Hazard Risk Assessment Calculations

Tliis cliapter is concerned with special probability distributions and teclutiques used in calculations of reliability and risk. Theorems and basic concepts of probability presented in Cliapter 19 are applied to tlie determination of tlie reliability of complex systems in terms of tlie reliabilities of their components. Tlie relationship between reliability and failure rate is explored in detail. Special probability distributions for failure time are discussed. The chapter concludes with a consideration of fault tree analysis and event tree analysis, two special teclmiques tliat figure prominently in hazard analysis and tlie evaluation of risk. 

In Section 20.2, equations for the reliability of series and parallel systems are established. Various reliability relations are developed in Section 

Sections 20.4 and 20.5 introduce several probability distribution models tliat are extensively used in reliability calculations in hazard and risk analysis. Section 20.6 deals witli Uie Monte Cario teclmique of mimicking observations on a random variable. Sections 20.7 and 20.8 are devoted to fault tree and event tree analyses, respectively. 

Many systems consisting of several components can be classified as series, parallel, or a combination of both. However, tlie majority of industrial and process plants (units and systems) have series of parallel configurations. 

A series system is one in which tlie entire system fails to operate if any one of its components fails to operate. If such a system consists of n components Utat function independently, Uien tlie reliability of the system is tlie product of tlie reliabilities of tlie individual components. If Rs denotes Ute reliability of a series system and R, denotes tlie reliability of the i component i = 1,. .., n, Uien 

A parallel system is one tliat fails to operate only if all its components fail to operate. If R, is Uie reliability of the i component, Uien (l-Rj) is the probability tliat Uie i component fails i = 1,. .., n. Assuming Uiat all n components function independenUy, Uie probability tliat all n components fail is (1-Ri)(l-R2)...(l-Rn). Subtracting Uiis product from unity yields the following formula for Rp, Uie reliability of a parallel system.  

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