TAILIEUCHUNG - Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 13

Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 13 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. . | Theoretical Overview of Reliability and Performance in Engineering Design 103 a0 the total number of items put on test at time t 0 aS the number of items surviving at time t or at t At. Substituting Eq. into Eq. leads to R. t 1 -J ft t dt. 0 A more common notation for the tth component reliability is expressed in terms of the mathematical constant e. The mathematical constant e is the unique real number such that the value of the derivative of f x ex at the point x 0 is exactly 1. The function so defined is called the exponential function. Thus the alternative commonly used expression for Rt t is Rt t e- f0Xt t dt where kt t is the tth component hazard rate or instantaneous failure rate. In this case component failure time can follow any statistical distribution function of which the hazard rate is known. The expressionRt t is reduced to R t 1 - F t Rt t e-u . A redundant configuration or single component MTBF is defined by ra MTBF jR t dt. o Thus substituting Eq. into Eq. and integrating the results in the series gives the model for MTBF which in effect is the sum of the inverse values of the component hazard rates or instantaneous failure rates of all the components in the series -1 MTBF jj t 1 MTBF sum of inverse values of component hazard rates instantaneous failure rates of all the components. b Parallel Network This type of redundancy can be used to improve system and equipment reliability. The redundant system or equipment will fail only if all of its components fail. To develop this mathematical model for application in reliability evaluation it is 104 3 Reliability and Performance in Engineering Design assumed that all units of the system are active and load sharing and units are statistically independent. The unreliability FP t at time t of a parallel structure with non-identical components is k Fp t n Fi t i 1 Fj t th component unreliability failure probability . Since RP t FP t 1 utilising Eq. .

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