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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 12

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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 12 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. . | 3.2 Theoretical Overview of Reliability and Performance in Engineering Design 93 The last part of the curve the increasing hazard rate region is designated the wear-out phase of the equipment. It starts when the equipment has passed its useful life and begins to wear out. During this phase the number of failures begin to increase exponentially and are known as wear-out failures . b Component Reliability and Failure Distributions In the calculations for reliability it is important to note that reliability is an indirect function of the probability of the occurrence offailure. The probability of the occurrence of failure is given by the failure distribution or failure probability FP statistic. Thus the probability of no failures occurring over a specific period of time is a measure of the component s or equipment s reliability and is given by the reliability probability RP statistic. Furthermore if FP is the probability of failure occurring and RP is the probability of no failure occurring then FP 1 - RP or RP 1 - FP . 3.34 Reliability of components can thus be determined through the establishment of various failure distributions originating from their failure density functions. Reliability evaluation in designing for reliability assumes that component reliability is known and we are only interested in using this component reliability to compute system reliability. However it is essential to understand how component reliability is determined specifically from two important failure distributions namely Exponential failure distribution. Weibull failure distribution. 3.2.3.2 The Exponential Failure Distribution When a component is subject only to functional failures that occur at random intervals and the expected number of failures is the same for equally long periods of time its probability density function and its reliability can be defined by the exponential equation Probability density function f t 9 1e-t e . 3.35 u Reliability R t 9 e-t u 3.36 94 3 Reliability and