Failure analysis, probability theory

Through the use of basic probability theory and statistical analysis, the system safety function can actually assign expected values to certain hazards and/or failures to determine the likelihood of their occurrence. The availability of such quantifiable information further enhances the management decisionmaking process and justifies the existence of the system safety effort within the organization. 

If the probability of a failure can be calculated as something less than one (i.e., 100%), then it follows that the probability of success is equal to one minus the probability of failure. In a previous example, the probability of experiencing a lost-time injury was calculated at. 02. The probability of having no lost-time injuries is equal to 1 —. 02, or. 98 (a 98% chance that no lost time injuries will occur). This ability to provide management with projected failure AND success rates for a given operation, task, system, and so on, demonstrates the advantage of using probability theory in system or project analysis. 

Probability Theory In failure analysis, the examination of the likelihood of a specific failure or fault event, given a single opportunity for occurrence of that event. 

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. 

Prototype composite vessels (Fig. 12) were manufactured in the conditions used in the FEM simulations using a 6-axes CNC controlled filament winding machine and submitted to hydraulic burst pressure tests. The obtained results have shown that vessel burst occurred for pressures between 8 and 11 MPa. Such results show that conservative results were obtained from FEM analysis probably because failure does not occur by interlaminar shear as other simplified theories, like the netting one, demonstrate. 

The calculated loading stress, L, on a component is not only a function of applied load, but also the stress analysis technique used to find the stress, the geometry, and the failure theory used (Ullman, 1992). Using the variance equation, the parameters for the dimensional variation estimates and the applied load distribution, a statistical failure theory can then be formulated to determine the stress distribution, f L). This is then used in the SSI analysis to determine the probability of failure together with material strength distribution f S). 

A review of the important aspects of current reliability theory has been published by the British Construction Industry Research and Information Association [61]. Only an outline of the basic ideas will be reviewed here. Methods of safety analysis grouped under the general heading of reliability theory have been categorised into three levels as follows level 1, includes methods in which appropriate levels of structural reliability are provided on a structural element (member) basis, by the specification of partial safety factors and characteristic values of basic variables level 2, includes methods which check probabilities of failure at selected points on a failure boundary defined by a given limit state equation this is distinct from level 3 which includes methods of exact probabilistic analysis for a whole structural system, using full probability distributions with probabilities of failure interpreted as relative frequencies. 

It is very clear from the complexity of the situations described in the case studies of the last two chapters, that simple factors of safety, load factors, partial factors or even notional probabilities of failure can cover only a small part of a total description of the safety of a structure. In this chapter we will try to draw some general conclusions from the incidents described as well as others not discussed in any detail in this book. The conclusions will be based upon the general classification of types of failure presented in Section 7.2. Subjective assessments of the truth and importance of the checklist of parameter statements within that classification are analysed using a simple numerical scale and also using fuzzy set theory. This leads us on to a tentative method for the analysis of the safety of a structure yet to be built. The method,however, has several disadvantages which can be overcome by the use of a model based on fuzzy logic. At the end of the chapte(, the discussion of the various possible measures of uncertainty is completed. 

Performing estimation and risk analysis in the presence of uncertainty requires a method that reproduces the random nature of certain events (such as failures in the context of reliability theory). A Monte-Carlo simulation addresses this issue by running a model many times and picking values from a predefined probability distribution at each run (Mun 2006). This process allows the generation of output distributions for the variables of interest, from which several statistical measures (such as mean, variance, skewness) can be computed and analyzed. 

ABSTRACT The paper proposes an alternative approach to the failure risk analysis of water supply network which includes random emergency events inaccuracy, diversity and a small amount of data. The presented method is based on the so-called theory of facts (Shafer) based on the concept of inaccurate probabilities and possibilities (Zadech), which combines the so-called distribution capabilities of the belonging function of fuzzy set. The main aim of this paper is to present the concept of failure risk analysis of water supply network. The proposed model was used for failure risk analysis of water supply system serving 63 thousand people in the east of Poland. 

The marine industry is recognising the need for powerful techniques that can be used to perform risk analysis of marine systems. One technique that has been applied in both national and international marine regulations and operations is Failure Mode and Effects Analysis (FMEA). This risk analysis tool assumes that a failure mode occurs in a system/component through some failure mechanism. The effect of this failure is then evaluated. A risk ranking is produced in order to prioritise the attention for each of the failure modes identified. The traditional method utilises the Risk Priority Number (RPN) ranking system. This method determines the RPN by finding the multiplication of factor scores. The three factors considered are probability of failure, severity and detectability. Traditional FMEA has been criticised to have several weaknesses. These weaknesses are addressed in this Chapter. A new approach, which utilises the fuzzy rules base and grey relation theory, is presented. 

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