Determination of burn‐in parameters and residual life for highly reliable products

Today, many products are designed and manufactured to function for a long period of time before they fail. Determining product reliability is a great challenge to manufacturers of highly reliable products with only a relatively short period of time available for internal life testing. In particular, it may be difficult to determine optimal burn‐in parameters and characterize the residual life distribution. A promising alternative is to use data on a quality characteristic (QC) whose degradation over time can be related to product failure. Typically, product failure corresponds to the first passage time of the degradation path beyond a critical value. If degradation paths can be modeled properly, one can predict failure time and determine the life distribution without actually observing failures. In this paper, we first use a Wiener process to describe the continuous degradation path of the quality characteristic of the product. A Wiener process allows nonconstant variance and nonzero correlation among data collected at different time points. We propose a decision rule for classifying a unit as normal or weak, and give an economic model for determining the optimal termination time and other parameters of a burn‐in test. Next, we propose a method for assessing the product's lifetime distribution of the passed units. The proposed methodologies are all based only on the product's initial observed degradation data. Finally, an example of an electronic product, namely contact image scanner (CIS), is used to illustrate the proposed procedure. © 2002 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Mean residual life of coherent systems consisting of multiple types of dependent components

Mean residual life is a useful dynamic characteristic to study reliability of a system. It has been widely considered in the literature not only for single unit systems but also for coherent systems. This article is concerned with the study of mean residual life for a coherent system that consists of multiple types of dependent components. In particular, the survival signature based generalized mixture representation is obtained for the survival function of a coherent system and it is used to evaluate the mean residual life function. Furthermore, two mean residual life functions under different conditional events on components’ lifetimes are also defined and studied.     

Signature based analysis of m‐Consecutive‐k‐out‐of‐n: F systems with exchangeable components

In this article, we study reliability properties of m‐consecutive‐k‐out‐of‐n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature‐based stochastic ordering results for the system's lifetime and investigate the IFR preservation property under the formulation of m‐consecutive‐k‐out‐of‐n: F systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A general approach to the shape of failure rate and MRL functions

Failure rate and mean residual life are two important characteristics for studying reliability of products. In literature, some work studied the shape of failure rate function based on the knowledge of the associated probability density function; some other work investigated the shape of mean residual life function based on the shape of the associated failure rate function separately for continuous case and discrete case. In this article, a general approach is developed which can be applied to the aforementioned studies. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Properties of a mean residual life function arising from renewal theory

The present article discusses the properties of the mean residual life function in a renewal process. We examine the relationship this function has with the failure rate function and the conventional mean, variance and coefficient of variation of residual life. We also discuss some monotonicity properties of the mean residual life function. A partial order based on the renewal mean residual function is introduced along with its interrelationship with some existing stochastic orders. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

残差GM（1，1）模型在恒加试验中的应用

介绍了目前恒加试验中,正常应力水平下特征寿命点估计的数据统计分析方法及其不足。针对恒加试验的特点和所需解决的问题,基于灰色预测理论的残差GM(1,1)模型,给出了一种新的求解方法。最后分别运用三种不同的方法对给出的应用实例进行正常应力水平下特征寿命值的求解,证明了本文所给出的方法确实可行。     

A model to predict the residual life of aircraft engines based upon oil analysis data

This paper reports on a study using the available oil monitoring information, such as the data obtained using the Spectrometric Oil Analysis Programme (SOAP), to predict the residual life of a set of aircraft engines. The relationship between oil monitoring information and the residual life is established using the concept of the proportional residual, which states that the predicted residual life may be proportional to the wear increment measured by the oil analysis programmes. Assuming such a relationship between wear and the residual life exists, we formulated a recursive prediction model for the item's residual life given measured oil monitoring information to date. A set of censored life data of 30 aircraft engines (right censored due to preventive overhaul) along with the history of their monitored metal concentration information are available to us. The metal concentration information includes many variables, such as Fe, Cu, Al, etc.; not all of them are useful, and some of them may be correlated. The principal component analysis (PCA) has been adopted to reduce the dimension of the original data set and to produce a new set of uncorrelated variables, which we shall use in the prediction model. The procedure associated with estimating model parameters is discussed. The model is fitted to the actual SOAP data from the aircraft engines, and the goodness‐of‐fit test has been carried out. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Model parameter estimation and residual life prediction for a partially observable failing system

We consider a partially observable degrading system subject to condition monitoring and random failure. The system's condition is categorized into one of three states: a healthy state, a warning state, and a failure state. Only the failure state is observable. While the system is operational, vector data that is stochastically related to the system state is obtained through condition monitoring at regular sampling epochs. The state process evolution follows a hidden semi‐Markov model (HSMM) and Erlang distribution is used for modeling the system's sojourn time in each of its operational states. The Expectation‐maximization (EM) algorithm is applied to estimate the state and observation parameters of the HSMM. Explicit formulas for several important quantities for the system residual life estimation such as the conditional reliability function and the mean residual life are derived in terms of the posterior probability that the system is in the warning state. Numerical examples are presented to demonstrate the applicability of the estimation procedure and failure prediction method. A comparison results with hidden Markov modeling are provided to illustrate the effectiveness of the proposed model. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 190–205, 2015     

焊接过程对焊接残余应力及残余变形的影响

采用热弹塑性有限元法 ,对直通焊和多人同时分段焊两种焊接过程的平板对接焊时焊接应力变形和圆柱壳板环缝的焊接变形进行比较 ,认为多人同时分段焊较直通焊无论在降低焊接残余应力还是焊接残余变形都具有非常显著的效果     

基于贝叶斯模型的装备剩余寿命预测研究

为了解决武器装备日益复杂及维修工作日趋繁重的问题,运用贝叶斯模型预测装备修理后的剩余寿命,为合理安排其修理计划提供依据。替代传统的指数分布,用威布尔分布描述系统寿命特征,并运用极大似然方法和贝叶斯方法估计威布尔分布的两个未知参数,给出其置信区间。在此基础上,对先验样本和后验样本两种不同情况,分别运用贝叶斯模型预测装备修理后的剩余寿命,并给出实例。结果表明了该方法的有效性。     

基于维纳过程金属化膜电容器的剩余寿命预测

金属化膜电容器是惯性约束聚变激光装置能源系统最重要的元器件,对个体电容器的剩余寿命进行有效的预测对整个装置的可靠性水平有着重要的影响.为有效地预测个体电容器的剩余寿命,提出了融合单个电容器性能退化数据与先验性能退化数据信息的预测方法.采用Wiener过程对其性能退化过程进行建模,并根据先验退化数据信息构造参数的先验分布...     

Some aging properties of parallel and series systems with a random number of components

In this article, we study aging properties of parallel and series systems with a random number of components. We show that the decreasing likelihood ratio property is closed under the formation of random minima. We also show, by counterexamples, that other aging properties are not closed under the formation of random minima or maxima. Some mistakes in the literature are corrected. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 238–243, 2014     

Log‐concave and concave distributions in reliability

Nonparametric classes of life distributions are usually based on the pattern of aging in some sense. The common parametric families of life distributions also feature monotone aging. In this paper we consider the class of log‐concave distributions and the subclass of concave distributions. The work is motivated by the fact that most of the common parametric models of life distributions (including Weibull, Gamma, log‐normal, Pareto, and Gompertz distributions) are log‐concave, while the remaining life of maintained and old units tend to have a concave distribution. The classes of concave and log‐concave distributions do not feature monotone aging. Nevertheless, these two classes are shown to have several interesting and useful properties. We examine the closure of these classes under a number of reliability operations, and provide sharp reliability bounds for nonmaintained and maintained units having life distribution belonging to these classes. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 419–433, 1999     

Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems

We consider the classical problem of whether certain classes of lifetime distributions are preserved under the formation of coherent systems. Under the assumption of independent and identically distributed (i.i.d.) component lifetimes, we consider the NBUE (new better than used in expectation) and NWUE (new worse than used in expectation) classes. First, a necessary condition for a coherent system to preserve the NBUE class is given. Sufficient conditions are then obtained for systems satisfying this necessary condition. The sufficient conditions are satisfied for a collection of systems which includes all parallel systems, but the collection is shown to be strictly larger. We also prove that no coherent system preserves the NWUE class. As byproducts of our study, we obtain the following results for the case of i.i.d. component lifetimes: (a) the DFR (decreasing failure rate) class is preserved by no coherent systems other than series systems, and (b) the IMRL (increasing mean residual life) class is not preserved by any coherent systems. Generalizations to the case of dependent component lifetimes are briefly discussed.     

Lot sizes under continuous demand: The backorder case

We study a deterministic lot-size problem, in which the demand rate is a (piecewise) continuous function of time and shortages are backordered. The problem is to find the order points and order quantities to minimize the total costs over a finite planning horizon. We show that the optimal order points have an interleaving property, and when the orders are optimally placed, the objective function is convex in the number of orders. By exploiting these properties, an algorithm is developed which solves the problem efficiently. For problems with increasing (decreasing) demand rates and decreasing (increasing) cost rates, monotonicity properties of the optimal order quantities and order intervals are derived.     

On the conditional residual lifetime of coherent systems under double regularly checking

In this paper, we consider a coherent system with n independent and identically distributed components under the condition that the system is monitored at time instances t₁ and t₂ (t₁ < t₂). First, various mixture representations for reliability function of the conditional residual lifetime of the coherent system are derived under different scenarios at times t₁ and t₂ (t₁ < t₂). Several stochastic comparisons between two systems are also made based on the proposed conditional random variables. Then, we consider the conditional residual lifetime of the functioning components of the system given that j components have failed at time t₁ and the system has failed at time t₂. Some stochastic comparisons on the proposed conditional residual lifetimes are investigated. Several illustrative graphs and examples are also provided.     

The logistic–exponential survival distribution

For various parameter combinations, the logistic–exponential survival distribution belongs to four common classes of survival distributions: increasing failure rate, decreasing failure rate, bathtub‐shaped failure rate, and upside‐down bathtub‐shaped failure rate. Graphical comparison of this new distribution with other common survival distributions is seen in a plot of the skewness versus the coefficient of variation. The distribution can be used as a survival model or as a device to determine the distribution class from which a particular data set is drawn. As the three‐parameter version is less mathematically tractable, our major results concern the two‐parameter version. Boundaries for the maximum likelihood estimators of the parameters are derived in this article. Also, a fixed‐point method to find the maximum likelihood estimators for complete and censored data sets has been developed. The two‐parameter and the three‐parameter versions of the logistic–exponential distribution are applied to two real‐life data sets. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Ambulance location for maximum survival

This article proposes new location models for emergency medical service stations. The models are generated by incorporating a survival function into existing covering models. A survival function is a monotonically decreasing function of the response time of an emergency medical service (EMS) vehicle to a patient that returns the probability of survival for the patient. The survival function allows for the calculation of tangible outcome measures—the expected number of survivors in case of cardiac arrests. The survival‐maximizing location models are better suited for EMS location than the covering models which do not adequately differentiate between consequences of different response times. We demonstrate empirically the superiority of the survival‐maximizing models using data from the Edmonton EMS system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

内腐蚀缺陷尺寸对DN150承插管线承压能力的影响

为了科学地指导DN150承插管线的使用与管理,采用非线性有限元法对带内腐蚀缺陷的DN150承插管线进行了剩余强度的评估。通过分析和计算,研究了腐蚀缺陷宽度、长度和深度对管线极限承载能力的影响。结果表明：腐蚀缺陷宽度对DN150承插管线的承载能力影响很小,可忽略不计;随着腐蚀缺陷长度的增加,管线的承载能力略微减小,当缺陷长度达到150mm,管道失效压力基本不变;随着腐蚀缺陷深度的增加,管道失效压力呈线性递减,其对管道失效压力的影响程度远远大于腐蚀缺陷长度。     

复合材料层合板疲劳寿命形状参数与门槛值分析方法

复合材料性能具有较大的分散性,在表征复合材料疲劳寿命时,必须考虑分散性的影响。以M21C复合材料开孔层合板为研究对象,采用Sendeckyj等效静强度模型和随机变量函数的概率分布方法推导了复合材料层合板疲劳寿命形状参数和剩余强度形状参数的关系,通过试验和统计的方法获得了M21C复合材料开孔层合板的疲劳寿命形状参数和疲劳门槛值,对载荷放大系数以及低载截除水平的确定提供了数据支持。