Bayesian Reliability Assessment Research Articles

Copula‐based Bayesian reliability assessment for series systems

AbstractBayesian reliability assessment plays an integral role in determining the success of product development and deployment into the market, especially when limited information is available to estimate the reliability of products. Nevertheless, the Bayesian reliability approach has untapped research potential when it is used to evaluate systems consisting of dependent components, that is, a situation that reflects real‐world conditions. This study addresses the research gap by applying a copula to encode the dependency structure between the failure rates of the components, particularly for the simple series systems. Unfortunately, this study found that Bayesian aggregation error still occurs when information is used at different levels. By employing Monte Carlo simulation and classification tree learning, this study also investigates the key factors affecting such error over a wide range of possible scenarios and derives useful guidelines for reliability practitioners so that they can choose a more suitable analysis under certain circumstances.

Bayesian Reliability Assessment of Permanent Magnet Brake Under Small Sample Size

Bayesian Reliability Assessment of Permanent Magnet Brake Under Small Sample Size

Fuzzy Bayesian Estimation of Linear (Circular) Consecutive k-out-of-n: F System Reliability

The consecutive k-out-of-n: F structure is broadly applicable in industrial and military frameworks. Without lifetime information about the entire design, it is appealing to use fuzzy earlier beliefs on its segments. In this paper the fuzzy Bayesian reliability assessment of the linear (circular) consecutive k-out-of-n: F system is proposed under the squared error loss function. The parameters are known as fuzzy random variables in the process of obtaining fuzzy Bayesian reliability. The conventional strategy for estimating Bayesian reliability will be utilized to construct the fuzzy Bayesian point estimator of the proposed system by applying the Resolution Identity theorem. A comparative study of the derived result with the literature is presented.
 HIGHLIGHTS
 
 Reliability Estimate of Consecutive k-out-of-n: F system
 Parameters are known as fuzzy random variables
 Applied Resolution Identity Theorem to estimate fuzzy Bayesian reliability
 Fuzzy Bayesian system reliability is calculated
 Fuzzy mean time to failure is calculated
 
 GRAPHICAL ABSTRACT

Research on Reliability Assessment Method of Emergency Escape Parachute

Aiming at the problem that emergency escape parachute cannot meet the requirements of the index using the binomial evaluation method, combined with the characteristics of emergency escape parachute products, comprehensively using emergency escape parachute components and system test data, the emergency escape parachute Bayesian reliability assessment method is proposed to solve the problem of reliability assessment in the case of small sample size of emergency escape parachute system test, which effectively reducing emergency escape parachute test expenses and development cycle.

Bayesian reliability assessment and degradation modeling with calibrations and random failure threshold

A degradation model with a random failure threshold is presented for the assessment of reliability by the Bayesian approach. This model is different from others in that the degradation process is proceeding under pre-specified periodical calibrations. And here a random threshold distribution instead of a constant threshold which is difficult to determine in practice is used. The system reliability is defined as the probability that the degradation signals do not exceed the random threshold. Based on the posterior distribution estimates of degradation performance, two models for Bayesian reliability assessments are presented in terms of the degradation performance and the distribution of random failure threshold. The methods proposed in this paper are very useful and practical for multi-stage system with uncertain failure threshold. This study perfects the degradation modeling approaches and plays an important role in the remaining useful life estimation and maintenance decision making.

The Bayesian Reliability Assessment and Prediction for Radar System Based on New Dirichlet Prior Distribution

This article studies on Bayesian reliability growth models of complex system based on new Dirichlet prior distribution when the sample of system is small. The model briefly describes expert experience as uniform distribution, then equivalent general Beta distribution of uniform distribution can be solved by optimization method when prior parameters are variables, mean is constraint condition, and variance is regarding as the optimization objective. The optimization method solves the problem of how to determine values of hyper-parameters of new Dirichlet distribution when these parameters have no specific physical meaning. Because the multidimensional numerical integration of posterior distribution is very difficult to calculate, WinBUGS software is employed to establish Bayesian reliability growth model based on a new Dirichlet prior distribution, and two practical cases are studied under this model in order to prove validity of model. The analysis results show that the model can improve the precision of calculation, and it is easy to use in engineering.

Hierarchical Bayesian reliability assessment of energy networks

It is often the case that data used for the systems reliability assessment comes from more than one information source. Whether they are power plants at different geographical locations, gas transmission pipelines operating in different environment or power transmission networks deployed within various areas. Therefore, different operating conditions, varying maintenance programs and efficiencies have its share in influencing the vulnerability and variability of reliability data. However, in practice it is usually the case that this heterogeneity is neglected leading to the underestimation of underlying uncertainty of the data. Bayesian models are capable of dealing with this kind of uncertainty as opposedto the frequentists statistical methods. Hierarchical Bayesian modelling technique provides means to quantify not only within-source, but also between-source uncertainties. Even in the case of small data samples it performs well, unlike for example the classical likelihood method which may provide degenerate estimates. In this paper authors investigate the possibility to incorporate this kind of uncertainty into the systems reliability and vulnerability assessment through the Bayesian framework in several cases: gas transmission networks and power transmission grids.

Bayesian reliability modeling and assessment solution for NC machine tools under small-sample data

Although Markov chain Monte Carlo(MCMC) algorithms are accurate, many factors may cause instability when they are utilized in reliability analysis; such instability makes these algorithms unsuitable for widespread engineering applications. Thus, a reliability modeling and assessment solution aimed at small-sample data of numerical control(NC) machine tools is proposed on the basis of Bayes theories. An expert-judgment process of fusing multi-source prior information is developed to obtain the Weibull parameters’ prior distributions and reduce the subjective bias of usual expert-judgment methods. The grid approximation method is applied to two-parameter Weibull distribution to derive the formulas for the parameters’ posterior distributions and solve the calculation difficulty of high-dimensional integration. The method is then applied to the real data of a type of NC machine tool to implement a reliability assessment and obtain the mean time between failures(MTBF). The relative error of the proposed method is 5.8020×10-4 compared with the MTBF obtained by the MCMC algorithm. This result indicates that the proposed method is as accurate as MCMC. The newly developed solution for reliability modeling and assessment of NC machine tools under small-sample data is easy, practical, and highly suitable for widespread application in the engineering field; in addition, the solution does not reduce accuracy.

Bayesian Reliability and Performance Assessment for Multi-State Systems

This paper develops a Bayesian framework to assess the reliability and performance of multi-state systems (MSSs). An MSS consists of multiple multi-state components of which the degradation follows a Markov process. Due to the lack of sufficient data, and only vague knowledge from experts, the transition intensities of multi-state components between any pair of states and the state probabilities cannot be precisely estimated. The proposed Bayesian method can merge prior knowledge from experts' judgments with continuous and discontinuous inspection data to obtain posterior distributions of transition intensities. A simulation method embedded with the universal generating function (UGF) is developed to estimate the posterior state probabilities, the reliability, and the performance of the entire MSS. Two numerical experiments are presented to demonstrate the effectiveness of the proposed method.

Bayesian System Reliability Assessment Method with Maximum Entropy as Prior Distribution

Bayesian system reliability assessment method with maximum entropy as prior distribution is developed in the present analysis. The system reliability assessment model is established, and the method and process of system reliability assessment are put forward. The method is based on the theory of information entropy. The probability density function and distribution function of system reliability parameters are given by using maximum entropy method. Prior distribution of Bayesian analysis method is the distribution function. Likelihood function is given by a small amount of field test data. According to Bayesian methods, posterior distribution is determined by using prior distribution and likelihood function. The point estimation and interval estimation of system reliability parameters are calculated in order to evaluate the system reliability. The method solves better the problem of system reliability assessment for small sample cases, and is an optimum method for reliability assessment of large and complex systems.

Bayesian reliability assessment of legacy safety-critical systems upgraded with fault-tolerant off-the-shelf software

This paper presents a new way of applying Bayesian assessment to systems, which consist of many components. Full Bayesian inference with such systems is problematic, because it is computationally hard and, far more seriously, one needs to specify a multivariate prior distribution with many counterintuitive dependencies between the probabilities of component failures. The approach taken here is one of decomposition. The system is decomposed into partial views of the systems or part thereof with different degrees of detail and then a mechanism of propagating the knowledge obtained with the more refined views back to the coarser views is applied (recalibration of coarse models). The paper describes the recalibration technique and then evaluates the accuracy of recalibrated models numerically on contrived examples using two techniques: u-plot and prequential likelihood, developed by others for software reliability growth models. The results indicate that the recalibrated predictions are often more accurate than the predictions obtained with the less detailed models, although this is not guaranteed. The techniques used to assess the accuracy of the predictions are accurate enough for one to be able to choose the model giving the most accurate prediction.

Study on Assessment Method of Reliability of Spaceflight Electronic Device

建立了一种综合利用航天电子设备分系统可靠性信息和试验数据以及整机系统试验数据的Bayes可靠性评估方法. 该方法利用最大熵方法融合分系统可靠性信息, 推导了从分系统可靠性矩到系统可靠性矩的计算公式, 然后建立了基于继承因子<I>ρ</I>的混合<I>β</I>先验分布, 结合整机系统试验数据确定后验分布, 最后, 基于后验分布推断航天电子设备可靠性. 采用该方法对航天电子设备可靠性进行了评估, 当整机系统试验数据为240次时, 航天电子设备在置信水平0.70的情况下可靠度可达到0.9991, 所要求的整机系统试验次数比经典方法约降低了4/5.

Optimal preventive maintenance policy under fuzzy Bayesian reliability assessment environments

Reliability assessment is an important issue in reliability engineering. Classical reliability-estimating methods are based on precise (also called “crisp”) lifetime data. It is usually assumed that the observed lifetime data take precise real numbers. Due to the lack, inaccuracy, and fluctuation of data, some collected lifetime data may be in the form of fuzzy values. Therefore, it is necessary to characterize estimation methods along a continuum that ranges from crisp to fuzzy. Bayesian methods have proved to be very useful for small data samples. There is limited literature on Bayesian reliability estimation based on fuzzy reliability data. Most reported studies in this area deal with single-parameter lifetime distributions. This article, however, proposes a new method for determining the membership functions of parameter estimates and the reliability functions of multi-parameter lifetime distributions. Also, a preventive maintenance policy is formulated using a fuzzy reliability framework. An artificial neural network is used for parameter estimation, reliability prediction, and evaluation of the expected maintenance cost. A genetic algorithm is used to find the boundary values for the membership function of the estimate of interest at any cut level. The long-run fuzzy expected replacement cost per unit time is calculated under different preventive maintenance policies, and the optimal preventive replacement interval is determined using the fuzzy decision making (ordering) methods. The effectiveness of the proposed method is illustrated using the two-parameter Weibull distribution. Finally, a preventive maintenance strategy for a power generator is presented to illustrate the proposed models and algorithms.

Bayesian Reliability Assessment Based on Dirichlet Prior Information

To resolve the reliability assessment of the large-sized complex products under small samples, with the aid of the Dirichlet prior distribution and Bayesian theory, a new method is proposed in this paper. The method can fully apply Dirichlet prior information and test data to estimate the reliabilities of the products, and forecasting the success times during the products test. Compared other methods, it is simple, direct, solid, and high-effective. The investigations show that the method is quit handy and effective.

Fully Bayesian reliability assessment of multi-state systems with overlapping data

The failure data at the system level are often limited,resulting in high uncertainty to system reliability assessment. Integrating data drawn from various structural levels of the target system (e.g. the system, subsystems, assemblies and components),i.e. the multi-level data, through Bayesian analysis can improve the precision of system reliability assessment. However, if the multi-level data are overlapping, it is challenging for Bayesian integration to develop the likelihood function. Especially for multistate systems (MSS), the Bayesian integration with overlapping data is even more difficult. The major disadvantage of previous approaches is the intensive computation for the development of the likelihood function caused by the workload to opt the appropriate combinations of the vectors of component states consistent with the overlapping data. An improved fully Bayesian integration approach from a geometric perspective is proposed for the reliability assessment of MSS with overlapping data. In this method, a specific combination of component states is regarded as a state vector, which leads to a specific system state of the MSS, and all state vectors generate a system state space. The overlapping data are regarded as the constraints which create hyperplanes in the system state space. And a point in a hyperplane corresponds to a particular combination of the state vectors. In the light of the features of the constraints, the proposed approach introduces space partition and hyperplane segmentation, which reduces the selection workload significantly and simplifies the likelihood function for overlapping data. Two examples demonstrate the feasibility and efficiency of the proposed approach.

Bayesian Reliability Assessment and Prediction During Product Development

A Bayesian reliability growth model of diverse populations based on the new Dirichlet prior distribution is studied.Aiming at some history and expert information during the development of a weapon,a Bayesian reliability growth model is presented based on the new Dirichlet distribution.Bayesian point assessment and confidence lower limit on product reliability at current stage are inputted by comprehensively making use of prior information and field test information at every stage.The method for determining prior distribution parameters is given by using the method,it is easy to confirm the parameters of prior distribution,it solves the problem of how to verify the hyper parameters of the new Dirichlet prior distribution in view of unclear physical meaning of these parameters.It solves the problem that the interference on parameters of Bayesian poster higher dimensions cannot be calculated indirectly.Then,the Gibbs sampling algorithm is used to compute the posterior inference.The Bayesian estimators and Bayesian lower bound are gained for the reliability of every stage.Furthermore,based on the test data,the model can be used to predict the product reliability,which extends the application range of the model.The analysis result of practical cases shows that the parameters of the Bayesian model have clear and definite meaning and are convenient to use for engineering applications.

Bayesian reliability assessment of repairable systems during multi-stage development programs

New repairable systems are generally subjected to development programs in order to improve system reliability before starting mass production. This paper proposes a Bayesian approach to analyze failure data from repairable systems undergoing a Test-Find-Test program. The system failure process in each testing stage is modeled using a Power-Law Process (PLP). Information on the effect of design modifications introduced into the system before starting a new testing stage is used, together with the posterior density of the PLP parameters at the current stage, to formalize the prior density at the beginning of the new stage. Contrary to the usual assumption, in this paper the PLP parameters are assumed to be dependent random variables. The system reliability is measured in terms of the number of failures that will occur in a batch of new units in a given time interval, for example the warranty period. A numerical example is presented to illustrate the proposed procedure.

Integrated Bayesian reliability assessment during equipment development

With the merit of Bayes’ theorem, this paper proposes an integrated Bayesian approach for reliability assessment during equipment development. By considering the prior information, this approach can provide useful information to use for decision‐making. A numerical example is given to illustrate the applicability of the proposed approach. It is believed that the proposed approach would be helpful for the project manager to focus attention on the key problems to resolve them early so as to ensure the greatest probability for project success.

Bayesian reliability assessment for discrete data—A case study

The ever-increasing reliability requirement and reduced programme schedules and budgets, particularly in the field of space research, make very real the problem of producing reliability assessments without a large volume of objective test data. In this paper, an attempt is made to utilize Bayesian statistics for reliability measurement of a complex system by combining prior information actual test data for each subsystem. Bayesian statistics, as applied herein, codes the information available from past experience into a prior probability distribution which is updated with test results as they became available. The study includes: 1. (i) Bayesian models for discrete data analysis; 2. (ii) application of the Monte Carlo simulation technique for convolving subsystem reliability distributions together in order to arrive at the overall system reliability and 3. (iii) implementation of the Bayesian reliability measurement programme for the evaluation of the reliability estimate of a typical system of the satellite launch vehicle.

Bayesian reliability assessment from test data : James E. Wolf. Proc. A. Reliability and Maintainability Symposium, Nevada, U.S.A. p. 411 (20–22 Jan. 1976)

In this study, we consider a flexible manufacturing cell (FMC) processing identical parts on which the loading and unloading of machines are made by a robot. The machines used in FMCs are predominantly CNC machines and these machines are flexible enough for performing several operations provided that the required tools are stored in their tool magazines. Traditional research in this area considers a flowshop type system. The current study relaxes this flowshop assumption which unnecessarily limits the number of alternatives. In traditional robotic cell scheduling literature, the processing time of each part on each machine is a known parameter. However, in this study the processing times of the parts on the machines are decision variables. Therefore, we investigated the productivity gain attained by the additional flexibility introduced by the FMCs. We propose new lower bounds for the 1-unit and 2-unit robot move cycles (for which we present a completely new procedure to derive the activity sequences of 2-unit cycles in a three-machine robotic cell) under the new problem domain for the flowshop type robot move cycles. We also propose a new robot move cycle which is a direct consequence of process and operational flexibility of CNC machines. We prove that this proposed cycle dominates all 2-unit robot move cycles and present the regions where the proposed cycle dominates all 1-unit cycles. We also present a worst case performance bound of using this proposed cycle.