Failure Time Distribution Research Articles

Shaping of the risk of a series-parallel manufacturing structure maintenance according to quasi-coherence and the [formula omitted]-th survival value

The paper presents the authors’ model for determining the probability value of the survival function of the difference of two random variables: TP – the amount of time of correct operation and TB – the amount of time of failure. For this purpose, the concept of K-th survival value is introduced. The K-th survival value defines the probability that the total time of correct operation of the production system will be longer by at least k time units (for k≥0) than the total amount of time of failures. The model was exemplified by a real production system with a series–parallel structure. In the nesting manufacturing structure, the availability of machines determines the number and the type of flow streams of the processed material. To formalise the chains of relations at a given Δt, this paper utilises the quasi-coherence property. The paper identifies four possible cases of system operation: 1) a fully operational system in which every machine is capable of meeting the assumed production schedule; 2) a system which has lost the property of quasi-coherence (certain system objects are in an inoperable state) but it is possible to meet the assumed production schedule; 3) a system which has lost the property of quasi-coherence but the assumed task schedule is possible to meet after redefining the material flow streams; 4) a system which has lost the property of quasi-coherence and it is impossible to meet the assumed production schedule. Based on the definition of the survival function [1] S of the random variable T: ST:=PT>τ=1-FTτ,τ∈R, the concept of K-th survival value was introduced. For possible cases, K-th survival value was defined as: KT1,Ti=PT1-Ti≥k=1-FT1-Tik (for i=2,3,4), where T1 and Ti are random variables with given probability distributions. In turn, k is a deterministic value that determines the total number of time units of correct system operation in relation to the total failure time. The application of the developed algorithm enables the system to be analysed in terms of three aspects: (1) to determine the probability of on-time execution of tasks, taking into account historical values of machine failure and correct operation durations; (2) to determine the stability of the system based on empirical data; (3) to monitor the level of risk in real time. The paper validates the model by determining the stability of the analysed system for real machine failure data. The introduced criterion of stochastic stability of the production system has been verified for data in which distributions of correct operation times and failure times are random variables from the family of Gamma distributions. The presented model can be included in the group of multifactorial risk assessment methods.

Pollution concentration monitoring using a new Birnbaum–Saunders control chart

AbstractAir pollution monitoring is an important issue in environmental science. The Birnbaum–Saunders (BS) distribution, originally applied to describe product failure time distribution to fatigue failures and general random wear failures, is also well to describe the pollutant concentration data due to accumulations of various pollutants in the air over time. Sulfur dioxide (SO2) is a critical factor in air pollution. Hence, it is important to monitor its concentration variation for air pollution prevention. Due to the complexity of its distribution form, there is no reliable and easy‐to‐use control chart for monitoring pollutant concentrations based on the BS distribution. We found that the SO2 concentration data follows the BS distribution. In this study, we propose a new median control chart based on the exact sampling distribution of the monitoring statistic to detect shifts in the median of BS distribution. Thus, given the false alarm rate, the control limits for such control charts can be obtained precisely satisfying a preset in‐control average run length using Monte Carlo simulations. The out‐of‐control average run lengths are calculated by simulation to evaluate the detection performance of the proposed chart when the median shifts occur. We further compare the detection performance of the proposed chart and those of the existing control charts based on asymptotic sampling distributions. In order to improve the detection ability of the proposed chart for small median shifts, an exponentially weighted moving average (EWMA) control chart is constructed. The results of numerical analyses demonstrated that the proposed EWMA chart performs much better than all existing control charts for monitoring the median of BS distribution. Finally, the proposed control charts are applied to monitor the median of SO2 concentrations for air pollution control, showing that both charts can effectively detect a shift in the median of SO2 concentrations. The proposed EWMA control chart even detects out a small shift in the median of SO2 concentrations. The results provide a continuous monitoring solution for air pollution prevention.

An analytical approach to evaluate life-cycle cost of deteriorating pipelines

Optimal inspection and maintenance planning for deteriorating pipelines is important for cost-effective risk management decisions. The objective of this study is to develop an analytical approach for determining the expected value and standard deviation of life-cycle cost (LCC) for deteriorating pipelines, which can incorporate imperfect repair and inspection actions without making independent assumptions of failure and repair events. The framework is developed based on a decision tree model by using analytical methods to evaluate events and considers the impact of the inspection schedules and possible repair actions on the probability distributions of failure times. To illustrate the proposed framework, a steel transmission pipeline with a corrosion defect is used, where a stochastic model of corrosion growth is assumed and burst failure is considered as the pipeline failure mode. The case study indicates that the failure cost due to two or more failure occurrences can be ignored; and the inspection interval, repair threshold and type, the length of lifetime considered, and unit failure cost all play important roles in the expected value of the total cost. The variation in the LCC estimation is found to be significant, and it has a great impact on determination of optimal decision variables.

A Nonlinear Quantile Regression for Accelerated Destructive Degradation Testing Data

Traditional regression approaches to accelerated destructive degradation test (ADDT) data have modeled the mean curve as representative. However, maximum likelihood estimates (MLEs) of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear quantile regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization (GEM) framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the τ th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

A Comparison of Additional Benefit Assessment Methods for Time-to-Event Endpoints Using Hazard Ratio Point Estimates or Confidence Interval Limits by Means of a Simulation Study.

For time-to-event endpoints, three additional benefit assessment methods have been developed aiming at an unbiased knowledge about the magnitude of clinical benefit of newly approved treatments. The American Society of Clinical Oncology (ASCO) defines a continuous score using the hazard ratio point estimate (HR-PE). The European Society for Medical Oncology (ESMO) and the German Institute for Quality and Efficiency in Health Care (IQWiG) developed methods with an ordinal outcome using lower and upper limits of the 95% HR confidence interval (HR-CI), respectively. We describe all three frameworks for additional benefit assessment aiming at a fair comparison across different stakeholders. Furthermore, we determine which ASCO score is consistent with which ESMO/IQWiG category. In a comprehensive simulation study with different failure time distributions and treatment effects, we compare all methods using Spearman's correlation and descriptive measures. For determination of ASCO values consistent with categories of ESMO/IQWiG, maximizing weighted Cohen's Kappa approach was used. Our research depicts a high positive relationship between ASCO/IQWiG and a low positive relationship between ASCO/ESMO. An ASCO score smaller than 17, 17 to 20, 20 to 24, and greater than 24 corresponds to ESMO categories. Using ASCO values of 21 and 38 as cutoffs represents IQWiG categories. We investigated the statistical aspects of the methods and hence implemented slightly reduced versions of all methods. IQWiG and ASCO are more conservative than ESMO, which often awards the maximal category independent of the true effect and is at risk of overcompensating with various failure time distributions. ASCO has similar characteristics as IQWiG. Delayed treatment effects and underpowered/overpowered studies influence all methods in some degree. Nevertheless, ESMO is the most liberal one. For the additional benefit assessment, the American Society of Clinical Oncology (ASCO) uses the hazard ratio point estimate (HR-PE) for their continuous score. In contrast, the European Society for Medical Oncology (ESMO) and the German Institute for Quality and Efficiency in Health Care (IQWiG) use the lower and upper 95% HR confidence interval (HR-CI) to specific thresholds, respectively. ESMO generously assigns maximal scores, while IQWiG is more conservative.This research provides the first comparison between IQWiG and ASCO and describes all three frameworks for additional benefit assessment aiming for a fair comparison across different stakeholders. Furthermore, thresholds for ASCO consistent with ESMO and IQWiG categories are determined, enabling a comparison of the methods in practice in a fair manner.IQWiG and ASCO are the more conservative methods, while ESMO awards high percentages of maximal categories, especially with various failure time distributions. ASCO has similar characteristics as IQWiG. Delayed treatment effects and under/-overpowered studies influence all methods. Nevertheless, ESMO is the most liberal one. An ASCO score smaller than 17, 17 to 20, 20 to 24, and greater than 24 correspond to the categories of ESMO. Using ASCO values of 21 and 38 as cutoffs represents categories of IQWiG.

Reliability Assessment of Power Plant Operations through Boolean Function Expansion and Mean Time to Failure Analysis

This paper presents an investigation into the reliability assessment of power plant operations using Boolean Function expansion and Mean Time to Failure (MTTF) analysis. The study focuses on a complex system comprising two power generators within a power house. The primary objective of this system i. This paper presents an investigation into the reliability assessment of power plant operations using Boolean Function expansion and Mean Time to Failure (MTTF) analysis. The study focuses on a complex system comprising two power generators within a power house. The primary objective of this system is to ensure uninterrupted power supply from the power house to critical consumers via an output main switch. Reliability calculations are conducted considering failure times of various components, including cables, generators, and main switchboards, assuming arbitrary distribution patterns. Additionally, MTTF for the system under an exponential failure time distribution is determined. Graphical representations are employed to illustrate the utility and efficacy of the proposed models to ensure uninterrupted power supply from the power house to critical consumers via an output main switch. Reliability calculations are conducted considering failure times of various components, including cables, generators, and main switchboards, assuming arbitrary distribution patterns. Additionally, MTTF for the system under an exponential failure time distribution is determined. Graphical representations are employed to illustrate the utility and efficacy of the proposed model.

Estimation of the percentile of Birnbaum-Saunders distribution and its application to PM2.5 in Northern Thailand.

The Birnbaum-Saunders distribution plays a crucial role in statistical analysis, serving as a model for failure time distribution in engineering and the distribution of particulate matter 2.5 (PM2.5) in environmental sciences. When assessing the health risks linked to PM2.5, it is crucial to give significant weight to percentile values, particularly focusing on lower percentiles, as they offer a more precise depiction of exposure levels and potential health hazards for the population. Mean and variance metrics may not fully encapsulate the comprehensive spectrum of risks connected to PM2.5 exposure. Various approaches, including the generalized confidence interval (GCI) approach, the bootstrap approach, the Bayesian approach, and the highest posterior density (HPD) approach, were employed to establish confidence intervals for the percentile of the Birnbaum-Saunders distribution. To assess the performance of these intervals, Monte Carlo simulations were conducted, evaluating them based on coverage probability and average length. The results demonstrate that the GCI approach is a favorable choice for estimating percentile confidence intervals. In conclusion, this article presents the results of the simulation study and showcases the practical application of these findings in the field of environmental sciences.

Generalized Confidence Interval for the Difference Between Percentiles of Birnbaum–Saunders Distributions and Its Application to PM2.5 in Thailand

The Birnbaum–Saunders distribution is of particular interest for statistical inference. This distribution represents the failure time distribution in engineering. In addition, the Birnbaum–Saunders distribution is commonly used in different areas of science and engineering. Percentiles are a frequently employed statistical concept. Percentiles help ascertain the position of an observation concerning the percentage of data points below it. These percentiles serve as indicators of both the central tendency and the dispersion of data. While comparing two data distributions, the mean is typically the most dependable parameter for describing the population. However, in situations where the distribution exhibits significant skewness, percentiles may sometimes offer a more reliable representation. Herein, the confidence intervals for the difference between percentiles of Birnbaum–Saunders distributions were constructed by the generalized confidence interval (GCI) approach, the bootstrap approach, the Bayesian approach, and the highest posterior density (HPD) approach. A Monte Carlo simulation was conducted to evaluate the performance of the confidence intervals. The performance was considered via coverage probability and average width. The findings suggest that utilizing the GCI approach is advisable for estimating confidence intervals for the disparity between two percentiles. Ultimately, the outcomes of the simulation investigation, coupled with an application in the field of environmental sciences, were outlined.

Sensitivity Analysis of Edible Oil Refinery Industry using Machine Learning

This research paper discusses the use of machine learning for sensitivity analysis in the edible oil refinery industry. The edible oil refinery consists of four units, and subsystem A (Cleaning) contains parallel subcomponents that enable it to function in reduced capacity when some of its components fail. As a result, the system operates in reduced capacity and fails entirely when unit A fails. There is single repairman who is available for 24x7. The failure and repair time distributions are distinct and constant for each unit. Subunits B (Shelling), D (Crushing/Ribbing), and E (Expeller Pressing) are connected in series, so, if any of them malfunctions, the entire system fail. System parameters' behavior for various repair and failure rates is discussed graphically and in tabular form. Comparison of the Performance of system parameters is carried out using linear Classifier and Logistic Regression and graphs are drawn. From the comparative analysis of models, it is concluded that the linear classifier is better than logistic regression for MTSF, Busy Period of server and Availability.

Dynamic multivariate Gamma-Gamma general path model: An alternative approach to time-variant degradation rates

We introduce a general path Gamma-Gamma model for degradation measures, related to different inspection times functions, obtaining flexible forms of degradation paths. One important contribution of the proposed model is the way the degradation rate is modeled. It is composed of two random components: one random effect quantifying the specific features of each device and a dynamic effect, common to all devices, measuring the impact of the environment on the degradation. The model is identifiable under mild constraints. Besides producing gains regarding the interpretability of the parameters, this decomposition generates a parsimonious model, reducing computational time. The relation between degradation and failure time is obtained, allowing a computational approximation for the failure time distribution. The model performance is evaluated through simulation, helping to guide the prior specifications to model identification. The proposed model is applied to analyze fatigue crack growth data. We compare the proposed model with the traditional linear Weibull model and with a dynamic linear Normal model. Results show that the proposed methodology is competitive in predicting failure times and estimating the remaining useful life.

Understanding NFV-Enabled Vehicle Platooning Application: A Dependability View

This paper aims to use analytical modeling technique to quantitatively study the dependability of Vehicle Platooning Application, which consists of Multiple Sub-Services (VPP-MSS) to achieve its functionality. Each sub-service (SS), based on network function virtualization technology, is executed in a container. Both SSes and OSes which SSes run on can suffer from software aging after a long and continuous running, reducing VPP-MSS dependability. Rejuvenation techniques are usually used to combat software aging, but they require the support of backup components. Quantitative study of VPP-MSS dependability enables in-depth understanding of the effectiveness of rejuvenation techniques based on analytical models. In contrast to the existing studies, we develop a semi-Markov process (SMP) model to jointly analyze the impact of rejuvenation technique trigger intervals (RTTIs), backup components' behaviors, time-dependent interactions between various behaviors and the number of active SSes deployed on an OS on the effectiveness of rejuvenation technique. Sensitivity analysis helps identify key parameters for improving the dependability of VPP-MSS. Extensive numerical experiments demonstrate the necessity of considering backup components' behaviors and investigating non-exponentially distributed failure times. We also determine both the optimal RTTI combination and the optimal combination of SSes and OSes, which can maximize VPP-MSS dependability.

Modeling of System Availability and Bayesian Analysis of Bivariate Distribution

To meet the desired standard, it is important to monitor and analyze different engineering processes to obtain the desired output. The bivariate distributions have received a significant amount of attention in recent years due to their ability to describe randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed by compounding two independent asymmetric univariate distributions and by using the nesting approach to study the effect of each component on reliability for better understanding. Furthermore, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution like mean median and quantile function are discussed. We used inverse Gamma prior to study its frequentist properties by conducting a Monte Carlo Markov Chain (MCMC) sampling scheme.

Research on life distribution model of electrical protection cover for energy meter in charging pile based on accelerated test technology

The electric protection cover for the energy meter in the charging pile is an important part to protect the power line terminal and signal line terminal from being damaged by pollution. However, due to the complex and diverse environment in which the charging pile is located, it is easy to cause damage such as damage to electrical protection cover in high temperatures, high humidity, and other harsh environments, resulting in pollution and corrosion of electrical terminals, affecting normal electricity metering. To solve this problem, this paper studies the important factors that affect the life distribution of the electric protective cover used for energy meters in charging piles in the process of use. The accelerated stress model and method are constructed by the comprehensive application of the accelerated test theory, and the accelerated life test is completed. Through experiments, the failure time distribution of typical electrical protection covers for energy meters in a natural service environment is found, the model is hypothesized, tested, and estimated, and the key parameters of life distribution are determined. This paper also provides a good technical idea for the research of aging failure data analysis of electric plastic materials.

Redundancy Allocation of Components with Time-Dependent Failure Rates

The Redundancy Allocation Problem (RAP) is well-known in the field of reliability optimization. In this paper, RAP is investigated assuming that the distribution of the time to failure of the components has the form of an Erlang distribution with a time-dependent rate parameter and considering that the choice of redundancy for each subsystem can be none, active, standby or mixed. A genetic algorithm is used to solve the problem of optimal allocation. To analyze the effect of the time dependence, some numerical examples are worked out. Then, a case study of RAP from the literature is analyzed. The obtained results show that time dependence of the failure time distribution parameters can lead to significant differences in the optimal redundancy allocation.

Інтервальна оцінка показників надійності за результатами випробувань компонентів складної системи

The goal of this work is to find the lower estimate of the no-failure probability (NFP) of a complex monotonic nonrecoverable system from the results of independent binomial tests of its components. Using the general-and-probabilistic method, the NFP is considered as a probability function polynomial, which is a linear homogeneous polynomial in each of the S variables where S is the number of system component types. Based on the method of confidence sets, the NFP lower estimate is found as the minimum of a function of an unknown multidimensional parameter at a probability of the aggregate test results (failure-free operation) of the system components equal to one minus the guaranteed confidence coefficient. The paper reports a system of equations, each of which for two component types relates the component reliability derivatives of the NFP (and one more equation relates the component reliability and the confidence coefficient). Conditions are found for the initial guess in a numerical solution of the above system of nonlinear equations (the number of the conditions is equal to the number of the component types minus one; each condition is a like sign for two functions each of which depends on the probability of the test results of a particular component type and the component reliability of this probability). In some specific cases, the program dimension can be reduced due to the simple structure of the probability function polynomial. The presented method gives a confidence reliability estimate with a guaranteed confidence coefficient for complex system that cannot be reduced to a serial-parallel or a parallel-serial structure and consist of components with an arbitrary type of failure time distribution. The method allows one to get an estimate at a small number of tests and a small number of failures or in their absence, which is of especial importance for high-reliability systems.

Towards UAV-Based MEC Service Chain Resilience Evaluation: A Quantitative Modeling Approach

Unmanned aerial vehicle (UAV) and network function virtualization (NFV) facilitate the deployment of multi-access edge computing (MEC). In the UAV-based MEC (UMEC) network, virtualized network function (VNF) can be implemented as a lightweight container running on UMEC host operating system (OS). However, UMEC network is vulnerable to attack, which can result in resource degradation and even UMEC service disruption. Rejuvenation techniques, such as failover technique and live container migration technique, can mitigate the impact of resource degradation but their effectiveness to improve the resilience of UMEC services should be evaluated. This paper presents a quantitative modeling approach based on semi-Markov process to investigate the resilience of a UMEC service chain consisting of any number of VNFs executed in any number of UMEC hosts in terms of availability and reliability. Unlike existing studies, the semi-Markov model constructed in this paper can capture the time-dependent behaviors between VNFs, between host OSes, and between VNFs and host OSes on the condition that the holding times of the recovery and failure events follow any kind of distribution. We perform the sensitivity analysis to identify potential resilience bottlenecks. The results highlight that migration time is the parameter significantly affecting the resilience, which shed the insight on designing the UMEC service chain with high-grade resilience requirements. In addition, we carry out the numerical experiments to reveal that: (i) the type of failure time distribution has a significant effect on the resilience; and (ii) the resilience increases with decreasing number of VNFs, while the availability increases with increasing number of UMEC hosts and the reliability decreases with increasing number of UMEC hosts, which can provide meaningful guidance for the UAV placement optimization in the UMEC network.

A Family of Additive Teissier–Weibull Hazard Distributions for Modeling Bathtub-Shaped Failure Time Data

The paper introduces a new failure time distribution called additive Teissier–Weibull distribution. Among its features, it is capable of modeling increasing and bathtub hazard rates. It is thus useful in modeling heterogeneous populations and can be viewed as the failure time model of the system having two modes of failures that follow the Teissier and Weibull distributions, respectively. Some of its important properties are obtained, such as quantiles, moments and shapes of the probability density and hazard functions. Four different methods of estimation such as the maximum likelihood, least squares, weighted least squares and maximum product spacing are proposed to estimate the unknown parameters. To compare the performance of the estimates, an extensive simulation study is carried out with varying sample sizes. Finally, failure times of primary reactor pumps and power generators are fitted and analyzed to show that the new additive hazard rate model may give a better fit than many other existing models.

New reliability model for complex systems based on stochastic processes and survival signature

For systems with complicated structures, reliability analysis based on survival signature has been carried out by modelling time-to-failure data with specific distributions. However, for highly reliable systems, only little or no failure data may be available. To enable reliability analysis without failure data, a new generalised reliability method is proposed for complex systems, based on the survival signature and using stochastic processes to model degradation. The combination of the survival signature and stochastic processes enables the proposed method to be applied to complex systems with different structures and stochastically degrading components. First, system reliability is analysed based on the survival signature and a generalised stochastic process. Then, component reliability analysis based on the generalised stochastic process is introduced using Wiener and Gamma processes. Finally, the approach presented in this paper is illustrated using two numerical examples, and the estimation results are compared with those calculated using failure time distribution functions.

Adaptive subset simulation for time-dependent small failure probability incorporating first failure time and single-loop surrogate model

High-precision time-dependent reliability analysis (TDRA) is essential for small failure probability estimation and life-cycle design and maintenance for engineering structures of high importance. However, existing small failure probability estimation methods, e.g., subset simulation (SS) and importance sampling (IS), might face challenges in accurate TDRA with relatively low computational costs. Thus, this paper presents a novel TDRA method for small failure probability based on point evolution kernel density (PKDE) and adaptive SS. To efficiently reduce the computational burden, single-loop surrogate modeling (SLSM) is employed, and TDRA is implemented by capturing the cumulative density function (CDF) of the first failure time. The proposed method is called First-failure-Time-PKDE-Adaptive-Surrogate-modeling-based-SS (FT-PASS). In FT-PASS, good-lattice-point-set-Partially-Stratified-Sampling (GLP-PSS) is performed to select uniform initial points and achieve the initial TDRA by PKDE. Subsequently, a Kriging model is built and trained by an advanced learning function to obtain the distribution of the first failure time with SS and revise the initial TDRA. Four different cases, a numerical case, a corroded steel beam, a turbine blade subject to stochastic loads, and a planar steel truss subject to stochastic load and corrosion effect, are used to validate FT-PASS. The results indicate that FT-PASS can accurately estimate time-dependent small failure probability and strike a balance between computational efficiency and accuracy compared with conventional TDRA methods.

Development and Validation of Thermal-Mechanical Creep Failure Module for Reactor Pressure Vessel Lower Head

For severe accidents, in-vessel retention (IVR) is a very effective and crucial severe accident mitigation measure. The lower head of the reactor pressure vessel plays a vital role in the IVR strategy. The failure of the lower head may lead to the release of radioactive substances into the environment. During the implementation of IVR, the lower head is in a high-temperature environment, and its main failure form is creep failure. Therefore, to ensure the successful implementation of the IVR strategy and prevent radioactive material leakage, it is necessary to conduct an in-depth analysis of the lower head. In this paper, the lower head thermal-mechanical creep failure (LHTCF) module is developed based on the theory of plate and shell and Norton-type constructive creep laws. Through the mechanical analysis of the lower head, seven failure criteria are used to evaluate the integrity of the lower head. Finally, the LHTCF module is integrated into the integrated severe accident analysis (ISAA) program, and the accuracy of the module is validated by numerical calculation of the Organisation for Economic Co-operation and Development Lower Head Failure (OLHF) experiment. Through the comprehensive judgment of different failure criteria, the final simulation results are in good agreement with the experimental data. The results show that the wall thickness at the crack decreases sharply before failure due to the effect of creep, and the stress increases abruptly at the failure time. The LHTCF module developed in this paper can accurately predict the creep behavior of the lower head, and the calculated failure time, position, and thickness distribution agree well with the experimental results.