Adaptive Optimal Sampling Methodology for Reliability Prediction of Series Systems

Modern products are complicated and standards of reliability are higher than ever before. Therefore, prediction of system reliability is essential, especially as the time available for developing products has decreased. Most of the previous studies assumed that the causes of failure are random. That is, the failure rates of components follow exponential distributions. To reflect various types of failure such as initial, random, or wear-out failure, we developed a novel procedure for estimating system reliability based on the Weibull distribution. We analyzed the effect of component selection on the types of system failure. Finally, we verified the proposed method by analyzing warranty data on actual Korean products.

In this paper, an original method is presented for evaluating the probability of failure in a precise manner in the tube hydroforming process (THP). This process consists to apply an inner pressure combined to an axial displacement to manufacture the part. During the manufacturing phase, inappropriate choice of the load paths can lead to failure. Our approach is to determine the space failure probability for each item in the area is critical. It is defined by identifying the critical element, and then a patch is defined on this item that represents the area of the most probable failure. The identification of the critical element for each failure mode is done by reference the state of strain on the forming limit curve (FLC) of the material. Access to the probability of space failure allows to give an idea on the stability of the process and also to predict the most likely area where plastic instability can appear. The failure probability estimation based on a characterization probabilistic principal strains (major and minor) for each failure mode and for each element. Access to this probability of failure in a direct manner is impossible given the complexity of the treated problem and the huge number of calculations by finite elements necessary. To compensate for this problem, approximation techniques have been used to replace the real model by metamodel that enables to evaluate the response quickly and allows us to get an idea on the stability of the process.Keywords: Hydroforming process, metamodels, random, forming limit curve (FLC), failure mode, finite element.

The concept of system reliability will be described in this chapter. A moment-based method for assessing the system reliability of series and non-series structures is investigated, with emphasis on series systems. The reliability index is directly calculated based on the first few moments of the system performance function of a structure. It requires neither the reliability analysis of the individual failure modes nor the iterative computation of derivatives, the computation of the mutual correlations among the failure modes, and any design points. As a practical topic, the evaluation of system reliability for ductile frame structures using methods of moment is introduced in the final part of this chapter. The difficulty in both failure mode identification and failure probability computation is still hard to overcome when using the traditional method for the system reliability assessment of ductile frame structures. To avoid the difficulties, a failure mode independent performance function with weak non-normality is introduced. The method of moments is then utilized to estimate the failure probability of ductile frame structures corresponding to the general performance function. From the numerical examples, it can be concluded that the introduced methodology successfully overcomes the two difficulties including the identification of significant failure modes and the computation of overall failure probabilities contributed from these significant modes in system reliability evaluation of ductile frame structures.

The effects of vibration loads on the reliability of printed circuit boards is gaining importance due to the increasing use in vibration-intensive areas such as the drive train of electric cars. When assessing the reliability of electronic systems, it is important to consider not only the general probability of failures, but also their effects at the system level. Different failure modes present varying degrees of safety risk, which is taken into account in the design process through target values for failure probabilities. However, the occurrence probabilities of specific failure modes are currently assessed mainly qualitatively, or based on literature values and expert estimations. This work presents a simulation-based failure modes and effects analysis (FMEA) to estimate the probability of failure modes depending on external vibration loads. The simulation-based FMEA combines a numerical simulation, a lifetime model and a probabilistic FMEA. The key to reliable estimations of failure probabilities is the quantification of uncertainties that cause variations of the structural dynamic properties and thereby variations of local stresses on the electronic components. Therefore, Bayesian model updating is conducted to find probability distributions representing the scattering of selected parameters. The method is applied to a test printed circuit board and validated with experimental failure data.

Introduction and Background Most engineering structures contain multiple failure modes or components in which the nonperformance of any of the events can lead to system failure. In addition, the different failure modes may be correlated due to common random variables between the events. In many cases the events are assumed independent and system failure is evaluated using unions and intersections of the events. However, neglecting correlation between events may lead to grossly over predicting the probability of failure. An upper and lower bound can be determined for the probability of system failure using first- and second-order techniques. While there is some contradiction in the literature, a complete treatment of first-order bounds is made in this research. The first- order bounds are identified for events with both positive and negative correlation. In practice the second-order bounds typically use a first-order approximation to the limit-state for each event and the intersection of the two events is estimated by the correlation between the events. For nonlinear limit-states, the bounds may not actually include the true solution based on the error of the event probabilities of failure or the predicted intersection of the events. Several numerical examples are used to evaluate the accuracy and effectiveness of

Offshore system safety and reliability considering microbial influenced multiple failure modes and their interdependencies

This paper demonstrates several analytical techniques used to predict units (from a group) that are more likely to fail in operation. The paper specifically examines the least reliable units used by a number of US space programs. In this paper, the methodology used to develop the Parametric Reliability Prediction Tool (PRPT) is presented. The parameter used is the failure rate/MTBF for the unit. The application of the tool to the DMSP X program has been presented as well. The PRPT will support ¿preventative¿ failure analysis by identifying items that could lead to failures and their probability of occurrence. PRPT will also capture lessons learned to mitigate failure reoccurrence. PRPT will facilitate design reliability trade studies. The PRPT will be expanded to include a process for prediction of early failure modes and mean life time of new products, based on comparisons and similarity derived from the analysis. PRPT provides a disciplined and adequate technique to obtain a more accurate reliability prediction for space systems and subsystems possibly up to line replaceable unit level. Utilizing PRPT in the concept, design and development phases will be an opportunity to improve reliability predictions for space vehicles.

Efficient system reliability analysis illustrated for a retaining wall and a soil slope

System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method

Failure and reliability prediction of engine systems using iterated nonlinear filters based state-space least square support vector machine method

In this paper, an efficient technique is developed to predict failure probability of three failure modes(case rupture, fracture and bolt breakage) related to solid rocket motor case due to the inner pressure during the mission flight. The overall procedure consists of the steps: 1) design parameters affecting the case failure are identified and their uncertainties are modelled by probability distribution, 2) combustion analysis in the interior of the case is carried out to obtain maximum expected operating pressure(MEOP), 3) stress and other structural performances are evaluated by finite element analysis(FEA), and 4) failure probabilities are calculated for the above mentioned failure modes. Axi-symmetric assumption for FEA is employed for simplification while contact between bolted joint is accounted for. Efficient procedure is developed to evaluate failure probability which consists of finding first an Most Probable Failure Point(MPP) using First-Order Reliability Method(FORM), next making a response surface model around the MPP using Latin Hypercube Sampling(LHS), and finally calculating failure probability by employing Importance Sampling.

In order to ensure high reliability of complex engineered systems against deterioration or natural and man-made hazards, it is essential to have an efficient and accurate method for estimating the probability of system failure regardless of different system configurations (series, parallel, and mixed systems). Since system reliability prediction is of great importance in civil, aerospace, mechanical, and electrical engineering fields, its technical development will have an immediate and major impact on engineered system designs. To this end, this chapter presents a comprehensive review of advanced numerical methods for system reliability analysis under uncertainty. Offering excellent in-depth knowledge for readers, the chapter provides insights on the application of system reliability analysis methods to engineered systems and gives guidance on how we can predict system reliability for series, parallel, and mixed systems. Written for the professionals and researchers, the chapter is designed to awaken readers to the need and usefulness of advanced numerical methods for system reliability analysis.

This paper derives equations for probability of success/failure and failure rate for a delta-star transformation and vice versa. An iterative procedure is suggested to solve three nonlinear algebraic equations for evaluating probability of failure in a star-delta transformation. The delta-star transformation is highly accurate whereas the star-delta is not, but has reasonable accuracy. The star-delta transformation is recommended only when the delta-star transformation is not feasible during network reduction. For low (high) values of probability of failure and the failure rate, the star-delta transformation yields higher (lower) than exact values of system probability and frequency of failure.

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.

5 - Potential loss from failure for non-repairable components and systems with multiple failure modes