Residual Lifetime Research Articles

Physical aspects of quantile residual lifetime sequence

Abstract The modeling of count data is found in many fields, such as statistical physics, public health, medicine, epidemiology, applied science, sociology, and agriculture. In many physical situations, it has been observed that many times in the real world, the original variables may be continuous in nature, but discrete by observation. In this study, the α {\rm{\alpha }} -quantile residual life function for discrete lifetime models is defined and some attributes are investigated. The relation between this measure and the hazard rate function is studied. We discuss how this measure could be useful for finding the burn-in time of a lifetime dataset. Then, a new stochastic order based on the α {\rm{\alpha }} -quantile residual life is proposed and studied.

Acoustic emission monitoring of a large-scale 50-year-old prestressed concrete bridge girder during an eccentric three-point bending test

Deterioration of reinforced and prestressed concrete structures is one of the main challenges in structural engineering. As the majority of our infrastructure is built around 1960-1980, most structures have reached or will soon reach their design lifetime, giving rise to more structural problems and costs in the coming decades. It is therefore important to develop efficient assessment schemes allowing to assure the safety and reliability of these existing structures and to estimate their residual lifetime. Within the framework of the Bridge|50 research project, a 50-year-old prestressed concrete bridge showing signs of corrosion damage was decommissioned. The bridge girders were recovered and have been subjected to large-scale load tests with varying loading patterns. This paper presents the results acquired during acoustic emission (AE) monitoring of one of the I-shaped girders during a monotonic three-point bending test with an eccentric point load. The results show that the failure mode and location could be detected based on AE activity and zonal AE localization. The onset of concrete cracking was observed by a decrease in peak frequency of the AE signals. Average frequency (AF) and rise angle (RA) value analysis was used to characterize the crack mode, which shifted from tensile to shear mode during bending.

Study on vibration fatigue of lifeguard in a metro bogie and methodology for damage estimation based on the measured acceleration

The lifeguard is more like a cantilever beam installed on the end of bogie frame, used to remove foreign body on the rail. Due to severe vibration condition, the lifeguard has been reported to be subjected to fatigue failure by railway operators. This paper thus studied on fatigue failure mechanisms of lifeguard through both the field test and numerical simulation. In the field test, the vibration acceleration and dynamic stress developed on the lifeguard were measured to identify main contributors to the fatigue failure. The test results showed that the structural resonance arising from the rail corrugation-induced high frequency impact serves as the main causal factor. To better understanding the failure mechanism, a numerical model considering the flexibility of lifeguard was established to determine the stress field of lifeguard based on the modal method, which was further used to estimate the residual fatigue lifetime for given loading conditions. The results showed that the obtained dynamic stress for given position on lifeguard is quite comparable with those obtained through the field test. Based on the obtained dynamic stress, the fatigue damage was further estimated and concluded that the fatigue lifetime of lifeguard is much less than the designed lifetime under the considered loading condition. The rail grinding and the structural improvement are thus suggested to mitigate the vibration fatigue of lifeguard.

Prediction of the residual lifetime of bitumen coatings on urban gas pipelines from the change in their mechanical characteristics during thermal-oxidative aging

Residual life of bitumen insulation is an important parameter of urban gas pipelines. Its fast and reliable estimation is necessary for timely health monitoring and coating restoration. In this study, we propose to define lifespan of bitumen insulation in situ from the mechanical characteristics measured during its thermal-oxidative aging. For evaluation of elastic and viscous properties, micro-impact dynamic indentation was applied. We determined the values of activation energy under thermal destruction and the dependence of transient electrical resistance on the critical values of coating's mechanical properties. Obtained experimental data foster real-time estimation of service time of insulation without coating removal.

Method for assessing the durability of structures under stationary and non-stationary random loading using variational mode decomposition (VMD)

In the era of digital transformation, most devices are equipped with a variety of sensors, which provide information to be used in developing intelligent models for predicting the fatigue life. The development of digital models of real objects for fatigue life estimation faces the lack of algorithms for performing such an estimation. The problem arises in the adaptive and automatic analysis of signals from real sensors installed on the object and their subsequent processing to estimate the fatigue life of the object. We propose a new method for assessing the fatigue life of structures based on application of the adaptive method of variational mode decomposition to signals gained from sensors, including non-stationary ones. Variational mode decomposition involves decomposition of an initial complex random process into simpler random processes (modes) that are stationary and narrowband. An original method of summarizing damage resulted from the action of the modes obtained as a result of the decomposition is used. The developed method can be used as an algorithmic support for the generation of digital doubles of the residual lifetimes of natural products. The proposed method is compared with the «rainflow» method in the time domain. Different realizations of random stationary and non-stationary signals with different bandwidths are compared numerically. In addition, the traditional frequency methods of Dirlik and Benasciutti have been compared with the «rainflow» method. The analysis showed good results for the proposed method, i.e., the error was smaller compared to traditional frequency methods, especially for non-stationary processes.

About the Residual Time of Human Life

Many researchers believe that human lifetime in the interval from 20 to 80 years is approximately described by the Gompertz distribution. It is natural to consider the problem of the distribution of the residual human lifetime at the final stage, that is, after 80 years. To do this, in this study, a statistical analysis of some statistical models on real data is carried out. Several models are presented, which, according to the authors, can adequately describe data on mortality after 80 years.

Stochastic properties of varentropy based on residual lifetime

The objective in the study of reliability and survival theory is to have precision in the extracted information. The measure of dispersion in the information content has been newly introduced in the information theory, known as varentropy. Studying the variability in the uncertainty measure is found productive for stochastic systems conditional on survival. In this paper, we provide a novel stochastic order based on the notion of residual varentropy and study its properties. Further on the basis of the residual varentropy, novel classes of life distributions are identified and investigated in detail. Moreover, some applications of the proposed order are produced at the end.

Stochastic Modeling of Crack Growth and Maintenance Optimization for Metallic Components Subjected to Fatigue-Induced Failure

Abstract The degradation of metallic systems under cyclic loading is subject to significant uncertainty, which affects the reliability of residual lifetime predictions and subsequent decisions on optimum maintenance schedules. This paper focuses two main challenges in developing a reliable framework for the lifecycle management of fatigue-critical components: constructing a stochastic model that captures uncertainties in crack growth histories, and presenting a computationally efficient strategy for solving the stochastic optimization associated with maintenance scheduling. Polynomial chaos (PC) representation is proposed to propagate uncertainty in the fatigue-induced crack growth process, using a database from constant amplitude loading experiments. Additionally, an optimization strategy is implemented based on Gaussian process surrogate modeling to solve the stochastic optimization problem under maximum probability of failure constraints. The sensitivity of the optimum solution to different probability of failure thresholds is examined. The proposed framework offers a decision support tool for informed decision-making under uncertainty, aiming to mitigate fatigue failure.

Bio-Inspired Energy-Efficient Cluster-Based Routing Protocol for the IoT in Disaster Scenarios.

The Internet of Things (IoT) is a promising technology for sensing and monitoring the environment to reduce disaster impact. Energy is one of the major concerns for IoT devices, as sensors used in IoT devices are battery-operated. Thus, it is important to reduce energy consumption, especially during data transmission in disaster-prone situations. Clustering-based communication helps reduce a node's energy decay during data transmission and enhances network lifetime. Many hybrid combination algorithms have been proposed for clustering and routing protocols to improve network lifetime in disaster scenarios. However, the performance of these protocols varies widely based on the underlying network configuration and the optimisation parameters considered. In this research, we used the clustering parameters most relevant to disaster scenarios, such as the node's residual energy, distance to sink, and network coverage. We then proposed the bio-inspired hybrid BOA-PSO algorithm, where the Butterfly Optimisation Algorithm (BOA) is used for clustering and Particle Swarm Optimisation (PSO) is used for the routing protocol. The performance of the proposed algorithm was compared with that of various benchmark protocols: LEACH, DEEC, PSO, PSO-GA, and PSO-HAS. Residual energy, network throughput, and network lifetime were considered performance metrics. The simulation results demonstrate that the proposed algorithm effectively conserves residual energy, achieving more than a 17% improvement for short-range scenarios and a 10% improvement for long-range scenarios. In terms of throughput, the proposed method delivers a 60% performance enhancement compared to LEACH, a 53% enhancement compared to DEEC, and a 37% enhancement compared to PSO. Additionally, the proposed method results in a 60% reduction in packet drops compared to LEACH and DEEC, and a 30% reduction compared to PSO. It increases network lifetime by 10-20% compared to the benchmark algorithms.

Residual and past varinaccuracy measures

Abstract Analysing the information measures’ dispersion index has garnered increasing attention. In this regard, variability of entropy has been explored for residual and past lifetimes. In a recent paper, Balakrishnan et al. (2023, Commun. Stat. Theory Methods, 53, 5574–5592) have studied the variability of the Kerridge inaccuracy measure. The dynamic measures of varinaccuracy, namely residual varinaccuracy and past varinaccuracy, have been introduced in this article. A detailed course of theoretical results has been investigated with examples. Further, some applications of the residual varinaccuracy have been added to show the functionality of the defined measure.

Modeling to COVID-19 and cancer data: Using the generalized Burr-Hatke model

This paper describes an extended version of the Burr–Hatke distribution via generalizing its survival function. This model is called as the generalized Burr-Hatke distribution. The suggested model's hazard rate function can be non-increasing (decreasing) form. Related statistical characteristics of the proposed model are identified. We provide closed-form expressions for the density function, hazard rate function, moments and their related metrics. In addition, some of the proposed model's reliability attributes, such as mean residual life and mean inactivity time, are determined both empirically and visually. The characterization of GBH model based on hazard rate, truncated and conditional moments is also provided. The maximum likelihood technique is employed for estimating the unknown model parameters. To explore the behavior of the estimates, Monte Carlo Simulation can be used. Finally, the new model's performance is verified using two sets of real data.

Extreme Values and Reliability Measures of Continuous Erlang Mixtures

This study delves into Extreme Value Theory, focusing on the limiting distributions of continuous Erlang mixtures and their mixing distributions. It categorizes Erlang mixtures based on their extreme value types, demonstrating that the limiting distributions of the Erlang mixtures can be either Type I (Gumbel) or Type II (Frechet), contingent on the mixing distribution. Further, this study derives the mean residual lifetime and equilibrium distributions of these mixed distributions.

Reliability and Residual Life of Cold Standby Systems

In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study proposes system equivalent models for various types of cold standby systems, all composed of components that follow the same exponential distribution. We use the equivalent model to determine the optimal timing for the use of cold spares and derive the reliability function and residual lifetime function for each type of system. To demonstrate the validity of our model, the Monte Carlo simulation is strategically designed based on the system failure rate function. The experimental results are then compared with those obtained from the numerical model, highlighting that the numerical method incurs a lower time cost.

Cyclic response and residual life prediction of Inconel 718 superalloy after overloading under hybrid stress-strain controlled creep-fatigue loading

Inconel 718 is a material for manufacturing turbine disks, which is subjected to complex loads of creep-fatigue during service. This paper examines the effect of constant stress overloading at various lifespan stages on subsequent cyclic deformation, fracture behavior, and residual lifetime in hybrid stress and strain-controlled creep-fatigue interaction (HCFI) experiments conducted at 650℃. Overloading of 800 MPa constant stress with 180 min dwell time is applied at the 10 %, 25 %, 50 %, 65 %, and 70 % lifespan of HCFI tests. Results show that overloading reduces the residual life of the material obviously and makes a significant impact on the subsequent creep-fatigue deformation behavior, and additional damage is induced when overloading is applied towards the end of the lifespan. Moreover, more severe grain boundary damage leading to the final intergranular fracture is identified through microstructural analysis following overloading. Finally, equivalent damage is proposed to quantify the creep-fatigue damage affected by overloading, resulting in accurate life prediction outcomes.

On the residual lifetimes of dependent components upon system failure

In this paper, we consider coherent systems composed of identical yet possibly dependent components. The dependence structure among components is modelled via copulas. We investigate residual lifetimes of components that survived the failure of the system. The main result of the paper is a new general formula describing the joint distribution of these residual lifetimes. Using the new formula we look more closely at this distribution in the cases of Clayton, Gumbel–Hougaard and Frank copulas and standard exponential and Weibull margins. In particular, we present some comparative numerical results that enable us to examine the influence of the dependence among components on the residual lifetimes of the surviving ones. We observe that the results obtained under the assumption of dependence and independence may differ significantly, especially when the system breaks down just after it started working.

Robust assessment of life insurance products

AbstractIn this paper we propose a robust assessment for the premium of a standard life insurance contract with respect to the uncertainty on the estimated residual lifetime distribution function. Specifically, we provide a method to derive the range of values that the premium of a given contract can attain when considering all residual lifetime distribution functions that satisfy an $$L^2$$ L 2 distance constraint to a reference distribution function. Furthermore, we show that the $$L^2$$ L 2 distance constraint can be used as flexible starting point to include further information regarding future mortality.

Uncertain process-based data integration and residual lifetime evaluation of PCB in airborne equipment with ADT and field data

Accurately evaluating the lifespan of the Printed Circuit Board (PCB) in airborne equipment is an essential issue for aircraft design and operation in the marine atmospheric environment. This paper presents a novel evaluation method by fusing Accelerated Degradation Testing (ADT) data, degradation data, and life data of small samples based on the uncertainty degradation process. An uncertain life model of PCB in airborne equipment is constructed by employing the uncertain distribution that considers the accelerated factor of multiple environmental conditions such as temperature, humidity, and salinity. In addition, a degradation process model of PCB in airborne equipment is constructed by employing the uncertain process of fusing ADT data and field data, in which the performance characteristics of dynamic cumulative change are included. Based on minimizing the pth sample moments, an integrated method for parameter estimation of the PCB in airborne equipment is proposed by fusing the multi-source data of life, degradation, and ADT. An engineering case illustrates the effectiveness and advantage of the proposed method.

Beautiful Gini

AbstractYou may very well be familiar with the Gini Coefficient, also known as the Gini index: a quantitative gauge with which socioeconomic inequality is measured, e.g. income disparity and wealth disparity. However, you may not know that the Gini Coefficient is an exquisite mathematical object. Enter this review paper—whose aim is to showcase (some of) the mathematical beauty and riches of the Gini Coefficient. The paper does so, in a completely self-contained manner, by illuminating the Gini Coefficient from various perspectives: Euclidean geometry vs. grid geometry; maxima and minima of random variables; statistical distribution functions; the residual lifetime and the total lifetime of renewal processes; increasing and decreasing failure rates; socioeconomic divergence from perfect equality; and weighted differences of statistical distribution functions. Together, these different perspectives offer a deep and comprehensive understanding of the Gini Coefficient. In turn, a profound understanding of the Gini Coefficient may lead to novel ‘Gini applications’ in science and engineering—such as recently established in the multidisciplinary field of restart research.

Surveillance of the recurrence time of the effectiveness of national and region-level quarantines of COVID-19 pandemic in Chile.

The World Health Organization has recommended a range of social and health measures to mitigate the spread of coronavirus disease 2019 (COVID-19), including strategies such as quarantines, border closures, social distancing, and mask usage, among others. Specifically, the Chilean authorities implemented the "step-by-step" plan, built on the concept of dynamic quarantine. Numerous studies have examined the effectiveness of these quarantines in Chile during the pandemic, utilizing data published by the Chilean Ministry of Health. This study's primary aim was to enhance our understanding of quarantine effectiveness in Chile during the pandemic. We accomplished this by analyzing the distributional behavior of the time until the COVID-19 pandemic was deemed under control or not. In our study, we defined an event with two potential outcomes related to the instantaneous reproductive number (Rt), which signifies the time until a change in the event outcome occurs. Importantly, we did not predefine a specific temporal observation unit. These findings allowed us to complement the concept of effective quarantine by considering the dynamics generated by the protocols, such as phase 1 of the quarantine, in achieving natural herd immunity in response to the number of COVID-19 cases and Rt. We assessed the behavior of the mean and median residual lifetime until the initiation of controlled/uncontrolled episodes of the COVID-19 pandemic based on Rt in all regions of Chile. Despite variations in the distribution of residual times for controlled/uncontrolled episodes in different regions, there was a similar observation during the period considered (between March 2020 and March 2021): the mitigation measures did not produce a clear positive effect for controlling the epidemic. The residual times of episodes with Rr,t > 1 were not different from those episodes with Rr,t ≤ 1.

Materials Science Analysis of RCCA Structural Materials and Calculations for Lifetime Extension

The paper considers the possibility of lifetime extending of the rod control cluster assemblies in operation by determining their residual lifetime using an approach that takes into account the actual position of the rod control cluster assembly in the core. Excessive conservatism was introduced by assuming that the immersion of the 10th working group in the core during all fuel campaigns is 70 %, while the actual position is 85-90 %. Taking into account the actual position of the rod control cluster assemblies indicates much less irradiation of the lower, most loaded part of control rod cladding and much less burnup of the 10B compared to 70 % immersion of the rod control cluster assemblies, since they are in the area of lower neutron flux density.
 The results of a comprehensive analysis of available studies and test results to determine the phenomena that can potentially approach the achievement of the boundary state of the structural components or limit the lifetime of control rods and rod control cluster assemblies in general are presented. Such phenomena include general corrosion of structural materials (42CrNiMo, Cr18Ni10Ti) (decrease in wall thickness, increased transfer of radioactive corrosion products the coolant); radiation resistance (degradation of mechanical characteristics) of control rod cladding materials (42CrNiMo) and other structural components of the rod control cluster assemblies (42CrNiMo, CrKh18Ni10Ti); radiation resistance of neutron-absorbing materials (B4C, Dy2O3∙TiO2); compatibility of absorbing materials with the control rod cladding.
 Based on the results of post-irradiation examinations of control rods tested in research reactors as dummy rods or rod control cluster assembly rods operated in the VVER-1000 core, the following boundary values were established that can be used as criteria for maintaining the integrity of the control rod cladding: maximum fast neutron fluence in the lower, most loaded part of the control rod cladding (in the weld area of the lower end plug and the cladding) should not exceed 34×1021 n/cm2; maximum burnup of the 10B isotope should not exceed 45 %. If these two criteria are met, the possibility of other potentially damaging phenomena is too low.
 According to the calculations that use the schedule of changes in the position of the rod control cluster assemblies of the control group and the power of one of the power units during one fuel cycle, one can preliminary conclude that the proposed approach will extend the lifetime of almost all rod control cluster assemblies from 25500 to 38000 hours in the automatic control group and from 75600 to 113500 hours in the shutdown group. The residual lifetime should be assessed for a particular power unit and each rod control cluster assembly separately, since each rod control cluster assembly has its own operating history.