapt to new conditions and changes caused by disruption, and (v) the ability to recover the CIS’s normal performance level after a disruption. It was shown that robustness is the most frequent resilience contributing factor among the reviewed primary studies. Resilience analysis approaches can be classified into four main groups: empirical, simulation, index-based, and qualitative approaches. Simulation approaches, as dominant models, mostly study real case studies, while empirical methods, specifically those that are deterministic, are built based on many assumptions that are difficult to justify in many cases.

No abstract

Resilience is about the ability of the system to resist, adapt to, and expeditiously recover from a disruptive event. The first and maybe the crucial step of resilience management is known as resilience analysis. However, there are many obstacles in front of the analyzers to analyze the resilience of systems. One of these obstacles is precise resilience data accessibility. Conventional resilience analysis methods frequently only consider historical data (e.g., time to repair and time to failure). However, to analyze the system resilience more precisely, the effect of the risk factors, which are known as observed and unobserved covariates, should be considered in the collected resilience database. These covariates will lead to the observed and unobserved heterogeneities among the collected database. Ignoring the effect of covariate may lead to erroneous conclusion about the resilience level of the system. Since it is hard to find a homogeneous operating condition, in this study, a formulation is proposed to model the effect of these covariates on complex system resilience. Finally, it is applied to a transportation system of a surface mine.

Spare-part management has a significant effect on the productivity of mining equipment. The required number of spare parts can be estimated using failure and repair data collected under the name of reliability data. In the mining industry, failure and repair times are decided by the operational environment, rock properties, and the technical and functional behavior of the system. These conditions are heterogeneous and may change significantly from time to time. Such heterogeneity can change equipment’s reliability performance and, consequently, the required number of spare parts. Hence, it is necessary for effective spare-part planning to check the heterogeneity among the reliability data. After that, if needed, such heterogeneity should be modeled using an adequate statistical model. Heterogeneity can be categorized into observed and unobserved caused by risk factors. Most spare-part estimation studies ignore the effect of heterogeneity, which can lead to unrealistic estimations. In this study, we introduce the application of a frailty model for modeling the effect of observed and unobserved risk factors on the required number of spare parts for mining equipment. Studies indicate that ignoring the effect of unobservable risk factors can cause a significant bias in estimation.