Modeling reliability with a two-sided power distribution

Modeling the reliability of a system typically involves the piecewise combination of mathematically disparate functions covering distinct periods (e.g., decreasing, constant, and increasing time-dependent failure rates defining the traditional bathtub curve) in the life of an engineered system. This work explores the two-sided power distribution, a nonlinear extension of the triangular distribution, for describing failure time and rendering a statistically valid bathtub curve with a single probability density function. The parameters of the two-sided power distribution also provide some flexibility to describe decreasing and increasing failure rates with a single distribution that are not available with similar distributions.     

Clustering Empirical Failure Rate Curves for Reliability Prediction Purposes in the Case of Consumer Electronic Products

In this paper, a methodology based on the combination of time series modeling and soft computational methods is presented to model and forecast bathtub‐shaped failure rate data of newly marketed consumer electronics. The time‐dependent functions of historical failure rates are typified by parameters of an analytic model that grabs the most important characteristics of these curves. The proposed approach is also verified by the presentation of an industrial application brought along at an electrical repair service provider company. The prediction capability of the introduced methodology is compared with moving average‐based and exponential smoothing‐based forecasting methods. According to the results of comparison, the presented method can be considered as a viable alternative reliability prediction technique. Copyright © 2015 John Wiley & Sons, Ltd.     

A reliability analysis for electronic devices under an extension of exponentiated perks distribution

This paper presents a reliability analysis for electronic devices (ED) with bathtub curve-shaped failure times. An extension of the exponentiated perks distribution (EPD) is proposed for the analysis. The extension of this new distribution is based on the Alpha Power Transformation, so the Alpha Exponentiated Perks Distribution (AEXP) is introduced. The AEXP has three shape parameters and one scale parameter, allowing greater flexibility to represent failure rates in an increasing, decreasing, or bathtub curve form. Some useful properties in the reliability engineering context are presented. AEXP parameters were estimated via the Maximum Likelihood Method. Finally, two case studies focused on ED are used to compare the proposed distribution and other distributions with similar failure rate representation properties. The obtained results show that the AEXP better describes the behavior of ED than the distributions considered in the analysis.     

Reliability Analysis of a conveyor system using hybrid data

The quantification of a fault tree is difficult without an exact probability value for all of the basic events of the tree. To overcome this difficulty in this paper, we propose a methodology which employs ‘hybrid data’ as a tool to analyse the fault tree. The proposed methodology estimates the failure probability of basic events using the statistical analysis of field recorded failures. Under these circumstances, where there is an absence of past failure records, the method follows a fuzzy set based theoretical evaluation based on the subjective judgement of experts for the failure interval. The proposed methodology has been applied to a conveyor system. The results of the analysis reveal the effectiveness of the proposed methodology and the instrumental role played by the experience of experts in providing reliability oriented information. Copyright © 2006 John Wiley & Sons, Ltd.     

Aging property of unimodal failure rate models

There is a family of statistical models, whose failure rate is unimodal or reverse bathtub shaped. For the situations where the failure is mainly caused by fatigue or corrosion, the time to failure is often represented by such models. This paper studies the aging property of such a class of models. It shows that a unimodal failure rate can be effectively viewed as increasing, decreasing, or constant, depending on the model parameters. Relevant quantitative measures are developed to identify to which case a given unimodal failure rate model belongs. Such two models, lognormal and inverse Weibull distributions, are analyzed.     

药品智能包装的模糊灰色故障树分析

目的对某款药品智能包装从系统层面进行可靠性分析。方法首先,通过失效分析建立药品智能包装的故障树;其次,利用专家判断知识和模糊数学理论,得到故障树底事件和顶事件的三角形式模糊失效率,以及采用模糊中值法进行底事件模糊重要度计算;最后,运用灰色关联分析求出表征各最小割集与顶事件相关行为关系的灰色关联度。结果定量分析计算显示,药品智能包装模糊失效率为(0.146 59,0.179 69,0.206 91),故障相关性最大的为包装材料本身的功能失效,其次为外界的振动和冲击以及包装尺寸误差等。结论模糊灰色关联故障树同时考虑包装系统的模糊性和灰色性,它可为预防药品智能包装失效、提高智能包装可靠性和安全性提供理论依据。     

基于梯形模糊数的数控磨床砂轮架系统故障树分析

数控磨床砂轮架系统故障树分析中的一大难点是确定基本事件的发生概率,基本事件的发生情况存在模糊性且由于时间和成本的限制往往无法通过实验获得足够的可靠性数据。为了解决这一问题,引入模糊集合论,用梯形模糊数来描述故障树分析中的基本事件和顶事件的发生概率。首先对数控磨床砂轮架系统的结构层次进行分析,建立砂轮架系统的故障树。然后以砂轮架系统主轴振动异响为例进行模糊故障树分析,求解顶事件发生概率的梯形模糊数;并类比传统故障树分析中"临界重要度"的概念,定义适用于模糊故障树分析的"模糊临界重要度"。最后根据求解的模糊临界重要度对基本事件进行排序,确定危害程度较高的基本事件,结果与企业的实际情况相符合。结果表明该方法能够有效解决数控磨床故障树分析中基本事件难于准确赋值的问题,为企业提高机械系统的可靠性提供了一种定量依据。     

A New Model for Repairable Systems with Nonmonotone Intensity Function

In this study, a new model based on the mixture of bounded Burr XII failure intensity and bounded intensity process is proposed to describe the failure intensity of minimally repaired systems with approximate bathtub behavior. The estimates of the model parameters are easily obtained using the maximum likelihood estimation method. The confidence intervals for the model parameters are also provided. Other existing models, such as superposed power law process, log‐linear process–power law process, and bounded bathtub intensity process are used to compare with our proposed model. Through numerical examples, the results show that our proposed model performs well regarding the Akaike information criterion value and the mean of square errors. Copyright © 2014 John Wiley & Sons, Ltd.     

Footprint of knowledge acquisition improvement in failure diagnosis analysis

Fault tree analysis (FTA) as an effective and efficient risk assessment tool are widely used to analyze the reliability of a complex system. In this context, FTA can properly improve the safety performance of the system by preventing an event which may lead to occurrence of a catastrophic accident. However, traditional FTA is still suffering from dynamic structure demonstration and importantly epistemic uncertainty processing. In this study, a novel methodology is introduced using Bayesian updating mechanism to deal with dynamic structure and 2‐tuple fuzzy set named as intuitionistic fuzzy numbers are employed to cope with subjectivity of uncertainty processing. Accordingly, the most critical system components which affect the system reliability are recognized by using an appropriate sensitivity analysis method. The proposed methodology is then applied on a real case study application (a brake fluid filling system) in order to examine the effectiveness and feasibility of the approach. The results illustrated that the new methodology can have enough benefits for diagnosing the systems' faults compared with listing approaches of safety and reliability analysis. In terms of empirical case study, “electromotor failure” was evaluated as the second most critical basic event in conventional‐based approaches, whereas in the novel methodology “high pressure liquefied material” was recognized as the second one.     

Handling Uncertainties in Fault Tree Analysis by a Hybrid Probabilistic–Possibilistic Framework

Fault tree analysis is a method largely used in probabilistic risk assessment. Uncertainties should be properly handled in fault tree analyses to support a robust decision making. While many sources of uncertainties are considered, dependence uncertainties are not much explored. Such uncertainties can be labeled as ‘epistemic’ because of the way dependence is modeled. In practice, despite probability theory, alternative mathematical structures, including possibility theory and fuzzy set theory, for the representation of epistemic uncertainty can be used. In this article, a fuzzy β factor is considered to represent the failure dependence uncertainties among basic events. The relationship between β factor and system failure probability is analyzed to support the use of a hybrid probabilistic–possibilistic approach. As a result, a complete hybrid probabilistic–possibilistic framework is constructed. A case study of a high integrity pressure protection system is discussed. The results show that the proposed method provides decision makers a more accurate understanding of the system under analysis when failure dependencies are involved. Copyright © 2015 John Wiley & Sons, Ltd.     

基于模糊故障树的军用气象物资包装可靠性分析

应用模糊故障树分析方法对军用气象物资包装可靠性进行了系统分析,简要介绍了模糊故障树分析方法的基本理论,利用专家判断和模糊集理论相结合的方法,评估了故障树底事件发生的模糊失效概率。并以"TFS-1通风干湿表包装"为例,建立了包装系统的故障树,采用下行法求解了引起顶事件发生的最小割集,定量分析计算,得出模糊失效率为0.0705,同时计算了各底事件的重要度。模糊故障树分析方法对于提高军用气象物资包装防护能力,确保物资装备质量,具有非常重要的意义。     

Master Logic Diagram: method for hazard and initiating event identification in process plants

Master Logic Diagram (MLD), a method for identifying events initiating accidents in chemical installations, is presented. MLD is a logic diagram that resembles a fault tree but without the formal mathematical properties of the latter. MLD starts with a Top Event "Loss of Containment" and decomposes it into simpler contributing events. A generic MLD has been developed which may be applied to all chemical installations storing toxic and/or flammable substances. The method is exemplified through its application to an ammonia storage facility.     

Fuzzy Fault Diagnosis of a Diesel Engine Non-start

The diesel locomotive plays an important role in the field of transport,and the engine maintenance work is the prerequisite and guarantee for the locomotive normal working.In this paper,we first establish the fault tree model of locomotive engine 16V240ZJ on the basis of engine non-start as the top event.Then we combines the fuzzy mathematics theory and fault tree analysis method for failure diagnosis of 16V240ZJ engine's abnormal start-up.We obtained the fuzzy probability curve and top events probability c...     

Reliability analysis for electronic devices using beta‐Weibull distribution

Today, in reliability analysis, the most used distribution to describe the behavior of electronic products under voltage profiles is the Weibull distribution. Nevertheless, the Weibull distribution does not provide a good fit to lifetime datasets that exhibit bathtub‐shaped or upside‐down bathtub–shaped (unimodal) failure rates, which are often encountered in the reliability analysis of electronic devices. In this paper, a reliability model based on the beta‐Weibull distribution and the inverse power law is proposed. This new model provides a better approach to model the performance and fit of the lifetimes of electronic devices. To estimate the parameters of the proposed model, a Bayesian analysis is used. A case study based on the lifetime of a surface mounted electrolytic capacitor is presented, the results showed that the estimation of the proposed model differs from the inverse power law–Weibull and that it affects directly the mean time to failure, the failure rate, the behavior, and the performance of the capacitor under analysis.     

A New Ordering Method of Basic Events in Fault Tree Analysis

The ordering of basic events is critical to fault tree analysis on the basis of binary decision diagrams (BDDs). Many attempts have been made to seek an efficient ordering result with the aim of reducing the complexity of BDD. In this article, a new ordering method, namely, priority ordering method, is proposed. The new method takes into account not only the effects of the layers of fault tree but also the repeated events, the neighboring events, and the number of events under the same gate. According to these four effects, the priorities that sort the basic events of the fault tree are defined. The new method inherits the merits of structure‐based and weight‐based methods. It is able to evaluate the basic events on the basis of the structure‐based method and the size of the subtree on the basis of the weighted‐based method. Demonstrated by the examples, the proposed priority ordering method is superior to the existing ordering methods in terms of reducing the nodes in the BDD and improving the efficiency in transforming a fault tree to a BDD. Copyright © 2011 John Wiley & Sons, Ltd.     

Statistical Inference about the Shape Parameter of the New Two‐parameter Bathtub‐shaped Lifetime Distribution

This paper proposes a simple and exact method for conducting a statistical test about the shape parameter of the new two‐parameter lifetime distribution with a bathtub‐shaped or increasing failure rate function, as well as an exact confidence interval for the same parameter. The necessary critical values of the test are given. The method provided in this paper can be used for type II right censored data. Moreover, Monte Carlo simulation and an example are used to compare this new method to the existing approach of Chen (Statistics and Probability Letters 2000; 49:155–161). Copyright © 2004 John Wiley & Sons, Ltd.     

Reliability analysis using exponentiated Weibull distribution and inverse power law

Today in reliability analysis, the most used distribution to describe the behavior of devices is the Weibull distribution. Nonetheless, the Weibull distribution does not provide an excellent fit to lifetime datasets that exhibit bathtub shaped or upside‐down bathtub shaped (unimodal) failure rates, which are often encountered in the performance of products such as electronic devices (ED). In this paper, a reliability model based on the exponentiated Weibull distribution and the inverse power law model is proposed, this new model provides a better approach to model the performance and fit of the lifetimes of electronic devices. A case study based on the lifetime of a surface‐mounted electrolytic capacitor is presented in this paper. Besides, it was found that the estimation of the proposed model differs from the Weibull classical model and that affects the mean time to failure (MTTF) of the capacitor under analysis.     

Gastric esophageal surgery risk analysis with a fault tree and Markov integrated model

Reliability methods have been widely used in risk analysis of medical surgeries. In this study, the authors combine a fault tree with Markov models to assess time independent- and dependent factors together. Dynamics are integrated in the traditional fault tree, and meanwhile the processes of solving Markov are simplified with the modular approach. Continuous time Markov chains are adopted in evaluating the failure probability of a gastric esophageal surgery after categorizing basic events in the fault tree, and a certain time dependent variables, such as failure rate of medical equipment, surgery frequency, and rescue timeliness are involved into risk analysis. A case is studied with data collected from a general hospital, to illustrate the operational process of the proposed method. Results based on the inputs show that taking rescue actions into consideration can reduce the gap between the result of fault tree analysis and the reality. Sensitivity analysis for measuring the impacts of the above time relevant variables is conducted, as well as limitations of the Markov model are discussed.     

The omega probability distribution and its applications in reliability theory

A new three‐parameter probability distribution called the omega probability distribution is introduced, and its connection with the Weibull distribution is discussed. We show that the asymptotic omega distribution is just the Weibull distribution and point out that the mathematical properties of the novel distribution allow us to model bathtub‐shaped hazard functions in two ways. On the one hand, we demonstrate that the curve of the omega hazard function with special parameter settings is bathtub shaped and so it can be utilized to describe a complete bathtub‐shaped hazard curve. On the other hand, the omega probability distribution can be applied in the same way as the Weibull probability distribution to model each phase of a bathtub‐shaped hazard function. Here, we also propose two approaches for practical statistical estimation of distribution parameters. From a practical perspective, there are two notable properties of the novel distribution, namely, its simplicity and flexibility. Also, both the cumulative distribution function and the hazard function are composed of power functions, which on the basis of the results from analyses of real failure data, can be applied quite effectively in modeling bathtub‐shaped hazard curves.     

Improved accuracy in quantitative fault tree analysis

The fault tree diagram defines the causes of the system failure mode or ‘top event’ in terms of the component failures and human errors, represented by basic events. By providing information which enables the basic event probability to be calculated, the fault tree can then be quantified to yield reliability parameters for the system. Fault tree quantification enables the probability of the top event to be calculated and in addition its failure rate and expected number of occurrences. Importance measures which signify the contribution each basic event makes to system failure can also be determined. Owing to the large number of failure combinations (minimal cut sets) which generally result from a fault tree study, it is not possible using conventional techniques to calculate these parameters exactly and approximations are required. The approximations usually rely on the basic events having a small likelihood of occurrence. When this condition is not met, it can result in large inaccuracies. These problems can be overcome by employing the binary decision diagram (BDD) approach. This method converts the fault tree diagram into a format which encodes Shannon's decomposition and allows the exact failure probability to be determined in a very efficient calculation procedure. This paper describes how the BDD method can be employed in fault tree quantification. © 1997 John Wiley & Sons, Ltd.