Using Accelerated Life Tests Results to Predict Product Field Reliability

Accelerated life tests (ALTs) provide timely assessments of the reliability of materials, components, and subsystems. ALTs can be run at any of these levels or at the full-system level. Sometimes ALTs generate multiple failure modes. A frequently asked question near the end of an ALT program is “what do these test results say about field performance?” ALTs are carefully controlled, whereas the field environment is highly variable. For example, products in the field have different average use rates across the product population. With good characterization of field use conditions, it may be possible to use ALT results to predict the failure time distribution in the field. When such information is not available but both life test data and field data (from, e.g., warranty returns) are available, it may be possible to find a model to relate the two data sets. Under a reasonable set of practical assumptions, this model then can be used to predict the failure time distribution for a future component or product operating in the same use environment. This paper describes a model and methods for such situations. The methods are illustrated by an example to predict the failure time distribution of a newly designed product with two failure modes. Supplemental material for this article is available online at the Technometrics website.     

On Distribution-Free Confidence Bounds for Pr{Y < X}

For X and Y unknown, distribution-free confidence intervals for Pr {Y < X} are obtained by means of the Chebyshev inequality and van Dantzig's upper bound for the variance of the Mann-Whitney statistic U. The (two-sided) intervals are reliable for small samples and are shorter than the upper bounds obtained by Birnbaum and McCarty, provided the confidence coefficient does not exceed .925 and the sample sizes are not too unequal.     

Reliability of Space-Shuttle Pressure Vessels With Random Batch Effects

In this article we revisit the problem of estimating the joint reliability against failure by stress rupture of a group of fiber-wrapped pressure vessels used on Space-Shuttle missions. The available test data were obtained from an experiment conducted at the U.S. Department of Energy Lawrence Livermore Laboratory (LLL) in which scaled-down vessels were subjected to life testing at four accelerated levels of pressure. We estimate the reliability assuming that both the Shuttle and LLL vessels were chosen at random in a two-stage process from an infinite population with spools of fiber as the primary sampling unit. Two main objectives of this work are (1) to obtain practical estimates of reliability taking into account random spool effects and (2) to obtain a realistic assessment of estimation accuracy under the random model. Here, reliability is calculated in terms of a “system” of 22 fiber-wrapped pressure vessels, taking into account typical pressures and exposure times experienced by Shuttle vessels. Comparisons are made with previous studies. The main conclusion of this study is that, although point estimates of reliability are still in the “comfort zone,” it is advisable to plan for replacement of the pressure vessels well before the expected lifetime of 100 missions per Shuttle Orbiter. Under a random-spool model, there is simply not enough information in the LLL data to provide reasonable assurance that such replacement would not be necessary.     

Statistical Inference From Censored Weihull Samples

In life testing experiments it is a fairly common practice to terminate the experiment before all items have failed. The Weibull distribution is often used as a model for the observations and when a computer is available maximum likelihood estimation of the parameters is to be recommended. The tables presented in this paper enable one to set confidence limits on the parameters and the reliability based on the maximum likelihood estimates for selected censoring and sample sizes.

It is also observed that, as in the case with no censoring, the maximum likelihood estimator of the reliability is very nearly unbiased and its variance is near the Cramér-Rao lower bound, Unbiasing factors for the maximum likelihood estimator of the shape parameter are given.     

Reliability based design optimization using response surfaces in application to multidisciplinary systems

Traditionally, reliability based design optimization (RBDO) is formulated as a nested optimization problem. For these problems the objective is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure corresponding to each of the failure modes or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large scale multidisciplinary systems which are likewise computationally intensive. In this research, a framework for performing reliability based multidisciplinary design optimization using approximations is developed. Response surface approximations (RSA) of the limit state functions are used to estimate the probability of failure. An outer loop is incorporated to ensure that the approximate RBDO converges to the actual most probable point of failure. The framework is compared with the exact RBDO procedure. In the proposed methodology, RSAs are employed to significantly reduce the computational expense associated with traditional RBDO. The proposed approach is implemented in application to multidisciplinary test problems, and the computational savings and benefits are discussed.     

Some new insights on informational entropy for water distribution networks

Several researchers have studied the use of informational entropy as a surrogate measure for the reliability of water distribution networks. The hypothesis is that the numerical value of network entropy in some way reflects the reliability of water distribution networks, and this appears to be supported by the analysis of some example water distribution networks. However, the precise relationship between the entropy value and some measures of reliability has not been formally established. The primary objective in this paper is to present an alternative methodology to calculate the informational entropy of water distribution networks. This methodology is termed as the Path Entropy Method (PEM), which provides some insights into the entropy of branching-tree networks and maximum-entropy flows of single-source networks. In addition, a quick method of computing the maximum-entropy value of single-source networks is presented and termed as the Simplified Path Entropy Method (SPEM).     

A QUANTIFIED ASSESSMENT OF THE RELATIONSHIP BETWEEN THE RELIABILITY AND ENTROPY OF WATER DISTRIBUTION SYSTEMS

Several researchers have suggested that it might be possible to use entropy as a general performance indicator for water distribution systems. It has several advantages over other performance and reliability indices, for example, it is extremely rapid and far easier to calculate than other measures, has minimal data requirements and lends itself to direct incorporation into design optimization frameworks.

This paper summarises the first proper attempt to investigate the apparent relationship between the entropy and reliability of water distribution systems. A maximum entropy-constrained approach was used to generate designs for a sample water distribution system which, along with traditional minimum-cost designs, formed the basis of this study. By varying the layout, number of loops and links and reversing the direction of flow in some pipes, it is shown statistically that the correlation between entropy and reliability is strong. Based on the results, a new method for sizing the pipes of water distribution systems is proposed. It is quick, easy to implement, finds optimal pipe sizes, does not require non-linear programming and always guarantees a high level of reliability.     

Prediction of high-cycle fatigue life reliability of aluminum cast alloy from statistical characteristics of defects at meso-scale

In this paper, a growth rate law of a small fatigue crack of an arbitrary metal and a method for predicting a size distribution of spheroidal defects cut by a specimen are proposed. And then, by combining the crack growth rate law and the prediction method for the surface defect size distribution, a method for predicting a high-cycle fatigue life reliability of a metal with defects is proposed. Rotating bending fatigue tests of plain specimens with/without a small blind hole (0.3 mm in diameter, 0.15 mm in depth) are carried out on an aluminum cast alloy JIS AC4B-T6 with eutectic Si, Fe compounds and porosities. By comparing analyzed results with experimental ones, the validity of the present method is examined.     

Confidence bounds on component reliability in the presence of mixed uncertain variables

Uncertainties in a physical system can be modeled and analyzed by using probability theory or possibility theory, depending on the amount of information available. In probability theory, uncertain variables are modeled using probability density functions (PDFs) and then propagated through the system to obtain its reliability. In the absence of sufficient data to model a PDF, possibility theory, in which variables are represented using fuzzy membership functions, can be used to propagate uncertainty. However, when dealing with a combination of both probability distributions and fuzzy membership functions, the computational cost involved in estimating the membership function of reliability increases exponentially because one reliability analysis, which is a computationally expensive procedure, is performed at each possibility level to obtain the bounds on the reliability of the structure. To improve the computational efficiency, a technique that uses response surface models and transformations of possibility functions is presented in this paper. The efficiency and accuracy of the proposed methodology is demonstrated using numerical examples.     

随机恒幅循环载荷疲劳可靠度异量纲干涉模型

用于与时间无关的失效模式(例如静强度失效)的失效概率或可靠度计算的"应力-强度干涉模型"已很成熟,但要将干涉分析的概念与方法应用于与时间相关的失效模式(例如疲劳、磨损和腐蚀等)还存在许多困难,即使对于存在不确定性的恒幅循环载荷下的疲劳可靠性问题,目前也还没有像静强度应力-强度干涉模型那样简单、直接、有效的方法及数学模型.在概率统计平均的意义上重新解释传统的两个随机变量干涉分析的基本概念及模型,将干涉模型解释为载荷加权平均模型.具体地讲,就是将应力-强度干涉模型解释、拓展为强度超越(载荷)概率的(载荷)统计加权平均模型,或给定应力下的条件失效概率的随机载荷加权平均模型.这样,传统上只能应用于相同量纲随机变量(例如应力与强度)的干涉模型就可以拓展应用于具有不同量纲随机变量(例如应力与寿命)的情形,例如随机载荷下的疲劳失效概率(寿命小于指定值的概率)或可靠度(寿命大于指定值的概率)计算.应用这样的模型,可以很方便地根据几个确定性恒幅循环载荷下的疲劳寿命分布,预测随机恒幅循环载荷作用下的疲劳失效概率或可靠度.