Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 64 studies the combination of various methods of designing for reliability, availability, maintainability and safety, as well as the latest techniques in probability and possibility modelling, mathematical algorithmic modelling, evolutionary algorithmic modelling, symbolic logic modelling, artificial intelligence modelling, and object-oriented computer modelling, in a logically structured approach to determining the integrity of engineering design. . | 614 5 Safety and Risk in Engineering Design e Critical Risk Theory in Designing for Safety In applying critical risk theory to a series process engineering system the following modelling approach is taken Assume the system consists of k independent components each with expected useful life lengths of z1 z2 z3 . zk all of which must function for the system to be able to function and where the useful life length of the system is Z. Denoting the survival function of the useful life expectancy of Z by F and of z by F- i 1 2 3 . k then Z min zi Z2 Z3 . Zk F z Poo O zi Then F Z nk 1 F Z . The hazard rate represented by the intensity function can now be formulated k h Z hi Z i 1 The probability of failure resulting from critical risk is expressed as Eq. Po O Z j F Z ht Z dz o Using the expression for the hazard rate hi z of useful life expectancy of Z - the survival function of the useful life expectancy of the series process engineering system is then expressed as F Z exp n f z C i tV f z f The Concept of Delayed Fatalities In assessing the safety of a complex process critical risk may be considered as resulting in fatalities due to an accident. These fatalities can be classified as immediate or as delayed. It is the delayed fatalities that are of primary interest in high-risk engineered installations such as nuclear reactors NUREG 75 014 1975 NUREG CR-0400 1978 . Critical risk analysis applies equally well to delayed fatalities as to immediate fatalities. To model the impact of delayed fatalities in the assessment of safety in engineering design consider the effect of a new constant risk with intensity h y which is delayed for time d. The model parameters include the following expressions Thompson 1988 Theoretical Overview of Safety and Risk in Engineering Design 615 The intensity function for the new risk is hnew y 0y d A y d The probability that the new risk is the critical risk resulting in fatality is from Eq. n P y C i Po O .
