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This paper proposes a model selection framework for analysing the failure data of multiple repairable units when they are working in different operational and environmental conditions. The paper provides an approach for splitting the non‐homogeneous failure data set into homogeneous groups, based on their failure patterns and statistical trend tests. In addition, when the population includes units with an inadequate amount of failure data, the analysts tend to exclude those units from the analysis. A procedure is presented for modelling the reliability of a multiple repairable units under the influence of such a group to prevent parameter estimation error. We illustrate the implementation of the proposed model by applying it on 12 frequency converters in the Swedish railway system. The results of the case study show that the reliability model of multiple repairable units within a large fleet may consist of a mixture of different stochastic models, that is, the homogeneous Poisson process/renewal process, trend renewal process, non‐homogeneous Poisson process and branching Poisson processes. Therefore, relying only on a single model to represent the behaviour of the whole fleet may not be valid and may lead to wrong parameter estimation. Copyright © 2015 John Wiley & Sons, Ltd.

Spare parts provision is a complex problemand requires an accurate model to analysis all factors that may affect the required number of spare parts. The number of spare parts required can be effectively estimated based on the reliability performance of the item. The reliability characteristics of an item are influenced not only by the operating time, but also by factors such as the operational environment. Therefore, for spare parts provisioning to be effective, the impact of these influence factors on the reliability performance of the item should be quantified. Hence, the statistical approach selected for reliability performance analysis must be able to handle the effect of these factors. One of the important models for reliability performance analysis that takes influence factors into account is the proportional hazard model (PHM), which has received less attention in the field of spare parts provisioning. In this paper the application of PHM to spare parts provision is discussed and demonstrated by a case study.

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Today's societies rely on electrical power distribution systems. Recent weather events have illustrated that the loss of such service can lead to severe consequences for societies and stakeholders. Hence, in order to reduce the impact of such extreme events on infrastructure systems and to limit the associated losses, it is crucial to design infrastructure that can bounce back and recover rapidly after disruptions (i.e. to be resilient). In this regard, it is vital to have knowledge of technical, organizational, internal, and external factors that influence the infrastructure's recovery process. These factors can broadly be categorized into two different groups, namely observed and unobserved risk factors. In most studies on resilience, the effect of unobserved covariates is neglected. This may lead to erroneous model selection for analyzing the time to recovery of the disrupted infrastructure, as well as wrong conclusions and thus decisions. The aim of this paper is to identify the risk factors (observed and unobserved) affecting the recovery process of disrupted infrastructure. To this aim, the paper extends the application of accelerated failure time (AFT) models, to model the recovery time of disrupted critical infrastructures in the presence of unobserved and observed risk factors. This model can be used to analyse how important these factors are from the viewpoint of resource allocation and decision-making. The application and implications of the model are presented in a case study, from both technical and management perspectives. The case study investigated in this paper applies the developed model, analysing recovery times from 73 disruption reports on Norwegian electric power distribution grids after four major extreme weather events. The analysis indicates that failures in the regional grid, natural conditions, area affected, and failures in operational control system have a significant impact on the recovery process.

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.