By Roy Billinton PhD, DSc, FEIC, FIEEE, PE, Ronald N. Allan PhD, FSRS, MIEEE, MIEE, CEng (auth.)
This booklet has developed from our deep curiosity and involvement within the improvement and alertness of reliability assessment ideas. Its scope isn't restricted to a person engineering self-discipline because the strategies and uncomplicated recommendations for reliability review haven't any disciplinary obstacles and are appropriate in so much, if no longer all, engineering functions. We firmly think that reliability review is a vital and imperative function of the making plans, layout and operation of all engineering platforms; from the smallest and most basic to the most important and most intricate. additionally, we think that every one engineers concerned with such platforms may be conscious of, and savour, not just the advantages which could accrue from reliability overview, but in addition how such exams might be made. Our basic target has been to assemble a booklet which gives practicing engineers and engineering graduates who've very little historical past in likelihood concept or information, with the ideas and easy options for comparing the reliability of engineering platforms. it truly is was hoping that the fabric awarded will allow them to arrive fast a degree of self-confidence so as to allow them to assimilate, comprehend and relish the extra distinctive purposes and extra fabric that is on hand within the journals and courses linked to their very own discipline.
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Extra info for Reliability Evaluation of Engineering Systems: Concepts and Techniques
Example text
The basic principle and the need for Application of the binomial distribution 47 sensitivity analysis is illustrated by means of the following examples which make use of the binomial distribution. 7 Consider a system consisting of 4 components. These components could be water pumps in a mechanical engineering problem, supporting structures in a civil engineering problem, generating station transformers in a power system problem, microprocessors in a control system problem or heat exchangers in a chemical engineering problem.
The possible outcomes are (HH), (HT), (TH) or (TT). If only the combination of the outcomes is of interest, and not the order, these may be expressed as (HH), 2(HT), (TT), with probabilities of occurrence of 1/4, 1/2, 1/4, respectively. The same result is obtained by expressing the outcomes and their probability of occurrence as P(H) . P(H) + 2P(H) . peT) + peT) . peT) = p 2(H) + 2P(H) . 2) Finally consider the case when the coin is tossed three times. If the order is again considered to be unimportant then, as previously, the outcomes and their probability of occurrence may be expressed as p 3(H) + 3p2(H) .
Also, using the same logic as that used to deduce E(X) E(X2) =np + f. n(n-I)(n-2)! p p q = np + p 2n(n -1) f. (n - 2)! (n-x)! = np + p 2n(n -1) . 10 it is seen that, although the expected value of success is different to the expected value of failure if p =1= q, the variance and standard deviation of success and failure are identical for all values of p and q. 4 A product is claimed to be 90% free of defects. What is the expected value and standard deviation of the number of defects in a sample of 4?