Initial Failure Probability Research Articles

A probabilistic analysis method for evaluating the safety & resilience of urban gas pipeline network

Urban gas pipeline networks (UGPN) provide important support for high-quality urbanization. Therefore, it is imperative to analyze and assess the potential failures of UGPN. A novel probabilistic analysis method is proposed for assessing the safety and resilience of UGPN. Firstly, Bow-Tie analysis is used to identify faults. Then, a four-dimensional resilience assessment network is developed. Bayesian network is utilized to model the relationship between the variables, while dynamic Bayesian network is used to consider the dynamic nature of the system. The results of the study show that the proposed model can accurately estimate faults, consequences, and influence paths. Furthermore, the resilience analysis shows that monitoring the objective conditions is crucial and that the initial failure probability of the UGPN decreases from 0.03767 % to 0.01435 % when connected to a resilience network, indicating that considering resilience can effectively improve the reliability and safety of the UGPN. Two application examples are presented in the paper to validate the functionality of the proposed model. The proposed model can be used to set the state of UGPN to predict the probability of occurrence of a specific event and its consequences and to simulate the improvement trend of UGPN based on the direction of focus of future work.

Risk based maintenance for Swiss railway bridges: concept, implementation and first experiences

The Swiss Federal Railway (SBB) has an inventory of approx. 6,000 bridges. So far, condition classes of the individual bridges have been used for maintenance management. To improve the efficiency of the maintenance management, a long-term change from the condition class-based approach to a risk-based approach is considered. Such a risk-based approach was developed and implemented during a two-stage process into software (Excel and Python). The software was also linked to the SBB databases to access the relevant data. The Python software now includes 12 parameters to adapt the initial failure probability to specific bridge conditions and 15 damage parameters. So almost 30 parameters are used to compute the risk for each bridge. The software is also linked to geographical maps to show the location of the bridges. Besides the development of the approach, also the first experience of the application of this methodology will be discussed. For example, the risk-based ranking of the bridges clearly showed that specific bridge types are dominating. Also, some original ideas and concepts were not applicable due to difficulties in providing the required input data. However, currently the risk-based bridge ranking complies well with former investigations carried out by hand.

Analysis of spring operated pressure relief valve proof test data: Findings and implications

Ten years of research into spring operated pressure relief valve (SOPRV) proof test data are reviewed. Previously unpublished results are also presented. The principle findings are: proof test data alone are insufficient to properly analyze SOPRV safety behavior; root cause analysis (RCA) of all failed SOPRV is also required; probability of initial failure is a real and concerning phenomenon in both new (not previously installed) as well as used (previously installed) SOPRV but does not affect all SOPRV equally; SOPRV failure rates and safety performances depend on many variables including set pressure, SOPRV design and manufacturing specifics, and end user safety and maintenance practices; certain SOPRV require shorter proof test intervals (2–3 years) to maintain desired safety ratings but others can endure much longer proof test intervals with only small additional safety risks. Understanding all of the parameters which impact SOPRV safety performance and collecting safety performance data (including RCA of failed SOPRV) at the individual facility level are the keys to optimizing commissioning and pre‐installation proof testing and proof test intervals, and potentially to extending turnaround times. © 2018 American Institute of Chemical Engineers Process Saf Prog 37: 467–477, 2018

Adaptive surrogate model with active refinement combining Kriging and a trust region method

The reliability analysis of engineering structural systems with limit state functions defined implicitly by time-consuming numerical models (e.g. finite element analysis structural models) requires the use of efficient solution strategies in order to keep the required computational costs at acceptable levels. In this paper, an adaptive Kriging surrogate model with active refinement is proposed to solve component reliability assessment problems (i.e. involving one single design point) with nonlinear and time-consuming implicit limit state functions with a moderate number of input basic random variables. The proposed model, in the first stage, uses an adaptive Kriging-based trust region method to search for the design point in the standard Gaussian space and predict an initial failure probability based on the first-order reliability method as well as sensitivity factors for the input basic random variables. This initial prediction is then verified or improved efficiently in a second stage using Monte Carlo simulation with importance sampling based on a Kriging surrogate model defined iteratively around the design point using an active refinement algorithm. A convergence criterion that detects the stabilization of the failure probability prediction during the active refinement process is also proposed and implemented. The usefulness of the proposed adaptive Kriging surrogate model in terms of accuracy and efficiency for reliability assessment of engineering structural systems is shown in the paper with two relevant numerical examples, involving a highly nonlinear analytical limit state function in two-dimensions and an advanced nonlinear finite element analysis structural model in a larger dimensional space.

A combinatorial estimation approach for storage reliability with initial failures based on periodic testing data

ABSTRACTStorage reliability that measures the ability of products in a dormant state to keep their required functions is studied in this paper. Unlike the operational reliability, storage reliability for certain types of products may not be always 100% at the beginning of storage since there are existing possible initial failures that are normally neglected in the models of storage reliability. In this paper, a new combinatorial approach, the nonparametric measure for the estimates of the number of failed products and the current reliability at each testing time in storage, and the parametric measure for the estimates of the initial reliability and the failure rate based on the exponential reliability function, is proposed for estimating and predicting the storage reliability with possible initial failures. The proposed method has taken into consideration that the initial failure and the reliability testing data, before and during the storage process, are available for providing more accurate estimates of both initial failure probability and the probability of storage failures. When storage reliability prediction that is the main concern in this field should be made, the nonparametric estimates of failure numbers can be used into the parametric models for the failure process in storage. In the case of exponential models, the assessment and prediction method for storage reliability is provided in this paper. Finally, numerical examples are given to illustrate the method. Furthermore, a detailed comparison between the proposed method and the traditional method, for examining the rationality of assessment and prediction on the storage reliability, is presented. The results should be useful for planning a storage environment, decision-making concerning the maximum length of storage, and identifying the production quality.

An integrated approach to estimate storage reliability with initial failures based on E-Bayesian estimates

Storage reliability that measures the ability of products in a dormant state to keep their required functions is studied in this paper. For certain types of products, Storage reliability may not always be 100% at the beginning of storage, unlike the operational reliability, which exist possible initial failures that are normally neglected in the models of storage reliability. In this paper, a new integrated technique, the non-parametric measure based on the E-Bayesian estimates of current failure probabilities is combined with the parametric measure based on the exponential reliability function, is proposed to estimate and predict the storage reliability of products with possible initial failures, where the non-parametric method is used to estimate the number of failed products and the reliability at each testing time, and the parameter method is used to estimate the initial reliability and the failure rate of storage product. The proposed method has taken into consideration that, the reliability test data of storage products containing the unexamined before and during the storage process, is available for providing more accurate estimates of both the initial failure probability and the storage failure probability. When storage reliability prediction that is the main concern in this field should be made, the non-parametric estimates of failure numbers can be used into the parametric models for the failure process in storage. In the case of exponential models, the assessment and prediction method for storage reliability is presented in this paper. Finally, a numerical example is given to illustrate the method. Furthermore, a detailed comparison between the proposed and traditional method, for examining the rationality of assessment and prediction on the storage reliability, is investigated. The results should be useful for planning a storage environment, decision-making concerning the maximum length of storage, and identifying the production quality.

Aleatory uncertainty and scale effects in computational damage models for failure and fragmentation

SummaryStress concentrations near grain boundaries, precipitates, and similar micro‐heterogeneities nucleate instabilities leading to macroscale fracture. As it is not practical to model each flaw explicitly, their ensemble effect is modeled statistically. Accounting for this aleatory uncertainty requires smaller specimens (e.g., small finite elements) to have generally higher and more variable strengths, which is necessary for the initial failure probability of a finite domain to be unaffected by its discretization into elements. Localization itself, which might be attributed to constitutive instability, requires realistic numerical perturbations to predict bifurcations such as radial cracking in axisymmetric problems. These perturbations, stemming from microscale heterogeneity, are incorporated in simulations by imposing statistical spatial variability in the parameters of an otherwise conventional (deterministic and scale‐independent) damage model. This approach is attractive for its algorithmic simplicity and straightforward calibration from standard strength tests. In addition, it results in virtually no loss of efficiency or robustness relative to deterministic models and accommodates general three‐dimensional loading. Despite these advantages, some significant challenges remain and are discussed. However, it is demonstrated that including aleatory uncertainty with associated scale effects significantly improves predictiveness on large‐scale computational domains, where it is impractical to resolve each crack or localization zone.Copyright © 2014 John Wiley & Sons, Ltd.

Analysis of pressure relief valve proof test data

AbstractThis article reports on our statistical analysis of pressure relief valve (PRV) proof test data for the failure mode, fail‐to‐open, i.e., the PRV remains closed when actual pressure reaches or exceeds 150% of set pressure. Three data sets, from two Fortune 500 operating companies, which met the intent of the quality assurance of proof test data as documented by the Center for Chemical Process Safety Process Equipment Reliability Database (CCPS PERD)1 initiative, were analyzed. Although the original intent of our analysis focused solely on estimating the failure rate during the “useful life”2 of the equipment, it became apparent that the probability of failure on initial installation or reinstallation after proof test, and the need to address what constituted end of useful life were very significant. This article provides three important findings that are summarized as follows: The statistical analysis of each data set predicted a 1–1.6% probability of initial failure where initial failure is understood to be at the time of initial installation or reinstallation after a proof test. This implies that most of the failures found during the useful life via proof test are pre‐existing failures from the time of installation or reinstallation rather than failures that occurred randomly after installation or reinstallation of the PRV. Our calculations, based on the three independent data sets, led to consistent estimates of PRV useful‐life failure rates between 10−8 and 10−7 failures/h. Additionally, we compared our estimates from data analysis to the prediction of useful‐life failure rate for a particular PRV model using the Failure Modes Effects and Diagnostics Analysis (FMEDA) method. The prediction was consistent with the data estimates. The data further indicated that the low useful‐life failure rate was not supported beyond a 4–5 year proof test interval as the threshold of wear‐out seemed to be approached. The importance of these finding cannot be overestimated. When taking credit for a PRV in a risk assessment and in calculating the probability of failure on demand, both the initial probability of failing to open, as well as the probability of PRV failure due to the useful‐life failure rate, must be taken into account (the article discusses how to do this). Even then, the results are only defensible when it can be demonstrated that the proof test occurs before wear‐out (i.e., end of useful life) begins. © 2009 American Institute of Chemical Engineers Process Saf Prog, 2009

A progressive damage model for unidirectional fibre-reinforced composites based on fibre fragmentation. Part II: Stiffness reduction in environment sensitive fibres under fatigue

The mechanical behaviour of glass–fibre composites under fatigue or under long term stress is strongly influenced by the stress corrosion cracking of the fibres. In this paper, a stress corrosion model for composite materials reinforced with environment sensitive fibres has been developed and incorporated into a progressive damage model. The model is based on the definition of an effective stress, σ*( t), which depends on the stress story, that permits the initial failure probability, given by a Weibull distribution, to be used at any later time. This methodology has been incorporated to a thermodynamically consistent constitutive model valid for early fragmentation stages. The model may be used to account for the fibre’s behaviour in numerical models based on the rule of mixtures. The ability of the extended progressive damage model to reproduce the stiffness loss of the composite under static or cyclic fatigue loads is demonstrated.

Analytical probabilistic modeling of initial failure and reliability of laminated composite structures

An analytical approach based on the theory of stochastic processes is developed for the stochastic initial failure analysis and reliability predictions of thin-walled laminated composite structures. The probability of initial failure is calculated using theory of rare passages of the random strain vector field out of the prescribed region of allowable states. The region is limited by the ultimate strain surfaces adopted for each individual layer in the laminate. The surfaces, in their turn, are defined in terms of the scatters in the ultimate strains for the composite layer. Reliability function of a composite layer having random elastic characteristics and loaded with random in-plane tractions is determined through the probability of its initial failure. The reliability function of the laminated composite structure is then calculated through the failure probabilities of individual layers, using the weakest link model. The proposed approach allows one to solve diverse stochastic problems and requires substantially less computational expenses than Monte Carlo simulation technique. The approach may be invaluable for a quick evaluation of various competitive design projects when considering laminated composite structures under the reliability constraint. Applications of the developed approach are illustrated on the examples of reliability predictions of laminated composite cylindrical shells under the effect of random internal pressure and laminated composite plates under random biaxial loading. Numerical results reveal specific probabilistic phenomena related to the effects of ply lay-up, scatters in mechanical and strength characteristics and random loading histories. Results obtained from the developed analytical approach are compared to those calculated with Monte Carlo simulation technique.

A model of storage reliability with possible initial failures

Abstract Recently, storage reliability has attracted attention because of the increasing demand for high reliability of products in storage in both military and commercial industries. In this paper we study a general storage reliability model for the analysis of storage failure data. It is indicated that the initial failures, which are usually neglected, should be incorporated in the estimation of storage failure probability. Data from the reliability testing before and during the storage should be combined to give more accurate estimates of both initial failure probability and the probability of storage failures. The results are also useful for decision-making concerning the amount of testing to be carried out before storage. A numerical example is also given to illustrate the idea.

An optimal choice problem for a set of checking procedures

An item having a known initial failure probability is to be controlled by some out of a finite set of possible checks. Every check costs a certain amount of money, and budget constraints must be met. A check is characterized by the probabilities of three events: (i) letting a workable item pass, (ii) overlooking a failure if one is present, (iii) introducing a failure into a workable item. We show how any subset of checks to be employed is ordered optimally, and how the optimal subsequence of checks depends on the initial failure probability and oil the budget constraint.