System safety 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. 

This chapter presents the fundamental principles of probabiUty theory and briefly examines the use of statistical analysis in the practice of system safety. The information discussed here should provide the reader with a very basic understanding of these concepts, which, by some accounts, is essential to the overall understanding of the system safety discipline. It should be noted that it is not within the scope of this Basic Guide to System Safety to provide aU there is to know regarding probability theory and statistical analysis. However, a certain level of understanding is essential and will therefore be discussed here. 

Therefore, Part I of this text focused primarily on the development of system safety, its military connections, the importance of including system safety requirements in contract acquisitions, the criticality of obtaining management commitment in support of the system safety effort, the process of risk analysis and assessment, probability theory and statistical analysis as they relate to system safety, and— perhaps of most value— how the fundamental principles of system safety are closely related to those of occupational safety and health management. 

There is a reality in Browning s observations System safety literature at the time he wrote his book was loaded with governmental jargon, and it easily repelled the uninitiated. It made more of the highly complex hazard analysis and risk assessment techniques requiring extensive knowledge of mathematics and probability theory than it did of concepts and purposes. 

A component failure is a dependent failure when a conditional relationship exists between two components, whereby the failure of one is conditional upon failure of the other the second failure depends on the first failure occurring. In probability theory, events are dependent when the outcome of one event directly affects or influences the outcome of a second event. To find the probability of two dependent events both occurring, multiply the probability of A and the probability of B after A occurs P(A and B) = P(A) P(B given A) = P(A) P(BIA). This is known as conditional probability. Two failure events A and B are said to be dependent if P(A and B) P(A)P(B). In the presence of dependencies, often, but not always, P(A and B) > P(A)P(B).This increased probability of two (or more) events is the reason dependent failures are of safety concern. It should also be noted that when redundant dependent components are used in a system, they are both susceptible to the same dependent failure, which creates a CCF dependency. 

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. 

The safety level for systems of operating aircraft fleets is analysed in a continuous manner. The safety level and its trends are expressed with the aid of various measures e g. risk, factors, event probability using for it analytical methods, e g. theory of probability, geometric methods, neural networks. According to relevant current requirements the most usual measure of the flight safety is defined by different coefficients and by the accident rate function FW. 

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