The design of reliability data bases, part I: review of standard design concepts

Main styles in the design of reliability data banks (RDB's) are reviewed. The conceptual and mathematical tools underlying these designs are summarized. A key point is the method for assessing failure rates for competing failure modes. The theory of independent competing risk and the relation to colored Poisson processes is explained. The notions of observed and naked failure rates are defined, and their equivalence under the assumption of independence is shown. In conclusion, the needs of different users are compared with the information currently offered.     

Common cause failure prediction using data mapping

To estimate power plant reliability, a probabilistic safety assessment might combine failure data from various sites. Because dependent failures are a critical concern in the nuclear industry, combining failure data from component groups of different sizes is a challenging problem. One procedure, called data mapping, translates failure data across component group sizes. This includes common cause failures, which are simultaneous failure events of two or more components in a group. In this paper, we present a framework for predicting future plant reliability using mapped common cause failure data. The prediction technique is motivated by discrete failure data from emergency diesel generators at US plants. The underlying failure distributions are based on homogeneous Poisson processes. Both Bayesian and frequentist prediction methods are presented, and if non-informative prior distributions are applied, the upper prediction bounds for the generators are the same.     

The analysis of failure data in the presence of critical and degraded failures

Reported failures are often classified into severityclasses, e.g., as critical or degraded. The critical failures correspond to loss of function(s) and are those of main concern. The rate of critical failures is usually estimated by the number of observed critical failures divided by the exposure time, thus ignoring the observed degraded failures. In the present paper failure data are analyzed, applying an alternative estimate for the critical failure rate, also taking the number of observed degraded failures into account. The model includes two alternative failure mechanisms, one being of the shock type, immediately leading to a critical failure, another resulting in a gradual deterioration, leading to a degraded failure before the critical failure occurs. Failure data on safety valves from the OREDA (Offshore REliability DAta) data base are analyzed using this model. The estimate for the critical failure rate is obtained and compared with the standard estimate.     

Likelihood-based inference for a frailty-copula model based on competing risks failure time data

A competing risks phenomenon arises in industrial life tests, where multiple types of failure determine the working duration of a unit. To model dependence among marginal failure times, copula models and frailty models have been developed for competing risks failure time data. In this paper, we propose a frailty-copula model, which is a hybrid model including both a frailty term (for heterogeneity among units) and a copula function (for dependence between failure times). We focus on models that are useful to investigate the reliability of marginal failure times that are Weibull distributed. Furthermore, we develop likelihood-based inference methods based on competing risks data, including accelerated failure time models. We also develop a model-diagnostic procedure to assess the adequacy of the proposed model to a given dataset. Simulations are conducted to demonstrate the operational performance of the proposed methods, and a real dataset is analyzed for illustration. We make an R package “gammaGumbel” such that users can apply the suggested statistical methods to their data.     

A Dependent Competing Risks Model for Technological Units Subject to Degradation Phenomena and Catastrophic Failures

This paper proposes a dependent competing risks model for the reliability analysis of technological units that are subject both to degradation phenomena and to catastrophic failures. The paper is mainly addressed to the reanalysis of real data presented in a previous work, which refer to some electronic devices subject to two failure modes, namely the light intensity degradation and the solder/Cu pad interface fracture, which in previous papers, were considered independent. The main reliability characteristics of the devices, such as the probability density functions, the cause‐specific cumulative distribution function and hazard rate of each failure mode in the presence of both modes, are estimated. Likewise, the fraction of failures caused by each failure mode during the whole life of the devices or their residual life is derived. Finally, the results obtained under the proposed dependent competing risks model are compared to those obtained in previous papers. Copyright © 2015 John Wiley & Sons, Ltd.     

Utility based maintenance analysis using a Random Sign censoring model

Industrial systems subject to failures are usually inspected when there are evident signs of an imminent failure. Maintenance is therefore performed at a random time, somehow dependent on the failure mechanism. A competing risk model, namely a Random Sign model, is considered to relate failure and maintenance times. We propose a novel Bayesian analysis of the model and apply it to actual data from a water pump in an oil refinery. The design of an optimal maintenance policy is then discussed under a formal decision theoretic approach, analyzing the goodness of the current maintenance policy and making decisions about the optimal maintenance time.     

Statistical inference on accelerated life testing with dependent competing failure model under progressively type-II censored data based on copula theory

In this paper, we discuss the statistical analysis of a constant-stress accelerated dependent competing failure model under progressively type-II censoring based on a copula function. The dependence structure of lifetimes is constructed when the copula is a bivariate Clayton copula. The maximum likelihood estimations (MLEs) of the model parameters are derived. We also get the coverage probability of the 95% confidence intervals of the parameters based on MLEs and bootstrap confidence intervals. Finally, a real data set of some insulation system for electric motors was demonstrated for illustrative purpose.     

Application of modern reliability database techniques to military system data

This paper focuses on analysis techniques of modern reliability databases, with an application to military system data. The analysis of military system data base consists of the following steps: clean the data and perform operation on it in order to obtain good estimators; present simple plots of data; analyze the data with statistical and probabilistic methods. Each step is dealt with separately and the main results are presented.Competing risks theory is advocated as the mathematical support for the analysis. The general framework of competing risks theory is presented together with simple independent and dependent competing risks models available in literature. These models are used to identify the reliability and maintenance indicators required by the operating personnel. Model selection is based on graphical interpretation of plotted data.     

Reliability modeling for competing failure processes considering degradation rate variation under cumulative shock

Most systems experience both random shocks (hard failure) and performance degradation (soft failure) during service span, and the dependence of the two competing failure processes has become a key issue. In this study, a novel dependent competing failure processes (DCFPs) model with a varying degradation rate is proposed. The comprehensive impact of random shocks, especially the effect of cumulative shock, is reasonably considered. Specifically, a shock will cause an abrupt degradation damage, and when the cumulative shock reaches a predefined threshold, the degradation rate will change. An analytical reliability solution is derived under the concept of first hitting time (FHT). Besides, a one-step maximum likelihood estimation method is established by constructing a comprehensive likelihood function. Finally, the reasonability of the closed form reliability solution and the feasibility and effectiveness of the proposed DCFPs modeling methodology are demonstrated by a comparative simulation study.     

System reliability prediction based on historical data

This paper describes the development and implementation of a computerized reliability prediction model at the IBM facility located in Research Triangle Park, North Carolina. Through the analysis of historical life-test data, the model provides maximum likelihood estimates of the assumed Weibull life distributions of various types of components. The resulting component life distribution estimates are used to predict the reliability of new system configurations. This approach is based upon the well-known theory of competing risks. Our model, however, is unique in that it allows for the analysis of a pooled set of life data, i.e. life data from different types of systems, to obtain component estimates. This feature greatly generalizes the competing risks framework and hence offers advantages over the more traditional approach. We present the model and discuss various issues that were found to be critical to its successful implementation at IBM.     

Analysis of OREDA data for maintenance optimisation

This paper provides estimates for the average rate of occurrence of failures, ROCOF (“failure rate”), for critical failures when also degraded failures are present. The estimation approach is exemplified with a data set from the offshore equipment reliability database “OREDA”. The suggested modelling provides a means of predicting how maintenance tasks will affect the rate of critical failures.     

Using higher-level failure data in fault tree quantification

This paper presents a Bayesian method which can simultaneously combine basic event and statistically independent higher event-level failure data in fault tree quantification. Such higher-level data could correspond to train, subsystem or system failure events. In fact, because highest-level data are usually available for existing facilities, the method presented here allows such data to be propagated to lower levels. The method has two stages: (1) a top-down propagation scheme which allocates the higher event-level information to the basic events, at a cost of making them dependent; and (2) a scheme for sampling the probabilities of the dependent basic events. A simple example illustrates the performance of the method.     

A competing risk model for the reliability of cylinder liners in marine Diesel engines

In this paper, a competing risk model is proposed to describe the reliability of the cylinder liners of a marine Diesel engine. Cylinder liners presents two dominant failure modes: wear degradation and thermal cracking. The wear process is described through a stochastic process, whereas the failure time due to the thermal cracking is described by the Weibull distribution. The use of the proposed model allows performing goodness-of-fit test and parameters estimation on the basis of both wear and failure data. Moreover, it enables reliability estimates of the state of the liners to be obtained and the hierarchy of the failure mechanisms to be determined for any given age and wear level of the liner. The model has been applied to a real data set: 33 cylinder liners of Sulzer RTA 58 engines, which equip twin ships of the Grimaldi Group. Estimates of the liner reliability and of other quantities of interest under the competing risk model are obtained, as well as the conditional failure probability and mean residual lifetime, given the survival age and the accumulated wear. Furthermore, the model has been used to estimate the probability that a liner fails due to one of the failure modes when both of these modes act.     

Score tests for independence in parametric competing risks models

A popular model for competing risks postulates the existence of a latent unobserved failure time for each risk. Assuming that these underlying failure times are independent is attractive since it allows standard statistical tools for right-censored lifetime data to be used in the analysis. This paper proposes simple independence score tests for the validity of this assumption when parametric regression models are used to model the individual risks. The score tests are derived for the alternatives that specify that copulas are responsible for a possible dependency between competing risks. The test statistics are functions of the Cox and Snell residuals. A variance estimator is derived by writing the score function and the Fisher information matrix for the marginal models as stochastic integrals. A simulation study and a numerical example illustrate the methodology proposed in this paper.      

Individual driver risk assessment using naturalistic driving data

Driving risk varies substantially among drivers. Identifying and predicting high-risk drivers will greatly benefit the development of proactive driver education programs and safety countermeasures. The objective of this study is twofold: (1) to identify factors associated with individual driver risk and (2) predict high-risk drivers using demographic, personality, and driving characteristic data. The 100-Car Naturalistic Driving Study was used for methodology development and application. A negative binomial regression model was adopted to identify significant risk factors. The results indicated that the driver's age, personality, and critical incident rate had significant impacts on crash and near-crash risk. For the second objective, drivers were classified into three risk groups based on crash and near-crash rate using a K-mean cluster method. The cluster analysis identified approximately 6% of drivers as high-risk drivers, with average crash and near-crash (CNC) rate of 3.95 per 1000 miles traveled, 12% of drivers as moderate-risk drivers (average CNC rate = 1.75), and 84% of drivers as low-risk drivers (average CNC rate = 0.39). Two logistic models were developed to predict the high- and moderate-risk drivers. Both models showed high predictive powers with area under the curve values of 0.938 and 0.930 for the receiver operating characteristic curves. This study concluded that crash and near-crash risk for individual drivers is associated with critical incident rate, demographic, and personality characteristics. Furthermore, the critical incident rate is an effective predictor for high-risk drivers.     

Simulation of craze failure in a glassy polymer: rate dependent drawing and rate dependent failure models

The failure of a craze ahead of a crack growing under steady state conditions in a glassy polymer is investigated by modeling the craze microstructure using a highly anisotropic network of springs. A rate dependent drawing law is used to determine the shape of the craze-bulk interface. Approximate analytical results are developed to link the normal stress on the craze-bulk interface, the thickness of the craze and the far field stress intensity factor to the crack propagating velocity, through the craze failure criterion and the craze microstructural parameters. The accuracy of the analytical results is examined using a detailed numerical simulation. Our analysis shows that the rate independent craze failure criterion, which assumes the failure stress for fibrils ahead of the crack tip to be a material constant independent of the crack growth rate, leads to predictions of the dependence of the craze thickness and the fracture toughness on crack growth rate that are contrary to what is found experimentally. Rate dependent craze failure criteria are then proposed. Specifically, we study a case where the crack tip fibril breaks down by rate dependent chain scission and a case where the crack tip fibril fails by rate dependent chain disentanglement. For the rate dependent chain scission criterion, the results given by the rate independent constant failure stress criterion are retrieved in the limit of low crack propagation velocity. Also, there exists a critical stress intensity factor below which steady state crack propagation is impossible, i.e., crack growth becomes unstable.     

A new combinatorial model for deterministic competing failure analysis

Components in many engineering and industrial systems can experience propagated failures, which not only cause the failure of the component itself but also affect other components, causing extensive damage to the entire system. However, in systems with functional dependence behavior where failure of a trigger component may cause other components (referred to as dependent components) to become unusable or inaccessible, failure propagation originating from a dependent component could be isolated if the corresponding trigger component fails first. Thus, a time-domain competition exists between the failure propagation effect and the failure isolation effect, which poses a great challenge to the system reliability modeling and analysis. In this work, a new combinatorial model called competing binary decision diagram (CBDD) is proposed for the reliability analysis of systems subject to the competing failure behavior. In particular, special Boolean algebra rules and logic manipulation rules are developed for system CBDD model generation. The corresponding evaluation algorithm for the constructed CBDD model is also proposed. The proposed CBDD modeling method has no limitation on the type of component time-to-failure distributions. A memory system example and a network example are provided to demonstrate the application of the proposed model and algorithms. Correctness of the proposed method is verified using the Markov method.     

Database development and uncertainty treatment for estimating pipe failure rates and rupture frequencies

Estimates of failure rates for nuclear power plant piping systems are important inputs to Probabilistic Risk Assessments (PRA) and risk informed applications of PRA. Such estimates are needed for initiating event frequencies for Loss of Coolant Accidents and internal flooding events and for risk informed evaluations of piping system in-service inspection programs. A critical issue in the estimation of these parameters is the treatment of uncertainties, which can exceed an order of magnitude deviation from failure rate point estimates. Sources of uncertainty include failure data reporting issues, scarcity of data, poorly characterized component populations, and uncertainties about the physical characteristics of the failure mechanisms and root causes. A methodology for quantifying these uncertainties using a Bayes' uncertainty analysis method was developed for the EPRI risk informed in-service inspection program and significantly enhanced in subsequent applications. In parallel with these efforts, progress has been made in the development of pipe failure databases that contain the quantity and quality of information needed to support piping system reliability evaluations. Examples are used in this paper to identify technical issues with previous published estimates of pipe failure rates and the numerical impacts of these issues on the pipe failure rates and rupture frequencies are quantified.     

基于比例危险模型的产品竞争失效分析

突发型失效与退化型失效共存的竞争失效问题在实践中大量存在，一般情况下突发失效是受退化量大小影响的。文中利用比例危险模型分析了突发失效与退化量的关系，给出了竞争失效的一般模型及模型的参数估计方法，最后利用所给模型对强激光装置所用的金属化膜脉冲电容器进行了可靠性分析。     

Comparison of roadside crash injury metrics using event data recorders

The occupant impact velocity (OIV) and acceleration severity index (ASI) are competing measures of crash severity used to assess occupant injury risk in full-scale crash tests involving roadside safety hardware, e.g. guardrail. Delta-V, or the maximum change in vehicle velocity, is the traditional metric of crash severity for real world crashes. This study compares the ability of the OIV, ASI, and delta-V to discriminate between serious and non-serious occupant injury in real world frontal collisions. Vehicle kinematics data from event data recorders (EDRs) were matched with detailed occupant injury information for 180 real world crashes. Cumulative probability of injury risk curves were generated using binary logistic regression for belted and unbelted data subsets. By comparing the available fit statistics and performing a separate ROC curve analysis, the more computationally intensive OIV and ASI were found to offer no significant predictive advantage over the simpler delta-V.