Robust failure probability

In the robust (updated) reliability approach, the plausibUity of all the possible structural models conditional on the amount of informatiOTi available is taken into account in a Bayesian framework (for more details, see Jaynes 2003 Papadimitriou et al. 2001 Beck and Au 2002 Jalayer et al. 2010 Zuev et al. 2012). The robust failure probability then can be calculated (in comparison to Eq. 21) by the following integral ... 

Toluene recovery process Maximization of economic benefit and minimization of environmental indicator. In addition to these two objectives, Kheawhom and Hirao (2002) considered process robustness measures (failure probability and deviation ratio) also. Normal boundary intersection method Sustainable process index was used as environmental indicator. Product revenue less capital and operating costs was the economic indicator Kheawhom and Hirao (2002)... 

As discussed in Chapter 6, the acceptance of a System Level 3 or 4 (see Fig. 1.1) failure probability is often based on the assnmption that failures are independent (AMC25.1309). However, this approach does not snfQciently recognise (refer, inter alia, SAE ARP4761 App I para 1) the threats which external events (outside of the immediate system boundary) have on assumptions made about the robustness of our fail safe designs. 

The difficulty in obtaining accurate values of the failure probabilities complicates the application of the reliability-based optimization approaches. A convenient alternative is the robust optimization approach, based on second order statistical information. 

An uncertainty analysis has been performed in order to assess the robustness of the results of the importance analyses. In fact, the importance measures depend on the values of the failure probabilities of the components of the storage system, which are uncertain. Thus, the results of the importance analysis need to be checked against the variability due to the uncertainty in the model input parameters. To do this, uncertainty in the occurrence probabilities of the most important basic events has been considered by uniform distributions with lower and upper bounds provided by SOL experts. The analysis has highlighted that the uncertainties in the occurrence probabilities of the basic events do not impact on the ranking of the most important causes identified for each TOP event thus, the results discussed above can be considered robust. 

For example, in reliability analysis, the quantity Q is considered as the probability that the structure with parameter vector 0 would fail, i.e., Q(0) = P(F 0, C). Then, the updated integral becomes the updated robust probability of failure for the structure, when it is subjected to some stochastic excitation [198] ... 

This updated robust probability of failure incorporates knowledge about 0 from C and from the updated information from the data. It is robust because the modeling uncertainties are taken into explicit account [198]. The updated structural reliability of the stmcture is P(5 P, C) = 1 - F(F D, C), where S denotes a safe status of the structure. 

Another failure mode for a material under mechanical load is the plastic strain. The stress concentration at the tip of a crack increases the probability that dislocations will nucleate and move at the head of the crack tip. However, unlike in brittle fracture, plasticity dissipates a lot of energy, thus reducing the stress concentration by blunting the crack. This type of ductile behavior, typical in metals, leads to robust structural materials the initiation of failure does not necessarily extend catastrophically through the entire specimen, and a lot of energy is dissipated during the process of the material strain. 

In the last twenty years, various non-deterministic methods have been developed to deal with optimum design under environmental uncertainties. These methods can be classified into two main branches, namely reliability-based methods and robust-based methods. The reliability methods, based on the known probabiUty distribution of the random parameters, estimate the probability distribution of the system s response, and are predominantly used for risk analysis by computing the probability of system failure. However, variation is not minimized in reliability approaches (Siddall, 1984) because they concentrate on rare events at the tail of the probability distribution (Doltsinis and Kang, 2004). The robust design methods are commonly based on multiobjective minimization problems. The are commonly indicated as Multiple Objective Robust Optimization (MORO) and find a set of optimal solutions that optimise a performance index in terms of mean value and, at the same time, minimize its resulting dispersion due to input parameters uncertainty. The final solution is less sensitive to the parameters variation but eventually maintains feasibility with regards probabilistic constraints. This is achieved by the optimization of the design vector in order to make the performance minimally sensitive to the various causes of variation. 

Type of membrane thin damp proof membranes (DPMs) are usually made of low density polyethylene (LDPE) and will have a greater risk of defects than specific gas-resistant membranes manufactured from more robust materials (polypropylene, linear low density polyethylene and high density polyethylene). As the strength and puncture resistance decrease the probability of defects increases For thin DPM material increase probability of failure defects 2000 g-200% 1200 g 00% 1000 g-600% Note these values do not apply to specific gas resistant membranes made from more robust materials than DPMs... 

According to the Table, our ideal detector would have signal-fluctuation limited operation it would react momentary when illuminated by IR radiation its response outside the desired spectral range would be zero it could not only operate at room temperature, but also on elevated and lower temperatures, and the probability of its failure would be neghgible it would be robust and insensitive to the changes of operating conditions it would emit neither any harmful radiation nor... 

Reliability is a discipline concerned with ensuring that system performs its mission successfully. It aims at finding potential failures determine their causes and probabilities in order to ensure more robust products. Reliability is an important attribute of final product. For this reason the manufacturer must ensure that reliability is considered during the design phase. 

In previous work (Karagiannis et al. 2010) develop a method laying on models to assess robustness of Emergency Response Plan in industrial context. This method is based on questionnaires to assess probability of resource failure modes, organize and combine them in a Fault-Tree (FT) specific to each category (human, technical, organizational and informational). In this way plan failure scenarios can be built. Authors developed also a resource taxonomy for Emergency Response Plan to build patterns of Fault-Tree. A limit of this work is that it considered for model elements (both resource and function) only two binary states and so does not take into account partial failures of these elements, specifically function element. As it can be noticed in real world many elements of a system may have more than two possible states of failure. Moreover, these states may be qualified by a real value (not only 0 and 1). 

The probabilistic reliability systems of events are analysed by Ziba (2000). The analysis is based on the concepts of entropy as defined in information theory and applied to probability theory. The recommended approach allows concentrating the system analysis only on important failure modes and connects uncertainty, redundancy and robustness of systems of events. Despite this approach, the system analysis leads to complicated computations. 

This section attempts to briefly introduce the main concepts of the subset simulation as an advanced stochastic simulation method for estimation of small probabilities corresponding to rare failure events. However, a detailed introductory description of methodology can be found in the chapter Subset Simulation Method for Rare Event Estimation An Introduction of the general section Reliability and Robustness of the Encyclopedia of Earthquake Engineering. 

In contrast, seismic PSA is an explicitly probabilistic approach, analyzing those combinations of component failures that prevent the plant from being transferred to a safe shutdown state, thus resulting in a damage to the reactor core. Compounding the probabilities of these combinations with the frequency of occurrence of seismic events of various intensity results in an estimate of the seismic-induced core damage frequency. A small value of the latter indicates a large seismic robustness of the plant. 

Systemic failures are due to human errors (e.g. mistakes, misconceptions, miscommunications, omissions) in the specification, design, build, operation and/or maintenance of the system. Errors in this case are taken to include both mistakes and omissions. Errors can be introduced during any part of the lifecycle and errors are caused by failures in design, manufacture, installation or maintenance. Systematic failures occur whenever a set of particular conditions is met and are therefore repeatable (i.e. items subjected to the same set of conditions will fail consistently) and thus apply to both hardware and software. It is difficult to quantify the rate at which systemic failures will occur and a qualitative figure based on the robustness of the development/build process is normally used. The probability of systemic failures is often evaluated by means of safety integrity (or development assurance) levels. 

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