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Calibrating parametric fragility curves via empirical damage data is one of the standard approaches to derive seismic structural vulnerability models. Fragilities based on empirical data require the characterization of the ground motion (GM) intensity at the building sites in the area affected by the earthquake producing the observed damages. This is commonly conducted via ShakeMap, that is, a map of the expected values of a Gaussian random field (GRF) of the logarithms of a GM intensity measure conditional to magnitude, location, and possibly a set of recordings of the earthquake. Once that intensity and damage data at the same sites are available, the typical approach calibrates a two‐parameter fragility model. However, ShakeMap estimates are affected by uncertainty deriving from that of the GM model used to characterize it. Furthermore, such an uncertainty can be reduced by building damage data, which provide information on the shaking intensity at the sites where damage is observed. It is shown herein that if this uncertainty is not addressed, also considering the shaking information provided by damage, the estimates of the fragility parameters obtained using a median ShakeMap only can be biased, and a recommended maximum likelihood estimation procedure – which exploits the expectation maximization algorithm – is provided. These arguments are illustrated via an application considering damage data from the 2009 L'Aquila earthquake in central Italy. [ABSTRACT FROM AUTHOR]

Albeit not equivalent, in many applications the gamma and the inverse Gaussian processes are treated as if they were. This circumstance makes the misspecification problem of these models interesting and important, especially when data are affected by measurement errors, since noisy/perturbed data do not allow to verify whether the selected model is actually able to adequately fit the real (hidden) degradation process. Motivated by the above considerations, in this paper we conduct a large Monte Carlo study to evaluate whether and how the presence of measurement errors affects this misspecification issue. The study is performed considering as reference models a perturbed gamma process recently proposed in the literature and a new perturbed inverse Gaussian process that share the same non‐Gaussian distributed error term. As an alternative option, we also analyze the more classical case where the error term is Gaussian distributed. We consider both the situation where the true model is the perturbed gamma and the one where it is the perturbed inverse Gaussian. Model parameters are estimated from perturbed data using the maximum likelihood method. Estimates are retrieved by using a new sequential Monte Carlo EM algorithm, which use allows to hugely mitigate the severe numerical issues posed by the direct maximization of the likelihood. The risk of incurring in a misspecification is evaluated as percentage of times the Akaike information criterion leads to select the wrong model. The severity of a misspecification is evaluated in terms of its impact on maximum likelihood estimate of the mean remaining useful life. [ABSTRACT FROM AUTHOR]

This paper proposes a new time scaled Wiener process with random effects that has been specially designed to allow the description of non‐monotonic degradation phenomena with bathtub shaped degradation rate, here intended as derivative of the mean function. Two different parameterizations of the proposed Wiener process are suggested, and the main features of the process are illustrated and discussed. The maximum likelihood estimation of its parameters is addressed. A failure threshold model is adopted to formulate and estimate the probability distribution function of the remaining useful life, which constitutes the core prognostic tool in condition‐based maintenance. As a motivating example, the proposed model is applied to a set of real degradation data of metal‐oxide‐semiconductor field‐effect transistors, where, as a result of preliminary analyses, some of the process parameters are assumed to be random in order to describe the considerable heterogeneity observed between the degradation paths of different units. Obtained results demonstrate the affordability and utility of the proposed model, especially for the estimation of unit‐specific features performed on the basis of degradation data collected in the early phase of the life of a unit belonging to the considered heterogeneous population. [ABSTRACT FROM AUTHOR]

Most of the stochastic models adopted to describe the evolution over time of degradation phenomena of technological units assume that their degradation level can increase indeterminately. However, these degradation phenomena are typically subjected to obvious bounds, if only because technological units have finite size. In fact, very often, this inconsistency does not significantly affect the effectiveness of unbounded degradation models, since degrading units are usually assumed to fail when their degradation level exceeds a failure threshold that is much smaller than the obvious bounds. Nevertheless, in some cases, due to the very nature of the underlying degradation mechanism, less obvious bounds could exist, which are not necessarily far from the failure thresholds. The question that arises is whether the use of a bounded degradation model, in this latter type of experimental situations, could be beneficial. For this purpose, since a bounded degradation process should necessarily have dependent increments, in this paper we investigate the potential of a new bounded transformed gamma (TG) process to adequately describe bounded degradation phenomena and predict their future evolution. Differently from other existing gamma process based bounded degradation models, here the upper bound is treated as an unknown parameter that has to be estimated from the available degradation data. A numerical example is presented where the parameters of the proposed model are estimated from simulated data. Then the model is applied to a set of wear measures of cylinder liners that equip a diesel engine for marine propulsion, which have also stimulated this study. Model parameters are estimated by using the maximum likelihood (ML) method. The fitting ability of the proposed new bounded process is compared to that of an unbounded gamma process, which was previously adopted to analyze the same liner wear data. Obtained results are critically discussed in the paper. [ABSTRACT FROM AUTHOR]

An s-based methodology that can be used to carry out a condition-based estimate of liner reliability with respect to failure through excessive wear, and to plan condition-based maintenance activity, is presented. The proposed method facilitates reducing maintenance costs within noticeably affecting liner reliability, and gives probability of inspecting or replacing liners only when there is a high likelihood that their wear level will exceed the wear limit before the next inspection date.