A comparison of reliability estimation methods for binary systems

This paper uses a simulation-based approach to compare the predictive accuracy of five different methods for estimating the risk of failure for binary failure/no failure systems such as US strategic missiles, space launch vehicles, and security systems based on the results of a number of tests. This paper tests two Bayesian approaches, two classical (frequentist) approaches, and the method currently used the US Air Force Strategic Command (STRATCOM) to estimate the reliability of strategic nuclear missiles. First, test results are simulated based on an assumed underlying reliability profile. Then the system's reliability is estimated by each of the approaches using the simulated test results, and these estimates are compared with the assumed underlying reliability. Statistical procedures are used to compare the errors from the different methods. The results of this study show that the STRATCOM approach and a classical approach using only the test data from the current period are significantly less accurate than the other three methods and that the accuracy of the Bayesian methods depend on the prior density functions used. The results in this paper provide a quantitative assessment of the accuracy of the tested methods.     

Bayesian modeling and test planning for multiphase reliability assessment

We propose a Bayesian hierarchical model to assess the reliability of a family of vehicles, based on the development of the joint light tactical vehicle (JLTV). The proposed model effectively combines information across three phases of testing and across common vehicle components. The analysis yields estimates of failure rates for specific failure modes and vehicles as well as an overall estimate of the failure rate for the family of vehicles. We are also able to obtain estimates of how well vehicle modifications between test phases improve failure rates. In addition to using all data to improve on current assessments of reliability and reliability growth, we illustrate how to leverage the information learned from the three phases to determine appropriate specifications for subsequent testing that will demonstrate if the reliability meets a given reliability threshold.     

System-level load–strength interference based reliability modeling of k-out-of-n system

The issue of information loss in the process of system reliability modeling through conventional load–strength interference analysis is discussed first, and the reason why it is impossible to construct dependent system reliability model simply by means of component reliability index is demonstrated. Then, an approach to modeling the reliability of dependent system with common cause failure (CCF) is presented. The approach is based on system-level load–strength interference analysis and a concept of ‘conditional failure probability of component’ as well. With the opinion that load randomness is the direct cause of failure dependence, a discrete type system reliability model is developed via the conditional component failure probability concept. At last, the model's capabilities to estimate system reliability with CCF effect and to predict high multiplicity failure probability based on low multiplicity failure event data are proved.     

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.     

Prediction Limits for the Inverse Gaussian Distribution

Prediction intervals for the inverse Gaussian are obtained from both a frequentist and a Bayesian viewpoint. The frequentist intervals are obtained by constructing pivotals that have the x ² and F distributions. The method involves inversion of probability statements, which results in two-sided prediction intervals. A Bayesian predictive density is obtained using a vague prior, from which one- or two-sided Bayesian prediction intervals can be determined. An example for which Bayesian prediction limits are narrower than the frequentist is given.     

Integration of computation and testing for reliability estimation

This paper develops a methodology to integrate reliability testing and computational reliability analysis for product development. The presence of information uncertainty such as statistical uncertainty and modeling error is incorporated. The integration of testing and computation leads to a more cost-efficient estimation of failure probability and life distribution than the tests-only approach currently followed by the industry. A Bayesian procedure is proposed to quantify the modeling uncertainty using random parameters, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimates, by combining prior computational prediction and test data. Two kinds of tests — failure probability estimation and life estimation — are considered. The prior distribution and confidence interval of failure probability in both cases are estimated using computational reliability methods, and are updated using the results of tests performed during the product development phase.     

Bayesian models and ageing indicators for analysing random changes in failure occurrence

The paper introduces ageing models of repairable components based on Bayesian approach. Models for the development of both failure rate and the probability of failure on demand are presented. The models are based on the assumption that the failure probability or rate has random changes at certain time points. This is modelled by assuming that the successive transformed failure probabilities (or rates) follow a Gaussian random walk. The model is compared with a constant increment model, in which the possible ageing trend is monotone. Monte-Carlo Markov Chain sampling is applied in the determination of the posterior distributions. Ageing indicators based on the model parameters are introduced, and the application of these models is illustrated with case studies.     

An architectural model for software reliability quantification: sources of data

Software reliability assessment models in use today treat software as a monolithic block. An aversion towards ‘atomic' models seems to exist. These models appear to add complexity to the modeling, to the data collection and seem intrinsically difficult to generalize. In 1997, we introduced an architecturally based software reliability model called FASRE. The model is based on an architecture derived from the requirements which captures both functional and nonfunctional requirements and on a generic classification of functions, attributes and failure modes. The model focuses on evaluation of failure mode probabilities and uses a Bayesian quantification framework. Failure mode probabilities of functions and attributes are propagated to the system level using fault trees. It can incorporate any type of prior information such as results of developers' testing, historical information on a specific functionality and its attributes, and, is ideally suited for reusable software. By building an architecture and deriving its potential failure modes, the model forces early appraisal and understanding of the weaknesses of the software, allows reliability analysis of the structure of the system, provides assessments at a functional level as well as at a systems' level. In order to quantify the probability of failure (or the probability of success) of a specific element of our architecture, data are needed. The term element of the architecture is used here in its broadest sense to mean a single failure mode or a higher level of abstraction such as a function. The paper surveys the potential sources of software reliability data available during software development. Next the mechanisms for incorporating these sources of relevant data to the FASRE model are identified.     

Application of conditional robust calibration to ordinary differential equations models in computational systems biology: a comparison of two sampling strategies

Mathematical modelling is a widely used technique for describing the temporal behaviour of biological systems. One of the most challenging topics in computational systems biology is the calibration of non‐linear models; i.e. the estimation of their unknown parameters. The state‐of‐the‐art methods in this field are the frequentist and Bayesian approaches. For both of them, the performance and accuracy of results greatly depend on the sampling technique employed. Here, the authors test a novel Bayesian procedure for parameter estimation, called conditional robust calibration (CRC), comparing two different sampling techniques: uniform and logarithmic Latin hypercube sampling. CRC is an iterative algorithm based on parameter space sampling and on the estimation of parameter density functions. They apply CRC with both sampling strategies to the three ordinary differential equations (ODEs) models of increasing complexity. They obtain a more precise and reliable solution through logarithmically spaced samples.Inspec keywords: sampling methods, parameter estimation, Bayes methods, differential equations, iterative methodsOther keywords: CRC, parameter space sampling, parameter density functions, sampling strategies, ordinary differential equations models, logarithmically spaced samples, computational systems biology, mathematical modelling, temporal behaviour, biological systems, challenging topics, nonlinear models, unknown parameters, frequentist approaches, Bayesian approaches, sampling technique, novel Bayesian procedure, parameter estimation, called conditional robust calibration, different sampling techniques     

可靠性工程中参数的一种估计方法

提出了可靠性工程中参数的一种估计方法——新Bayes估计法，给出了失效概率、失效率的新Bayes估计的定义及其新Bayes估计。最后，结合实际问题的数据，进行了具体计算和分析，结果表明所提出的新Bayes估计法有效、可行，便于工程技术人员在工程中应用。     

Evaluation of operational system structures based on reliability data

Systems of components have a structure that plays an important role in determining how the reliability of the individual components relates to the reliability of the system. The system reliability can be computed from component reliabilities using results from basic probability theory in the simplest case with all of the components assumed to act independently of one another. However, in the case of dependence, such calculations can be much more involved. When reliability data have been independently collected on both the system and each component in the system, it can be difficult to model any possible dependence between components. Established methods use the known structure of a system, along with these data, to assess whether the reliability of the individual components are mutually independent. In this paper, we expand this methodology to include an assessment of the type of dependence that may exist between the components. This is based on finding the system structure that would most likely produce the observed reliability data, under independence. In the frequentist setting, the likelihood approach is used to find these structures and an observed confidence measure is used to assess the strength of the statistical evidence in favor of each possible structure. In the Bayesian setting, posterior probabilities along with Bayes factors are used. An example demonstrates how these methods can be used in an applied setting.     

钢框架结构基于变形可靠度的全概率抗震设计

我国抗震设计规范的抗震设计方法并不是真正意义上的概率极限状态设计,结构可靠度的应用也没有体现出结构的体系可靠度设计水平,因此该文提出了基于变形可靠度验算的二阶段抗震设计方法.该方法采用结构可靠度的数值模拟方法,通过验算小震作用下结构构件承载能力极限状态下的抗震可靠度,验算结构小震作用下正常使用极限状态下和大震作用下侧向...     

Probability matching priors for linear calibration

Summary In the linear calibration problem, a model is fit to paired observations arising from two measurement techniques, one known to be far more accurate (but also more expensive) than the other. The fitted model is then used with univariate observations from the less accurate technique to impute values from the more accurate one. The Bayesian paradigm emerges as attractive in this context, but the choice of an appropriate noninformative prior distribution has been controversial. In this paper we derive a class of such distributions, and provide sufficient conditions under which they lead to proper posterior densities. These priors, which we refer to asprobability matching priors, are designed to produce posterior credible intervals which are asymptotically identical to their frequentist counterparts. We provide details on the implementation of our procedure using sampling-based methods, and obtain significant simplifications over previous Bayesian approaches in this area. We compare the performance of several members of our prior class in the context of two illustrative examples.     

Practical reliability growth modeling

Reliability growth models are commonly used in the Department of Defense (DoD) to plan, track, and project reliability during system acquisition and testing. We describe two commonly used classes of reliability growth models for continuous failure time data and the metrics appropriate for their use. We also present two Bayesian reliability growth models that are based on the DoD models. The Bayesian models are easily interpretable in a statistical framework, which supports estimation and uncertainty quantification. Our goal is to provide a practical understanding of the development, implementation, and use of reliability growth models across a sequence of DoD testing events.     

The reliability physics approach to failure prediction modelling

Empirically based failure rate modelling methodologies employed in reliability prediction handbooks, and deterministic modelling methods are both critically examined using microelectronic packages as vehicles. As an alternative, a coupled mechano-stochastic approach to reliability prediction modelling is presented. The goal is to use physics of failure principles with appropriate failure probability density distributions to design for failure-free operation and predict failure times for components now available, as well as new components resulting from new materials, technologies and processes. In addition, an approach for extending the model to aid in logistics support analysis is discussed.     

Reliability estimation of a multicomponent stress-strength model for unit Gompertz distribution under progressive Type II censoring

We consider the problem of estimating multicomponent stress-strength (MSS) reliability under progressive Type II censoring when stress and strength variables follow unit Gompertz distributions with common scale parameter. We estimate MSS reliability under frequentist and Bayesian approaches. Bayes estimates are obtained by using Lindley approximation and Metropolis-Hastings algorithm methods. Further, we obtain uniformly minimum variance unbiased estimates of the reliability when common scale parameter is known. Asymptotic, bootstrap confidence interval and highest posterior density credible intervals have been constructed. We perform Monte Carlo simulations to compare the performance of proposed estimates and also present a discussion. Finally, three real data sets are analyzed for illustrative purposes.     

Automotive reliability inference based on past data and technical knowledge

The constantly increasing market requirements of high quality vehicles ask for the automotive manufacturers to carry out—before starting mass production—reliability demonstration tests on new products. However, due to cost and time limitation, a small number of copies of the new product are available for testing, so that, when the classical approach is used, a very low level of confidence in reliability estimation results in. In this paper, a Bayes procedure is proposed for making inference on the reliability of a new upgraded version of a mechanical component, by using both failure data relative to a previous version of the component and prior information on the effectiveness of design modifications introduced in the new version. The proposed procedure is then applied to a case study and its feasibility in supporting reliability estimation is illustrated.     

A model for Bayesian software reliability analysis

Two problems which are of great interest in relation to software reliability are the prediction of future times to failure and the calculation of the optimal release time. An important assumption in software reliability analysis is that the reliability grows whenever bugs are found and removed. In this paper we present a model for software reliability analysis using the Bayesian statistical approach in order to incorporate in the analysis prior assumptions such as the (decreasing) ordering in the assumed constant failure rates of prescribed intervals. We use as prior model the product of gamma functions for each pair of subsequent interval constant failure rates, considering as the location parameter of the first interval the failure rate of the following interval. In this way we include the failure rate ordering information. Using this approach sequentially, we predict the time to failure for the next failure using the previous information obtained. Using also the relevant predictive distributions obtained, we calculate the optimal release time for two different requirements of interest: (a) the probability of an in‐service failure in a prescribed time t; (b) the cost associated with a single or more failures in a prescribed time t. Finally a numerical example is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

First excursion probabilities for linear systems by very efficient importance sampling

An analytical study of the failure region of the first excursion reliability problem for linear dynamical systems subjected to Gaussian white noise excitation is carried out with a view to constructing a suitable importance sampling density for computing the first excursion failure probability. Central to the study are ‘elementary failure regions’, which are defined as the failure region in the load space corresponding to the failure of a particular output response at a particular instant. Each elementary failure region is completely characterized by its design point, which can be computed readily using impulse response functions of the system. It is noted that the complexity of the first excursion problem stems from the structure of the union of the elementary failure regions. One important consequence of this union structure is that, in addition to the global design point, a large number of neighboring design points are important in accounting for the failure probability. Using information from the analytical study, an importance sampling density is proposed. Numerical examples are presented, which demonstrate that the efficiency of using the proposed importance sampling density to calculate system reliability is remarkable.